[{"content":" Berk Demir\nUnderground engineer specialized in tunnels, structural design and geotechnical engineering.\nM: +45 60 25 49 01\nE: bdberkdemir@gmail.com\nW: berkdemir.github.io / LinkedIn\nA: Copenhagen, Denmark Brief Summary I started my career as a geotechnical engineer and worked on many aspects of geotechnics such as deep excavations, deep foundations, liquefaction remediation and so on. Later, I continued my work on the Istanbul metro as lead tunnel designer for both TBM and NATM tunnels. After moving to Denmark, I continued to work on various underground projects with an increasing focus on structural design.\nProfessional Experience Period Role Company Location 2023 – Present Senior Tunnel Engineer COWI Copenhagen, Denmark 2021 – 2023 Senior Tunnel Engineer Niras A/S Copenhagen, Denmark 2018 – 2021 Senior Geotechnical and Tunnel Engineer Tekfen Engineering Istanbul, Turkey 2017 – 2018 Geotechnical Design Engineer Destech Consultancy Izmir, Turkey \u0026amp; Tanzania 2015 – 2017 Geotechnical Design Engineer Kilci Engineering Ankara, Turkey 2014 – 2015 Technical Office Engineer Sonar Drilling Ankara, Turkey Academic Background Degree University Field Years MSc Middle East Technical University, Turkey Geotechnical Engineering 2014–2019 BSc Middle East Technical University, Turkey Civil Engineering 2009–2014 Technical Publications Recommendations for Pseudo-Static Deformation for Seismic Analyses of Tunnels, Berk Demir \u0026amp; Pinar Akdogan Demir, 2022 Master Thesis: Performance of Short Anchors Inside the Failure Wedge (2019) Comparison of Simplified Piled Raft Calculation Methods with Plaxis 3D and Details of Hardening Soil Model (2019) — ResearchGate P-Y Curves and Turkish Building Earthquake Code Requirements (2 papers), B. Demir, A. S. Peker, S. K. Tomaç, 4th Bridges and Viaducts Symposium, 2019 — Part 1 / Part 2 Comparison of Construction Methods of Jet Grout Columns, B. Demir, M. S. Nalçakan, 16th National Conference on Soil Mechanics and Geotechnical Engineering, Erzurum, Turkey, 2016 Skills Software High: Plaxis 2D \u0026amp; 3D | Python | Lusas | Strusoft FemDesign | Rocscience (Settle, Slide, RS2) | Ensoft (LPile, Group, Shaft) | Geologismiki | Optum G2\nIntermediate: Autodesk Robot | Grasshopper\nPython tools built in Streamlit for daily design work: RC Beam Design · Tunnel Analytical Lining Forces · Tunnel Deformation Assessment · M-N Interaction Curve · Hoek Brown Analysis · Convergence Confinement Method · Drawdown due to Tunnel · Steel Strut Capacity · Tunnel Relaxation Factor · Tunnel Face Stability · 3D Settlement Analysis · Longitudinal Pipe Capacity · Steel Fibre Crack Width · Volume Loss Fit for Measurements\nLanguages: Turkish (native) · English (fluent) · Danish (intermediate)\nRecent Key Projects Copenhagen M5 Metro (2023–2025) JV: COWI \u0026amp; Arup | Client: Metroselskabet A/S, Denmark | Amount of Hours: \u0026gt;2500 hrs\nDesign of the M5 Metro reference design for the tender for Metroselskabet. M5 Metro is the next metro line in Copenhagen, Denmark.\nResponsibilities during Phase-1:\nInnovation study - Removal of lining wall in metro stations and use of retaining walls as the main lining wall. Innovation study - Geopolymer concrete - use in the M5 metro. Innovation study - Minimum reinforcement methodology - update on Danish square root formula. Responsibilities during Phase-2:\nStation lead - Coordination of all disciplines for the design of two underground stations, including ARC and M\u0026amp;E. Structural design lead - for the two underground stations. Design has been carried out with Sofistik for the main station \u0026amp; FemDesign for smaller structures. metrolinjem5.kk.dk\nNordhavnstunnel (2022–2023) JV: MT Højgaard \u0026amp; Besix | Client: Vejdirektoratet, Denmark | Amount of Hours: \u0026gt;800 hrs\nNordhavnstunnel is a 1.6 km cut-and-cover, cast-in-situ tunnel in Copenhagen, Denmark.\nTypical Responsibilities:\nAll design works during the tender: Lusas models of representative sections, reinforcement calculations and quantity take-off, uplift anchor calculations for all segments, settlement calculations and discussions regarding shear key requirements. Design coordination after the tender: Design lead for structural and fire design, relationship to 3rd party, coordination of design works and QA of design reports. Valby Cloudburst Tunnel (2021–2023) Client: HOFOR | Amount of Hours: \u0026gt;1300 hrs\nDetailed design of 4 shafts (~15 m diameter, ~20 m depth) and DN3400/OD4000 pipe jacking.\nTBM-related studies, pipe and alignment studies Settlement analyses due to tunnelling and excavations Technical coordination of structural and geotechnical shaft design Kransen Culvert Deep Excavation (2021–2022) JV: Acciona \u0026amp; Implenia | Client: Bane Nor, Norway | Amount of Hours: 800 hrs\nDesign of excavation for the Sandbukta–Moss–Såstad (SMS2A) project, Kransen culvert section, using diaphragm walls and prestressed struts in a quick clay slope.\nDesign lead for all temporary works, including design basis and safety discussions All finite element analyses including detailed temperature studies of structural elements Design activities have been paused due to risks in the area.\nGFRP Reinforcement in TBM Tunnel Segments (2023) Client: Metroselskabet, Copenhagen | Amount of Hours: 200 hrs\nAs part of Metroselskabet\u0026rsquo;s innovation study initiative, the feasibility of GFRP reinforcement for TBM tunnel segments was investigated — including detailed CO2 comparisons, fire behaviour discussions, durability studies for possible TBM tunnel depths, and load scenarios using Lusas.\nIstanbul Metro / Çekmeköy–Sultanbeyli Line (2019–2021) JV: Doğuş \u0026amp; Yapı Merkezi \u0026amp; Özaltın | Client: Istanbul Municipality | Amount of Hours: \u0026gt;2500 hrs\nDetailed design of TBM and NATM tunnels issued to 3rd party and client review, including construction details, 2D and 3D NATM/TBM models and seismic assessments.\nTypical Responsibilities:\nTBM design: EPB TBM with 6.57 m diameter. Design packages include segment design and EPB pressure estimates for alignment. Construction details such as thrust frame, thrust ring inside NATM and launching/receiving schemes were successfully delivered. NATM design: Temporary support design of all NATM tunnels (including very soft soil conditions) was delivered. Coordinated, supported and QA\u0026rsquo;d the structural teams for design deliverables regarding the permanent lining design. Other Projects Klimatilpasning af det centrale Lyngby (2021–2022) — 9 pipe jacking drives (DN1200) and 12 shafts in Lyngby Çanakkale 1915 Bridge (2018–2019) — Peer review of design including anchor block foundations, deep foundations in liquefiable areas and technical specifications Bodrum Highway Tunnels (2018–2019) — 2-lane NATM highway tunnels in mountainous terrain Akyazi–Dokurcun Road (2018) — Balanced cantilever viaduct foundation and 40 m excavation in weathered rock Dar es Salaam–Morogoro Railway (2018) — Geotechnical designer for 205 km design-and-build project, Tanzania Cargo Building Foundation, Istanbul New Airport (2018) — Turkish Airlines Excavation Design in Galataport, Istanbul (2017) — Salipazari Port Management Grand Canyon Sofia (2017) — Remediation of problematic diaphragm wall panels Çanakkale Children\u0026rsquo;s Science Museum (2017) — Liquefaction remediation near Aegean Sea Hopa–Borçka Highway Cutting (2017) Dam Landslide (1.5 km × 0.6 km) Stabilization (2017) — Kalehan Energy Polatlı–Afyon High Speed Train (2015–2017) — 88 km stretch, 57 embankments, stone columns, 40+ structures Ataköy Sea Pearl (2015–2017) — Retaining systems near Marmara Sea Ulus Cultural and Convention Center (2016–2017) — Deep excavation up to 22 m in variable ground Çukurova Regional Airport (2016) — Ground improvement of various buildings Mavişehir Optimum Mall (2016) — Deep excavation with diaphragm wall, anchor systems and jet grout foundations Dalaman Airport International Arrivals (2016) — Jet grout improvement for very soft clay and liquefiable sands Turkmenistan Gas to Gasoline (GTG) (2015–2016) — Plaxis 2D analyses and ground improvement design to reduce settlements to structural limits Melen Dam Road Landslide Stabilization (2015) — Stabilization of 3 million m³ landslide with heel fill Buski East Waste Water Treatment Facility (2015) — Jet grout ground improvement to prevent liquefaction and excessive settlements Technical Office support (2014–2015) — Ozdilek Mall, Riyadh Metro Line 3, Balkupu silo foundations, various deep excavation projects ","permalink":"https://berkdemir.github.io/cv/","summary":"\u003cdiv style=\"display:flex; gap:2rem; align-items:flex-start; margin-bottom:1.5rem;\"\u003e\n\u003cimg src=\"_assets/profile.jpg\" alt=\"Berk Demir\" style=\"width:130px; border-radius:8px; flex-shrink:0;\"\u003e\n\u003cdiv style=\"line-height:1.6;\"\u003e\n\u003cp style=\"margin:0; font-weight:700; font-size:1.05em;\"\u003eBerk Demir\u003c/p\u003e\n\u003cp style=\"margin:0 0 0.6rem 0; font-style:italic; color:var(--secondary); font-size:0.95em;\"\u003eUnderground engineer specialized in tunnels, structural design and geotechnical engineering.\u003c/p\u003e\n\u003cp style=\"margin:0; font-size:0.95em;\"\u003e\n\u003cstrong\u003eM:\u003c/strong\u003e +45 60 25 49 01\u003cbr\u003e\n\u003cstrong\u003eE:\u003c/strong\u003e bdberkdemir@gmail.com\u003cbr\u003e\n\u003cstrong\u003eW:\u003c/strong\u003e \u003ca href=\"https://berkdemir.github.io/\"\u003eberkdemir.github.io\u003c/a\u003e / \u003ca href=\"https://www.linkedin.com/in/bdberkdemir/\"\u003eLinkedIn\u003c/a\u003e\u003cbr\u003e\n\u003cstrong\u003eA:\u003c/strong\u003e Copenhagen, Denmark\n\u003c/p\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003chr\u003e\n\u003ch2 id=\"brief-summary\"\u003eBrief Summary\u003c/h2\u003e\n\u003cp\u003eI started my career as a \u003cstrong\u003egeotechnical engineer\u003c/strong\u003e and worked on many aspects of geotechnics such as deep excavations, deep foundations, liquefaction remediation and so on. Later, I continued my work on the Istanbul metro as \u003cstrong\u003elead tunnel designer\u003c/strong\u003e for both TBM and NATM tunnels. After moving to Denmark, I continued to work on various underground projects with an increasing focus on \u003cstrong\u003estructural design\u003c/strong\u003e.\u003c/p\u003e","title":"CV"},{"content":"Source: Scott Roberts\nMemories from 2007 back in Durban, building a 2010 World Cup Stadium; we hit a problem with the diaphragm wall excavation, when the grabber got stuck in the bedrock about -20m down. So we sent commercial divers down through the bentonite slurry to fix a new steel cable to the grabber so we could retrieve it and keep the project going. Those boys were hardcore.\n","permalink":"https://berkdemir.github.io/posts/dwall-intervention/","summary":"\u003cp\u003eSource: \u003ca href=\"https://www.linkedin.com/posts/scottantonyroberts_memories-from-2007-back-in-durban-building-share-7181386616664449024-6_e1/\"\u003eScott Roberts\u003c/a\u003e\u003c/p\u003e\n\u003cblockquote\u003e\n\u003cp\u003eMemories from 2007 back in Durban, building a 2010 World Cup Stadium; we hit a problem with the diaphragm wall excavation, when the grabber got stuck in the bedrock about -20m down. So we sent commercial divers down through the bentonite slurry to fix a new steel cable to the grabber so we could retrieve it and keep the project going. Those boys were hardcore.\u003c/p\u003e\n\u003c/blockquote\u003e\n\u003cp\u003e\u003cimg src=\"/posts/_assets/dwall-intervention.png\" alt=\"\"\u003e\n\u003c/p\u003e","title":"Diaphragm Wall Intervention"},{"content":"Demir et. al. 2024 — Nordhavnstunnel.pdf\n","permalink":"https://berkdemir.github.io/posts/paper-on-nordhavnstunnel/","summary":"\u003cp\u003e\u003ca href=\"_assets/Demir_et._al._2024_Nordhavnstunnel.pdf\"\u003eDemir et. al. 2024 — Nordhavnstunnel.pdf\u003c/a\u003e\u003c/p\u003e","title":"Paper on Nordhavnstunnel"},{"content":"It started with ITA (International Tunnelling Association) WG 11’s catalogue of immersed tunnels. The third one (and also the fourth) in the list is from Copenhagen. Actually, the culvert is located in the most photographed region of the country - under Nyhavn. In this excellent catalogue prepared by Nestor Rasmussen (DK) and Walter Grantz (USA), the S.3 tunnel has been described as shown below. Then, search is started. With the help of people from Reddit, we found the location of the tunnel in the HOFOR database. The possible location is under Nyhavn’s connection to the sea - which shown with blue dashed line. In one of the documents, it says “Den dykkede ledning i Nyhavn blev nu også lagt. Den gik fra Kvæsthusgade til Havnegade.” which translates to “The submerged pipe in Nyhavn was now also laid. It ran from Kvæsthusgade to Havnegade.” Afterwards, I contacted the Københavns Museum, and Jakob Ingemann Parby, Senior Researcher and Museum Inspector, has reached out to me to provide more resources. In one of the resources online, Københavns Energi A/S’s (previous name of HOFOR) book called “Fra stinkende rendestene til computerstyrede kloakker” (in English “From smelly gutters to computerized sewers”) had more information on the topic. This beautiful image shows the lowered steel pipes: Let’s zoom in a little bit. I think they used barrel as ballast to sink the pipes. Pipe may look like very flexible, but it’s not actually, the design of the pipe is with bent corners as shown in the image. Actually, we even have a construction drawing. We can see the backfilling and longitudinal profile of the pipe. They had gate valves to periodically flush the pipes that accumulate dirt and sediments. Another construction stage photo is coming from Københavns Museum archive - Jakob Ingemann Parby. You can see the cranes and same shape: Also the fourth… In this search, again in the same book from Københavns Energi A/S, we can see the fourth immersed tunnel in the catalogue: The tunnel under Langebro harbour - which is around 1 km south-west of the Nyhavn Look at these beatuies in Langebro: Both of these immersed tunnels have been carried out by double steel shell - with cement grout injected between the shells. The shells can clearly be seen on the tube at the right side on the figure above. Also, after the backfill, they have poured concrete to avoid ship anchor damages. Wow! Apparently, Langebro tunnel is relocated during dredging at 1963. And this is the NC Monberg (1856-1930), the contractor of the tunnels. ","permalink":"https://berkdemir.github.io/posts/searching-for-an-immersed-tunnel-from-1900/","summary":"\u003cp\u003eIt started with ITA (International Tunnelling Association) WG 11’s catalogue of immersed tunnels. The third one (and also the fourth) in the list is from Copenhagen.\n\u003cimg src=\"/posts/_assets/Untitled-12.png\" alt=\"\"\u003e\n\nActually, the culvert is located in the most photographed region of the country - under Nyhavn. In this excellent catalogue prepared by Nestor Rasmussen (DK) and Walter Grantz (USA), the S.3 tunnel has been described as shown below.\n\u003cimg src=\"/posts/_assets/Untitled-13.png\" alt=\"\"\u003e\n\nThen, search is started. With the help of people from Reddit, we found the location of the tunnel in the HOFOR database.\n\u003cimg src=\"/posts/_assets/Untitled-14.png\" alt=\"\"\u003e\n\nThe possible location is under Nyhavn’s connection to the sea - which shown with blue dashed line.\n\u003cimg src=\"/posts/_assets/Untitled-15.png\" alt=\"\"\u003e\n\nIn one of the documents, it says \u003cem\u003e“Den dykkede ledning i Nyhavn blev nu også lagt. Den gik fra Kvæsthusgade til Havnegade.”\u003c/em\u003e which translates to \u003cem\u003e“The submerged pipe in Nyhavn was now also laid. It ran from Kvæsthusgade to Havnegade.”\u003c/em\u003e\nAfterwards, I contacted the Københavns Museum, and Jakob Ingemann Parby, Senior Researcher and Museum Inspector, has reached out to me to provide more resources.\nIn one of the resources online, Københavns Energi A/S’s (previous name of HOFOR) book called \u003cem\u003e“Fra stinkende rendestene til computerstyrede kloakker\u003c/em\u003e” (in English \u003cem\u003e“From smelly gutters to computerized sewers”\u003c/em\u003e) had more information on the topic.\nThis beautiful image shows the lowered steel pipes:\n\u003cimg src=\"/posts/_assets/Untitled-16.png\" alt=\"\"\u003e\n\nLet’s zoom in a little bit. I think they used barrel as ballast to sink the pipes.\n\u003cimg src=\"/posts/_assets/Untitled-17.png\" alt=\"\"\u003e\n\nPipe may look like very flexible, but it’s not actually, the design of the pipe is with bent corners as shown in the image. Actually, we even have a construction drawing.\n\u003cimg src=\"/posts/_assets/Untitled-18.png\" alt=\"\"\u003e\n\nWe can see the backfilling and longitudinal profile of the pipe. They had gate valves to periodically flush the pipes that accumulate dirt and sediments.\nAnother construction stage photo is coming from Københavns Museum archive - Jakob Ingemann Parby. You can see the cranes and same shape:\n\u003cimg src=\"/posts/_assets/Untitled-19.png\" alt=\"\"\u003e\n\u003c/p\u003e","title":"Searching for an Immersed Tunnel from 1900"},{"content":"The beauty of Streamlit with Plaxis is the simplicity of the UI and how minimalistic it looks. Also, the 2x2 output figure for a retaining wall is the most compact output you can imagine. Everything you need to show for all these stages is inside one figure. Moreover, this tool can deliver a really detailed excel sheet to share with other designers. Watch the video to see it on action: Also fixed-end anchors and node-to-node anchors! And lastly, how to start the Streamlit directly from Plaxis as shown in videos:\nimport streamlit as st from streamlit.web import cli as stcli if __name__ == \u0026#34;__main__\u0026#34;: if st.runtime.exists(): main() else: sys.argv = [\u0026#34;streamlit\u0026#34;, \u0026#34;run\u0026#34;, sys.argv[0]] sys.exit(stcli.main()) ","permalink":"https://berkdemir.github.io/posts/plaxis-output-program/","summary":"\u003cp\u003eThe beauty of \u003cstrong\u003eStreamlit\u003c/strong\u003e with \u003cstrong\u003ePlaxis\u003c/strong\u003e is the simplicity of the UI and how minimalistic it looks. Also, the 2x2 output figure for a retaining wall is the most compact output you can imagine. Everything you need to show for all these stages is inside one figure. Moreover, this tool can deliver a really detailed excel sheet to share with other designers.\n\u003cimg src=\"/posts/_assets/Untitled.png\" alt=\"\"\u003e\n\nWatch the video to see it on action:\n\u003cvideo controls style=\"max-width:100%\"\u003e\u003csource src=\"_assets/Screenshot-20230806-1599.mp4\" type=\"video/mp4\"\u003e\u003c/video\u003e\nAlso fixed-end anchors and node-to-node anchors!\n\u003cvideo controls style=\"max-width:100%\"\u003e\u003csource src=\"_assets/Screenshot-20230806-1600.mp4\" type=\"video/mp4\"\u003e\u003c/video\u003e\n\u003cvideo controls style=\"max-width:100%\"\u003e\u003csource src=\"_assets/Screenshot-20230806-1601.mp4\" type=\"video/mp4\"\u003e\u003c/video\u003e\nAnd lastly, \u003cstrong\u003ehow to start the Streamlit directly from Plaxis as shown in videos:\u003c/strong\u003e\u003c/p\u003e","title":"Plaxis Output Program"},{"content":"Introduction Table of Content\nLast month, we had an interesting and long discussion over the email with the creator of PCTempflow, a widely used software for fire analysis, and others like PCSheetPileWall and Framework: Gerrit Wolsink. Over the course of the many emails, we have agreed that there is something wrong (or incompatible) in the Eurocodes. This brief article is our joint effort on clarifying our views on this problem. If you have any input, please feel free to reach out.\nSummary The article might be hard to follow if the reader has not dived in to the same issues before. Therefore, a brief summary is presented here:\nEN-1992-1-2 (Structural Fire Design) recommendations for stress-strain curve at elevated temperatures are not in-line with EN-1992-1-1. This inconsistency might results in under-estimation of structural forces during fire, and worse, in case of coupled analysis, both during fire and in statical conditions. (If the software uses the same stress-strain curve at room temperature.) There is no direct solution for non-linear analyses aside from tweaking the curves to reach a reasonable stiffness. For linear analyses, E-modulus degradation recommendations in literature should be taken into account.\nUse of fcm instead of fck in EN-1992-1-2 curves helps, but does not solve the issue. (EN-1992-1-1 uses fcm, EN-1992-1-2 uses fck). Problem Statement EN 1991-1-2 clarifies the requirements for structural fire design. For a proper fire analysis, we need at least two of the stress, strain and stiffness of concrete at elevated temperatures. EN 1991-1-2 gives us the strength degredation with increasing temperature as a table and stress-strain relationships at elevated temperatures.\nEN 1991-1-2 does not have any recommendation for stiffness and we know that we can calculate the stiffness of the concrete by dividing stress to strain. The problem starts here.\nStiffness using EN-1992-1-2 Approach All comparisons throught the article will be performed for C40/50 concrete with siliceous aggregates. The main problem\n[!note] 📌 Stiffness at room temperature calculated by EN 1992-1-2 stress-strain diagram is not equal to EN-1992-1-1 recommendation.\nLet’s do this for C40 concrete. As per definition in Eurocode, the stiffness is secant stiffness measured from approximately 40% of the fck. Of course we do not expect to reach the exact E-modulus in Eurocode, but difference is significant. Compared to 35 GPa at EN-1992-1-1 for C40 concrete, the calculation using EN-1992-1-2 results in 23.7 GPa. fck vs. fcm? As shown in the figure from EN-1992-1-2 in the previous chapters, the EN-1992-1-2 refers to fck when presenting the compressive strength degradation at elevated temperatures. Therefore, reader has to select the fck, reduce it based on the temperature and then, use it to derive the stress-strain diagram. However, this is not the case in EN-1992-1-1, we use fcm = fck + 8 MPa. Therefore, our interpretation is that this is due to a mistake in the standard and users should derive the stress-strain relationship using fcm. When same calculations are carried out using fcm with stress-strain relationship recommended in EN 1992-1-2, the results are still far off from EN 1992-1-1 with E = 28.5 GPa. So, the first note:\nThe stress-strain diagram of EN 1992-1-2 should be drawn for fcm, not fck, although the standard refers to fck.\nBut there is still difference between room temperature stress-strain diagrams of EN 1992-1-1 and EN 1992-1-2 which results in E value of 35 GPa vs. 28.5 GPa, respectively. Comparison of Stiffness at Elevated Temperatures If we draw the same stress-strain diagram for all temperatures with fcm, we get something like this. If we calculate the modulus of elasticity for each temperature level, we get the following: Note that the difference between Ecm calcualted by EN-1992-1-1 and EN-1992-1-2 at room temperature is more pronounced at lower strengths. A comparison with the methods are shown below for both EN-1992-1-2 methodology, fck and fcm. Implications [!note] 📌 The stiffness of the structural elements are much lower during fire analysis. The structural forces calculated by the software will be significantly lower than actual.\nEN 1992-1-1 stress-strain curve does result in a modulus close to the recommended modulus of the same standard as shown below. The methodology is also described clearly in FIB Bulletin 42. So, the problem is only with the stress-strain curves recommended by the EN 1992-1-2. Literature After our discussions, our literature investigation has resulted in very little arguments about this inconsistency. Authors from Ukraine (Fomin et. al. 2017, Fomin et. al. 2021) observed similar inconsistency.\nWorkaround There is not a clear solution for non-linear analyses. Because, in non-linear analyses (such as Hydra in Sofistik), the stress-strain diagram should be defined. We are not sure how the software jumps from static case (EN-1992-1-1) to fire case (EN-1992-1-2), but:\nIf the non-linear analyses are not coupled completely: Software is probably using two different curves - one for static analyses (EN 1992-1-1 curve) and one for fire analyses (EN-1992-1-2 curve). This partially decoupled approach reduces the error since static analyses are carried out with correct stress-strain diagram. If the non-linear analyses are coupled: (meaning both fire and static load cases are solved simultaneously), the error in the results will be more pronounced since the static analyses will be carried out at t=0 with (most probably) stress-strain diagram taken from EN-1992-1-2 for room temperature. For linear analyses, however, if the user can feed time-dependent stress and stiffness, the problem can be solved easily by adapting a E-modulus degradation curve from literature. For example, Danish Annex of EN-1992-1-2 proposes a different reduction in fc with temperature, and recommends square of the reduction in fc for E-modulus reduction. Comparison is shown below. However, we should state that the this solution is not *legal *in terms of contractual requirements, because EN-1992-1-2 gives us the stress-strain diagrams which does not leave any discussions regarding using a different Ecm. Lastly, in addition to the discrepancy between EN 1992-1-2 and EN 1992-1-1 regarding the E-modulus at room temperature, the large scatter in experimental results at higher temperatures reported in the literature means that no unambiguous solution is likely available. ","permalink":"https://berkdemir.github.io/posts/inconsistency-between-eurocodes-for-fire-analyses/","summary":"\u003ch1 id=\"introduction\"\u003eIntroduction\u003c/h1\u003e\n\u003cp\u003e\u003cu\u003e\u003cstrong\u003eTable of Content\u003c/strong\u003e\u003c/u\u003e\u003c/p\u003e\n\u003cp\u003eLast month, we had an interesting and long discussion over the email with the creator of PCTempflow, a widely used software for fire analysis, and others like PCSheetPileWall and Framework: \u003ca href=\"https://gerritwolsink.nl/\"\u003eGerrit Wolsink\u003c/a\u003e.\nOver the course of the many emails, we have agreed that there is something wrong (or incompatible) in the Eurocodes.\nThis brief article is our joint effort on clarifying our views on this problem. If you have any input, please feel free to reach out.\u003c/p\u003e","title":"Inconsistency Between Eurocodes for Fire Analyses"},{"content":"Another couple nights to experiment on the parametric design with FEM-Design and Grasshopper. No problem with geometry and load definitions except couple of small bumps. The load combinations require more than couple nights, so I just move to the GUI if I need.\nI\n","permalink":"https://berkdemir.github.io/posts/rectangular-parametric-tunnel-in-fem-design/","summary":"\u003cp\u003eAnother couple nights to experiment on the parametric design with FEM-Design and Grasshopper. No problem with geometry and load definitions except couple of small bumps. The load combinations require more than couple nights, so I just move to the GUI if I need.\u003c/p\u003e\n\u003cp\u003e\u003cimg src=\"/posts/_assets/Untitled-27.png\" alt=\"\"\u003e\n\n\u003cvideo controls style=\"max-width:100%\"\u003e\u003csource src=\"_assets/Screenshot-20230121-1447.mp4\" type=\"video/mp4\"\u003e\u003c/video\u003e\nI\u003c/p\u003e","title":"Rectangular Parametric Tunnel in FEM-Design"},{"content":"Note that when the apps are not used for a while, you might need to “wake” them. It might take up to a min.\nhttps://bdem-hb.streamlit.app/ https://bdem-hs.streamlit.app/\n","permalink":"https://berkdemir.github.io/posts/open-source-tools/","summary":"\u003cp\u003e\u003cem\u003eNote that when the apps are not used for a while, you might need to “wake” them. It might take up to a min.\u003c/em\u003e\u003c/p\u003e\n\u003chr\u003e\n\u003cp\u003e\u003ca href=\"https://bdem-hb.streamlit.app/\"\u003ehttps://bdem-hb.streamlit.app/\u003c/a\u003e\n\u003ca href=\"https://bdem-hs.streamlit.app/\"\u003ehttps://bdem-hs.streamlit.app/\u003c/a\u003e\u003c/p\u003e","title":"Open Source Tools"},{"content":"During 2019 Plaxis User Meeting in İstanbul, I have presented a detailed discussion on Hardening Soil Model. The presentation was really welcomed by the audience and in fact, later on, I have been invited to two other companies for the same presentation. This short post will be a summary of that presentation. Hardening Soil model (will be called HS from now on) was presented in an excellent conference for 10th year of Plaxis in a paper called The hardening soil model: Formulation and Verification by Schanz, Vermeer and Bonnier. However, HS is tightly bonded to previous studies on the literature such as Lade, Tatsuoka and Ishihara, Cam-Clay model, Kondner and Zelasko, Jardine, Duncan and Chang, Al Tabbaa, Simson et. al.\nWhat is Hardening? Hardening behaviour of soils is shown on the experiments on Tatsuoka and Ishihara (1978) on sand samples. On each cycle, yield starts on the previous cycle’s maximum stress. We will see that later on on the preconsolidation pressure concept of HS. Vermeer (1978) defines a hardening parameter to expand the yield surface which is also an integral part of the HS model.\nThe yield surface moves in conjunction with some measure for the plastic strains which is called the hardening parameter.\nHe clearly describes the hardening effect on the soils with the following:\nThe concept of a yield locus or yield surface is felt to be the most important concept of plasticity theory. It is a surface in stress space (a curve in the p, q-plane) separating stress states which can be reached elastically (the elastic domain) from those which can only be obtained after plastic deformation or cannot be achieved at all.\nHardening means that yield surface is not fixed as described in Plaxis Material Manual. There are two types of hardening:\nShear Hardening Compression Hardening Let’s take a look at these concepts.\nShear Hardening According to Plaxis Material Manual, shear hardening is used to model irreversible strains due to primary deviatoric loading. If we ignore the fancy functions for calculating strain, simply it can be defined as the ratio of failure divided by the E50. So, here comes the difference between each stiffness modulus in HS. E50 if used for shear deformations. (Also, Eu is used in the formulations.) Primary deviatoric loading is used everywhere in HS literature. However, I went over 875 google results 2 years ago and there are only two definition. One of them is given in first sentence of this chapter and other is “When subjected to primary deviatoric loading, soil shows a decreasing stiffness”. This is a concept deriven from Kondner (1963) and Duncan and Chang (1963): Hyperbolic relationship between deviatoric stress and stiffness. Primary simply means virgin loading. Deviatoric loading is same as we know from triaxial test. To simplify;\nShear hardening depends on $E_{50}$ Plastic strains occur before the yield. Compression Hardening Compression hardening is not something unfamiliar to us. It is around here since Terzaghi. Preconsolidation pressure is used in consolidation calculations to seperate the virgin loading and reloading parts. We should know that: Plastic yielding depends on the position of yield surface. So, if we exceed the yield surface, plasticity comes into action. Puzrin (2012) describes it really well:\nThe plastic yielding always begins when the current pre-consolidation stress (i.e. the largest mean effective stress before the unloading) is exceeded in reloading.\nContrary to shear hardening, in compression hardening Eoed is used for strains.\nGraphical Representation I have prepared a colorful figure to describe the yield surfaces in HS model. We have different regions:\nElastic part is shown in green region. In this region, we have elastic behaviour and material stiffness is derived from Eur. If we move on K0 line, we will reach compression yield surface (cap) and in that zone, $E_{oed}$ is used. If we have shear we can move to shear hardening zone where $E_{50}$ is used for shear strains. Or naturally, we can have combined hardening due to both shear and compression. If we get too far from the K0 line, we can reach to Moh-Coulomb failure line. Strain types are shown in the figure below. Journey of a Particle Let’s see what happens when we load a initially elastic particle as shown below with red star. If we load the particle on K0 loading type, it will move on the K0 line. The initial preconsolidation pressure is now recalculated based on the maximum new stress. Based on the new preconsolidation pressure, yield surface expands. With expanding yield surface, elastic part where we use Eur is expanded too. So, if load is reduced now between blue star and red star, soil move on elastic region. If we load the soil in given direction below, it will cause shear hardening and this time initial shear yield surface will expand. If we load the soil in compression hardening zone with shear loading, it will enter to combined hardening part. In this case, both yield surface will expand. If we expand these surfaces up to Mohr Coulomb failure line and rotate it around the origin, we can have the classical shape we see in literature. Other Points Regarding Implementation of HS Some additional random points:\nStrains affect each other due to nature of equations. Volumetric strains (compression) affect shear strains. Shear strains affect volumetric strains. Therefore, they pull others to themselves, i.e. combined loading. Preconsolidation pressure is not related to vertical loading only as in soil mechanics. Shear loads also affect the preconsolidation pressure. Normally Consolidated Soil is the soil where preconsolidation pressure is equal to soil’s current loading. So, that soil is located on the yield surface. As Brinkgreve (2005) says:\nStarting from a normally consolidated stress state, any stress path involving ‘loading’ leads to plastic straining, but this should not be confused with failure.\nExamples Let’s see some examples. Using the Plaxis’ option to see plastic points, we can observe these hardening behaviours. Another example is shown below. We can see that due to load beneath the retaining piles and (maybe) due to little overturning, there is combined and compression hardening below the piles. Parameters Stiffness Modulus Stiffness modulus of soil in HS depends on:\nReference stiffness modulus $\\sigma_3$: Lateral pressure on the soil $p_{ref}$: Reference pressure $m$: Power for stress-level dependency of stiffness Strength parameters What do we see here? For a reference pressure of 100 kPa (we will talk about later), we see that stiffness modulus is directly proportional to lateral pressure (or pressure on soil, in general). If lateral pressure on soil is different than $p_{ref}$, E will not be equal to $E^{ref}$. Dependency of the E on the Eref, pref and other parameters are visualized in the following open-source Streamlit page. Users can play with the parameters to see the changes in the stiffness with depth. https://berkdemir-hardeningsoilpowerm-hs-8j381v.streamlit.app/\nE50 Reference modulus means that stiffness modulus calculated at all-around pressure equal to pref. (Update: I find the need to stress this over and over again. The reference pressure is nothing to do with the effective stresses that soil layer experience. It is about the laboratory tests to determine the Eref. If you don’t have the laboratory tests and derive the E values from the correlations with site investigations and other parameters, it depends on the all around pressures during the tests that author of that correlation used.) Plaxis uses 50% secant modulus. So, our procedure will be:\nPerform triaxial test up to failure load qu at reference pressure (all-around pressure) pref. Find the strain at qu/2 and calculate the $E_{50}^{ref}$. $$ E_{50}^{ref}=\\frac{0.5q_u}{\\varepsilon_{1,50}} $$ An example calculation is given below. Calculated E50 = 30.8 MPa is valid for pref = 100 kPa. So, when we define the material model in Plaxis, the default pref = 100 kPa value is correct for this case. Let’s see another case. In this case, since y axis is given in a different configuration, some adjustments are needed. We can see from the calculations that E=200 MPa but it is valid for pref = 795 kPa. So, we have to change the reference pressure to 795 kPa before defining the stiffness modulus. Best way to calculate input values for different stiffness and all-around pressure values, if you have the enough number of data, is to plot the data on $E_{50}/p_{ref}$ \u0026amp; $\\sigma_3/p_{ref}$. An example calculation is shown below. In this case, if pref = 100 kPa, E is equal to 71 MPa and m = 0.66. We know that we don’t always have good quality laboratory tests on hand. So, we usually use correlations with different site investigation methods. It is not very often to see reference pressure for stiffness correlations in literature. In that case, reference pressure of 100 kPa is usually selected since a good percentage of triaxial tests can be assumed to be performed on 100 kPa all-around pressure. However, there is no justification for this assumption.\nEoed There is also a simple method to calculate Eoed from oedometer tests although some can find this method unreliable. We can use elastic equations or simply $E_{oed}=1/m_v$. How do we select the mv value to be used in the equation? In soil mechanics, we select the mv value based on the pressure we expect since mv depends on the pressure level. What about in Plaxis? For example, if we expect 300 kPa embankment load, should we select the mv from 300 kPa range? No! We have to select it based on the pref value we use. If we use pref = 100 kPa, we have to select the mv at 100 kPa range. Using the same approach described before, we can calculate the Eoed as below:\nTake the 1/mv values and pressures from the oedometer tests. Select a pref. Divide Eoed and pressured to pref. Draw the Eoed/pref and pressure/pref on logarithmic axes. Draw a trendline in Excel using power function. An example of this procedure is shown below: Eur Eur is usually correlated to E50. Usual range is 2-6. In my opinion, we can use cr and cc ratio obtained from oedometer test to determine this ratio. Kulhawy \u0026amp; Mayne (1990) correlations on cc and cr shows that cr/cc=5.27. Duncan et. al. (1980) recommends a range between 1.2 and 3.0.\nm, Power for Stress Level Power for stress level, m, is recommended by Plaxis as 0.5 for sands and 1.0 for clays. There are also correlations given by Hicher (1996) and Viggiani and Atkinson (1995) quoted in Z-Soil’s Hardening Soil manual. Hicher (1996) Correlation: $$ m=1.13-\\frac{49}{LL+78} $$ Viggiani and Atkinson (1995) Correlation: $$ m=1-\\frac{10.83}{PI+18.7} $$ Also, Brinkgreve et. al. (2010) recommends following equation for granular soils. (See the original paper for other correlations regarding the HS parameters.) $$ m = 0.7 − RD/320 $$\nReloading Poisson’s Ratio, v_ur Unloading/reloading poisson’s ratio is denoted as vur. It should be noticed that vur is not classical poisson’s ratio! In the absence of laboratory data, it should be left as the default value 0.2.\nOCR / POP Overconsolidation Ratio (OCR) and Pre-Overburden Pressure (POP) are used to define the initial state of the material. In case of high OCR values, K can be too high since K depends on OCR. This may cause plastic points in initial stage.\nRf Failure ratio, Rf, is defined by Duncan \u0026amp; Chang (1970) to come up with a value at failure pressure due to asymptotic behaviour. It is recommended to keep the value between 0.75 and 1.00. In the absence of data, default value recommended by Plaxis (0.9) can be used.\n","permalink":"https://berkdemir.github.io/posts/hardening-soil-model/","summary":"\u003cp\u003eDuring 2019 Plaxis User Meeting in İstanbul, I have presented a detailed discussion on Hardening Soil Model. The presentation was really welcomed by the audience and in fact, later on, I have been invited to two other companies for the same presentation. This short post will be a summary of that presentation.\nHardening Soil model (will be called \u003cstrong\u003eHS\u003c/strong\u003e from now on) was presented in an excellent conference for 10th year of Plaxis in a paper called \u003cem\u003eThe hardening soil model: Formulation and Verification\u003c/em\u003e by Schanz, Vermeer and Bonnier. However, HS is tightly bonded to previous studies on the literature such as Lade, Tatsuoka and Ishihara, Cam-Clay model, Kondner and Zelasko, Jardine, Duncan and Chang, Al Tabbaa, Simson et. al.\u003c/p\u003e","title":"Hardening Soil Model"},{"content":"I have just published a new tool and this post will detail the methods that are being used in this tool. What it does: Performs Hoek-Brown analyses for rock and recommends additional parameters based on the inputs.\nhttps://berkdemir-bd-hoek-brown-bd-hoek-brown-vsh6i6.streamlit.app/\nTheory Introduction The Hoek-Brown material model is the most widely used rock mechanic model due to its simplicity and ease-of-use in continuum based numerical models such as finite element or finite difference models. Hoek-Brown model is published in Hoek \u0026amp; Brown (1980) and after that, it is constantly updated. Latest update was published in 2019.\nInput Parameters There are 4 main input parameters for Hoek-Brown material model. Additional inputs are required to estimate rock mass modulus or equivalent Mohr-Coulomb parameters.\nUniaxial Compressive Strength: Uniaxial compressive strength is the compressive strength of intact rock. In field, the intact samples are selected to be tested in UCS test. If required samples are not found, point load tests can also be performed and the results of these tests can be converted to UCS using various correlations.\nGeological Strength Index (GSI) GSI is a number between 0-100 that defines the weathering or joint degree of a rock mass. This value is usually determined on the field based on the tunnel or slope faces, boreholes or outcrops. It is possible to correlate GSI to RMR (Rock Mass Rating) value using variety of correlations available in the literature. The most commonly used correlation is GSI=RMR-5. However, it should be noted that RMR’ should be recalculated by neglecting the effect of groundwater and tunnel orientation. GSI can also be estimated using the graph below. It is usually advised to keep the GSI above 25 for rock mass conditions. Material Constant for Intact Rock Material constant (mi) is a fitting parameter which can be determined using the curve fitting technique on high quality triaxial tests or can be estimated using the ranges given in the table or figure below. Disturbance Factor Disturbance Factor is used to reflect the disturbance due to blast damage or stress relaxation. It is very unlikely to reach very high disturbance factors or very thick disturbed zones with the current technology. Hoek and Brown (2019) emphases that disturbance factor should not be applied to the whole rock mass. It should only be applied to a limited thickness. Literature shows that the usual thicknesses for disturbed zones are around 0.5-1.0 m. However, it is very usual to apply 3 m disturbed zone in drill and blast tunnelling.\nA common error is to assume that the disturbance factor D should be applied to the entire rock mass in which the excavation is conducted. This will result in an extremely conservative and inappropriate design.\nModulus Ratio (MR) Modulus ratio is the ratio of elastic modulus of intact rock to compressive strength of intact rock. In case of absence of any laboratory data, following ranges can be used. General Equations General equation for maximum and minimum effective principal stress at failure is calculated using the following equation: $$ \\sigma_1\u0026rsquo;=\\sigma_3\u0026rsquo;+\\sigma_{ci}(m_b \\frac{\\sigma_3\u0026rsquo;}{\\sigma_{ci}}+s)^\\alpha $$ Equations for Hoek-Brown parameters are summarized below: $$ m_b = m_i \\cdot exp \\left(\\frac{GSI-100}{28-14D}\\right) $$ $$ s=exp(\\frac{GSI-100}{9-3D}) $$ $$ \\alpha =\\frac{1}{2}+\\frac{1}{6}(e^{-GSI/15-e^{-20/3}}) $$ Uniaxial compressive strength of rock mass is calculated using the general equation by setting lateral pressure equal to zero. $$ σ_c = σ_{ci} ⋅ s_a $$ Tensile strength of rock mass is: $$ \\sigma_t = -\\frac{s \\sigma_{ci}}{m_b} $$\nElasticity Modulus Calculations There are tens of methods to calculate the rock mass modulus using GSI, RMR or other rock strength parameters. A good review of available methods is presented by Zhang (2017). Few of them are widely used and summarized here:\nGeneralized Hoek and Diederichs (2016) Method $$ E_{rm} = E_i \\cdot \\left( 0.02+\\frac{1-D/2} {1+e^{((60+15D-GSI)/11)}} \\right) $$\nSimplified Hoek and Diederichs (2016) Method $$ E_{rm} = 100000\\cdot \\left( 0.02+\\frac{1-D/2} {1+e^{((75+25D-GSI)/11)}} \\right) $$\nHoek, Carranza-Torres \u0026amp; Corkum (2002) Method For UCS \u0026lt; 100 MPa: $$ E_{rm} = 1000 \\cdot (1-D/2) \\sqrt{\\sigma_{ci}/100} \\cdot 10^{(GSI-10)/40} $$ For UCS \u0026gt; 100 MPa: $$ E_{rm} = 1000 \\cdot (1-D/2) \\sqrt{\\sigma_{ci}/100} \\cdot 10^{(GSI-10)/40} $$\nYang (2006) Method $$ E_{rm} = \\frac{E_i}{100} \\cdot e^{GSI/21.7} $$\nEquivalent Mohr-Coulomb Parameters Equivalent Mohr-Coulomb (MC) parameters can be estimated using the equations below. MC fit for HB parameters is just an approximation for the nonlinear HB curve on the given minor stress. Therefore, the MC parameters should be estimated using the expected pressures. In any case, Hoek and Brown recommends using HB parameters when possible. Maximum lateral pressure, sigma_3 can be estimated using the approximate equations given by Hoek. Note that sigma_cm is rock mass strength and can be calcualated using the equation below: Lateral Pressure for Tunnels Lateral Pressure for Slopes H is the height of the slope. General For general cases, it is recommended to keep the lateral pressure around 25% of the UCS.\nAdditional Parameters Additional parameters are not part of the usual Hoek-Brown calculations. These parameters are listed as a supplementary aid to design.\nShear Wave Velocity Calculation by Brocher 2005 To calculate the shear wave velocity in rock Q (Barton) - Vp an Vs relationship will be utilized. To calculate the Q value, FHWA-NHI-10-034 recommends following equation: $$ Q = 10^{\\frac{RMR - 50}{15}} $$ RMR will be calculated assuming GSI = RMR - 5. Barton (2002), described the relationship between Q and Vp (km/sec) as: $$ V_{p} = 3.5 + \\log Q_{c}Vp=3.5+logQc $$ The Qc in this equation is the Q normalized with uniaxial compressive strength which can be calculated as $$ Q_{c} = Q \\cdot \\left( \\frac{\\text{UCS}}{100} \\right) $$ with UCS in MPa. Lastly, the relationship between Vp and Vs is adapted from a USGS research project, Brocher (2005): $$ V_{s} = 0.7858 - 1.2344 \\cdot V_{p} + 0.7949 \\cdot V_{p}^{2} - 0.1238 \\cdot V_{p}^{3} + 0.0064 \\cdot V_{p}^{4}Vs=0.7858−1.2344⋅Vp+0.7949⋅Vp2−0.1238⋅Vp3+0.0064⋅Vp4 $$ Vs and Vp in this equation is in km/sec. Poisson’s Ratio by Brocher 2005 $$ v = 0.8835-0.315V_p + 0.0491V_p^2-0.00024V_p^3 $$ Shear Wave Velocity by Cha 2006 References Brown, E. T., \u0026amp; Hoek, E. (1980). Underground excavations in rock. CRC Press. Hoek, E., \u0026amp; Brown, E. T. (2019). The Hoek–Brown failure criterion and GSI–2018 edition. Journal of Rock Mechanics and Geotechnical Engineering, 11(3), 445-463. Carter, T. G., \u0026amp; Marinos, V. (2020). Putting geological focus back into rock engineering design. Rock Mechanics and Rock Engineering, 53(10), 4487-4508. Hoek, E., \u0026amp; Diederichs, M. S. (2006). Empirical estimation of rock mass modulus. International journal of rock mechanics and mining sciences, 43(2), 203-215. Zhang, L. (2017). Evaluation of rock mass deformability using empirical methods–A review. Underground Space, 2(1), 1-15. Hoek, E., \u0026amp; Diederichs, M. S. (2006). Empirical estimation of rock mass modulus. International journal of rock mechanics and mining sciences, 43(2), 203-215. Hoek, E., Carranza-Torres, C., \u0026amp; Corkum, B. (2002). Hoek-Brown failure criterion-2002 edition. Proceedings of NARMS-Tac, 1, 267-273. Yang, K. (2006). “Analysis of laterally loaded drilled shafts in rock.” PhD Thesis, Univ. of Akron, Akron, OH Brocher, T. M. (2005). Empirical relations between elastic wavespeeds and density in the Earth’s crust. Bulletin of the seismological Society of America, 95(6), 2081-2092. Cha, Y. H., Kang, J. S., \u0026amp; Jo, C. H. (2006). Application of linear-array microtremor surveys for rock mass classification in urban tunnel design. Exploration Geophysics, 37(1), 108-113. ","permalink":"https://berkdemir.github.io/posts/hoek-brown-model/","summary":"\u003cp\u003eI have just published a new tool and this post will detail the methods that are being used in this tool. What it does: Performs Hoek-Brown analyses for rock and recommends additional parameters based on the inputs.\u003c/p\u003e\n\u003cp\u003e\u003ca href=\"https://berkdemir-bd-hoek-brown-bd-hoek-brown-vsh6i6.streamlit.app/\"\u003ehttps://berkdemir-bd-hoek-brown-bd-hoek-brown-vsh6i6.streamlit.app/\u003c/a\u003e\u003c/p\u003e\n\u003cp\u003e\u003cimg src=\"/posts/_assets/Untitled-1.png\" alt=\"\"\u003e\n\u003c/p\u003e\n\u003ch1 id=\"theory\"\u003eTheory\u003c/h1\u003e\n\u003ch2 id=\"introduction\"\u003eIntroduction\u003c/h2\u003e\n\u003cp\u003eThe Hoek-Brown material model is the most widely used rock mechanic model due to its simplicity and ease-of-use in continuum based numerical models such as finite element or finite difference models. Hoek-Brown model is published in Hoek \u0026amp; Brown (1980) and after that, it is constantly updated. Latest update was published in 2019.\u003c/p\u003e","title":"Hoek Brown Model"},{"content":"Introduction By now, everything should have been settled about modulus of subgrade reaction. We all know some typical statements about it:\nIt depends on the soil properties It depends on the foundation size It depends on loading type, temperature, bitcoin prices and others. However, let\u0026rsquo;s think about a weathered rock with E=500 MPa and a foundation to be built on top of this rock with 20 x 50 m dimensions. You can say it depends on many factors as much as you like, everybody has a rough idea already: 100,000 kN/m3. So, if you are a fancy engineer and dare to make some calculations, you can find much lower values. Will they believe you or will they think that you are being too conservative (if lowering the subgrade reaction means being conservative)? Let\u0026rsquo;s start with simple terms. The equation that everybody knows and nobody wants to use: $$ K=\\frac{q}{s} $$ So, the subgrade reaction is equal to a spring stiffness distributed under the foundation. If you divide the pressure by the settlement, you will find the subgrade reaction, amount of deformation for unit pressure. If we think about how we calculate settlement (how it depends on many factors), we can see actually how complex this modulus is.\nUsing Settlement Calculations Use any method you like. If you calculate the settlement of a foundation (say for 200 kPa uniform loading) with dimensions of 20 x 50 m on a weathered rock with elasticity modulus of 500 MPa, you will find something around 7-8 mm (or someting close) that will result in 25000 kN/m3 modulus of subgrade reaction You know the easiest method without bothering with any influence factor: $$ s=\\frac{qB(1-v^2)}{E} $$ If you do that, you will find 28000 kN/m3. If you use Settle 3D with flexible foundation, you will find something similar: So, the question is: Where does this 100000 kN/m3 comes from?\nBowles Bowles was a great engineer and teacher. His books have guided most of us. Since he was a practicing engineer, his recommendations were pin-point to most of the problems we had. It was the first geotechnical book I have read from the cover to the end. But he didn\u0026rsquo;t know his recommendations will be misunderstood. I will try to explain the two of the most misunderstood recommendations of Bowles and you will be the judge.\nRelationship Between Modulus of Subgrade and Bearing Capacity He was such a clever engineer, he have found a simple equation to relate bearing capacity and modulus of subgrade reaction. And he was 100% correct. But I can say that 95% of use of this equation is not correct. $$ K=40\\cdot FS\\cdot q_{all} $$ What a magical formula. Let\u0026rsquo;s start with the wrong use: If you ever calculated the bearing capacity from general bearing capacity formula (cNc+qNq+\u0026hellip;) and use this equation with that bearing capacity, you were wrong. This is the derivation of this equation: Since general bearing capacity equation for granular soils results in very high bearing capacity, it was the general tendency to calculate a bearing capacity for settlement limits and that limit was 1 inch - 25 mm. You can calculate an allowable bearing capacity using SPT which is in fact the load that corresponds to 25 mm settlement. An example from Bowles is Parry (1977) equation: $$ q_a=30N_{55} $$ If you have the required load to generate a 25 mm settlement, you can also calculate the modulus of subgrade reaction using the logic below. $$ K=\\frac{q}{s}=\\frac{q_{all}\\cdot FS}{25\\ mm}=\\frac{q_{all}\\cdot FS}{0.025\\ m}=q_{all}\\cdot FS \\cdot 40=40\\cdot q_{ult} $$ As you can see, it is not even slightly logical to use any bearing capacity that is calculated using some other method.\nModulus of Subgrade Reaction Table for Different Ground Types Bowles also has a table. And if you recommend something like 10-20 MN/m3 for a weathered rock to a client, they will come back with this table saying Bowles is clear. Bowles recommended 128000 kN/m3 for dense sand, do we dare to say our weathered rock is softer than dense sand? Of course not. The only thing we can say is: Bowles knows very well that modulus of subgrade reaction depends on the foundation width. So, how can he recommend a constant value for a soil type? He does not. He is -most probably- recommending the ranges for plate loading test or in worst case, for a foundation with a size of 2-3 m which he repeatedly uses in his book to demonstrate the methods. He usually does not use a foundation with 20 or 40 m width. Assuming k1 = 150000 kN/m3 from plate loading test on a plate with B1 = 0.3 m, we can estimate our ks using several methods given in Bowles: Equation for clays from Terzaghi: $$ k_s = k_1 \\cdot \\frac{B1}{B}=150000 \\cdot \\frac{0.3}{20}=2250 kN/m3 $$ Equation for sands from Terzaghi: $$ k_s = k_1 \\cdot (\\frac{B+B1}{2B})^2=150000 \\cdot (\\frac{20+0.3}{2 \\cdot 20})^2=38633kN/m3 $$ If we go back to our Settle 3D model where we found K=27000 kN/m3 and reduce the foundation size to 0.3x0.3m to represent a plate, the resulting deformation is 0.147 mm for 200 kPa loading. The modulus of subgrade reaction for plate loading on our weathered rock is 1,360,544 kN/m3. If you do the same with immediate settlement hand calculations (such as Mayne \u0026amp; Poulos or Gazetas), the results are even higher (3 to 7 million kN/m3) What do we say? 100000 kN/m3 is very low for our rock, it should be much higher! But not for our foundation, for plate loading. In fact, if we draw a curve using Mayne and Poulos\u0026rsquo; settlement equation, it will look like this: You can see that for elasticity modulus of 50 MPa (stiff clay / dense sand), it is around what Bowles proposed. What we understand from these text was given at the beginning: IT DEPENDS ON THE FOUNDATION SIZE. For our weathered rock, you can see how much it depends on the foundation size. What Should We Do? You have to calculate the settlement of the foundation using any method you like or your project specification requires: Hand calculations, plate loading tests, FE analyses using the parameters you have estimated. Any method. Use the settlement you have found in our holy formula and find the modulus. Up to this point, we haven\u0026rsquo;t discussed varying the modulus of subgrade reaction along the foundation. As you know, if our foundation is not rigid, we expect a dished shape settlement. However, if you enter uniform subgrade modulus under a plate loaded with uniform pressure, it will not bend, it will uniformly settle. So, you can see how wrong can our results be with uniform subgrade modulus: The plate will not bend in beam-on-spring model. Very dangerous. But, if you are not on that level, just get an average deformation using any method mentioned above and divide the average pressure to the average deformation. If you want to use different modulus of subgrade reaction throughout the foundation, you can estimate some ranges using the deformation along the foundation. I think Settle calculates the subgrade reaction along a query line directly in the new versions. An example calculation: You have many methods to calculate modulus of subgrade reaction. A modulus that can be calculated with a fair accuracy even with an hand calculation shouldn\u0026rsquo;t be a problem anymore.\n","permalink":"https://berkdemir.github.io/posts/modulus-of-subgrade-reaction/","summary":"\u003ch1 id=\"introduction\"\u003eIntroduction\u003c/h1\u003e\n\u003cp\u003eBy now, everything should have been settled about modulus of subgrade reaction. We all know some typical statements about it:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eIt depends on the soil properties\u003c/li\u003e\n\u003cli\u003eIt depends on the foundation size\u003c/li\u003e\n\u003cli\u003eIt depends on loading type, temperature, bitcoin prices and others.\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eHowever, let\u0026rsquo;s think about a weathered rock with E=500 MPa and a foundation to be built on top of this rock with 20 x 50 m dimensions. You can say it depends on many factors as much as you like, everybody has a rough idea already: 100,000 kN/m3. So, if you are a fancy engineer and dare to make some calculations, you can find much lower values. Will they believe you or will they think that you are being too conservative (if lowering the subgrade reaction means being conservative)?\nLet\u0026rsquo;s start with simple terms. The equation that everybody knows and nobody wants to use:\n$$\nK=\\frac{q}{s}\n$$\nSo, the subgrade reaction is equal to a spring stiffness distributed under the foundation. If you divide the pressure by the settlement, you will find the subgrade reaction, amount of deformation for unit pressure.\nIf we think about how we calculate settlement (how it depends on \u003cstrong\u003emany\u003c/strong\u003e factors), we can see actually how complex this modulus is.\u003c/p\u003e","title":"Modulus of Subgrade Reaction"},{"content":"Update on the Post (13/10/2022) New update of the Plaxis, partially, solves the problem mentioned in the post below. Now, if you define a manual tensile strength, this will be reduced during safety analysis. But if you rely on the tensile strength automatically calculated by Plaxis, it will not be reduced and same problem continues for that case, in my opinion. But at least, for the users that are aware of this distinction, there is an option to correctly use Hoek-Brown model. See the note on Plaxis\nIntroduction This is an investigation of a problem about Hoek-Brown model in FE codes. If you have any addition, test results or correction in my statements, please reach me.\nProblem Recently, we have been involved with a lot of FE analyses of excavations in rock with my colleagues in Niras. During the embedment depth and sensitivity analyses, we noticed weird behaviour and started small tests. Our tests showed us a behaviour that worried us - so this article is for people that have dealt with the Hoek-Brown models in Plaxis (or in any FE software) before - especially if tensile behaviour was governing the overall response.\nTest Model So, the simple test model. We define two material model - one Hoek-Brown and one Mohr-Coulomb. Stiffness parameters do not matter. For Mohr-Coulomb, enter some strength and for tensile strength, enter 34.5 kPa. For Hoek-Brown, here are the parameters - they result in 34.5 kPa too. What do we expect if we pull them in extension and make a safety analysis? FS = 34.50 / 30.00 = 1.15. This should be the result. But, in Hoek-Brown, we get 3.40. Discussion There are two questions. Why do we see FS of Hoek Brown much higher than what it is supposed to be and what happens here? Why? Plaxis does not reduce the tensile strength during safety calculation. Plaxis follows Benz et. al. (2008) approach and this paper does not talk about tensile strength. Plaxis material manual also does not mention any factorization of tensile strength. If tensile strength is not reduced during safety analysis, what happens? What Happens? Our guess here is that Plaxis starts to increase the safety factor to find instability during steps of safety analysis. However, even though it increases it to values around 9, it cannot find a instability, because we are looking for a full tensile failure while Plaxis only reduces the compressive/shear strength. When it reduces other parameters but not tensile strength, with the wording of Plaxis support, the failure surface rotates around the tensile strength while actually it should both rotate and move to the right, because tensile strength is reduced. You can see the failure surface with Hoek-Brown. Due to an another bug in Plaxis, you cannot see the updated failure surface in Info viewer, but I have drawn an approximate one with red. So, this is why it fails with an higher value instead of never failing, infinity safety factor. Why Should We Care? If you are analyzing a deep excavation, the bottom of the excavation will mostly resist to tension. In that case, all plug stability will have a different behaviour if you use safety analysis. What can you do until Plaxis corrects it or if you are using an older version? You can reduce the material properties by yourself instead of relying on safety analysis. However, you will be very crude, because you can reduce the UCS of rock. But this is a very conservative approach, because you will be reducing the strength significantly. But, at least, you will be reducing the tensile strength too. So, this is what we have used as a temporary solution. Dividing the UCS in SLS case by material factor and using that material model as the ULS. You cannot define the safety factor with this approach of course, you can only say if it is above 1 or below 1. You shouldn\u0026rsquo;t worry if you used Hoek-Brown only for slope stability. Because, only the crown of the slope will work in tension.\nWhat About Other Softwares? I didn\u0026rsquo;t have time to investigate all the softwares. But, I recommend everyone to make the simple test I described above. I have summarized couple of them below based on the information I get from their manuals:\nOptum G2/G3 Optum should have the same problem as per the information given here. I haven\u0026rsquo;t tested. Flac Flac does not give any information, but as far as I understand from the manuals, it has two FS calculation options. If I should guess, I would say, option 1 should reduce the tensile strength. Rocscience A big congrats to Rocscience. They define two methods in their manual: First one is applying the safety factor to shear strength. In that case, it recalculates the tensile strength. \u0026ldquo;The factored maximum tensile strength, equation 6.9, is calculated based on the new factored generalized Hoek Brown parameters.\u0026rdquo; Second one is Benz. et. al. (2008) approach that Plaxis also uses. But it seems that Rocscience noticed the problem and warned the users. \u0026ldquo;The factored maximum tensile strength in this approach, is the same as in the original material. The intersection of yield criterion with minor principal axis and first invariant of stress tensor will remain the same.\u0026rdquo; I don\u0026rsquo;t know if you can choose between these two approaches or how you choose. But, I would assume that there is a toggle for selection of factoring approach just as Flac has.\nZsoil Another congrats to Zsoil. They specifically showed the tensile strength reduction in the manual. Summary This problem should be and probably, will be solved just in a short while. But this case proves us that there can be problems. Just beware.\n","permalink":"https://berkdemir.github.io/posts/hoek-brown-model-in-finite-element-analysis/","summary":"\u003ch1 id=\"update-on-the-post-13102022\"\u003eUpdate on the Post (13/10/2022)\u003c/h1\u003e\n\u003cp\u003eNew update of the Plaxis, partially, solves the problem mentioned in the post below. Now, \u003cstrong\u003eif you define a manual tensile strength\u003c/strong\u003e, this will be reduced during safety analysis. \u003cstrong\u003eBut if you rely on the tensile strength automatically calculated by Plaxis\u003c/strong\u003e, it will not be reduced and same problem continues for that case, in my opinion. But at least, for the users that are aware of this distinction, there is an option to correctly use Hoek-Brown model.\nSee the note on \u003ca href=\"https://communities.bentley.com/products/geotech-analysis/w/wiki/62782/tensile-behaviour-in-the-hoek-brown-model\"\u003ePlaxis\u003c/a\u003e\u003c/p\u003e","title":"Hoek Brown Model in Finite Element Analysis"},{"content":"Before Introduction This is the paper we have written with my dear wife Pinar Akdogan Demir, based on our experience from Istanbul tunnels. I was already considering uploading the paper here, but when I saw that my paper was not inside the proceedings USB due to a mistake (which also was almost preventing me from presenting - because they simply forgot us), it was a must. So, here it is. As always, get in touch if you have any comments.\nIntroduction Due to comprehensive soil-structure interaction during and after tunnelling, estimation of structural forces on the linings depends on many factors which can be categorized into ground properties, structural properties, and loading properties. Estimation of ground properties has been discussed in the literature in detail and proper modelling of tunnels or any other structure that interacts with ground requires in-depth knowledge of ground properties. In geotechnical engineering, structural properties are thought to be rather well known, however, due to the strictly time-dependent excavation and loading process, even structural components cannot be represented by simpler constitutive or structural models.(Neuner, Cordes, et al., 2017; Neuner, Gamnitzer, et al., 2017; Schädlich et al., 2014; Schädlich \u0026amp; Schweiger, 2014) Static loadings on the tunnels are also discussed in detail and it is either represented by stage-by-stage modelling using finite element method (FEM) or finite difference methods (FDM) or empirical formulations such as Prodotyakonov, Terzaghi, and others to be used on beam-on-foundation solutions. (Celada \u0026amp; Bieniawski, 2019; Széchy, 1967; Terzaghi, 1943) Seismic forces, on the other hand, may impose the greatest load on the tunnels based on the seismicity of the project location. (Kontoe et al., 2008; Roy \u0026amp; Sarkar, 2017; Z. Z. Wang \u0026amp; Zhang, 2013; Zhang et al., 2018) Behaviour of underground tunnels differs significantly from above-ground structures due to complex interaction with the ground around it. (Hashash et al., 2001; Tsinidis et al., 2020) Although theoretical studies present a great deal of material to estimate seismic forces on the tunnels, there are still important points to be considered in the daily design. In this paper, practical seismic analyses of tunnels will be discussed along with recommendations for practice.\nSeismic Loads on Tunnels Available Methods There are several up-to-date methods to calculate the structural forces on tunnel lining which are summarized in the table below. Full dynamic analysis is, currently, the most advanced method that is available to both practitioners and academics. In this method, earthquake excitation is applied from the bottom boundary of the model and this boundary usually extended up to bedrock to reduce the steps to move the earthquake from bedrock to an upper level using an additional step of site response analysis. Since dynamic analyses are more sensitive to model conditions, the effects of boundary distance and mesh size are significant. (Fabozzi, 2017; Tsinidis, 2015) It is also advisable to use advanced constitutive models such as Hardening Soil Small Strain model which takes the stiffness-strain degradation relationship and damping into account. Analytical methods are very easy to use and proven to provide a reasonable estimation of earthquake induced forces on the lining. (Hashash et al., 2001; J. N. Wang, 1993) However, analytical methods require crude simplifications such as circular geometry and monolithic lining. To account for joints of segmental lining of TBM tunnels, following simplified approach can be used. (Wood, 1975) $$ I_{eqv}=I_{joint}+I_{seg} (4/n)^2 $$ Ieqv is the equivalent moment of inertia of the tunnel ring composed of joints and segments, Iseg is the moment of inertia of the segments (full section), Ijoint is the moment of inertia of the joints and n is the number of joints. Joint thickness is the clear concrete thickness after gasket. Compared to full dynamic analyses and analytical methods, pseudo-static methods are in between of these methods in terms of both advantages and disadvantages. Pseudo static methods can be divided into both deformation-based methods and force-based methods. Pseudo-static force-based methods such as prescribed acceleration can be a fast approach to seismic problems. However, since ovalling is the main reason of the seismic loading of underground structures, uniform acceleration profile may result in incorrect loads. Therefore, it is advised to check the response of model without tunnels to ensure the strain profile is correct. Pseudo-Static Deformation Method Pseudo static methods can be used with reasonable accuracy to estimate seismic tunnel lining forces. The main idea behind the pseudo-static deformation method is imposing ovalling deformation to whole model without any prior assumption about racking coefficient. Concept of pseudo-static deformation method is developed by Newmark (1968) and simplified derivation of strain due to waves is described below. In this equation, PGV is the peak ground velocity (m/s) and Vs is the shear wave velocity (m/s). Different notations (Vs for PGV and Cs for Vs) are available in the literature. Since PGV depends on the depth and shear wave velocity depends on the level of strain, effective parameters can be used for better notation: PGVe is effective peak ground velocity for the depth in consideration and Vse is the effective shear wave velocity calculated for the expected strain level.\nEffective Shear Velocity There are several guidelines for the reduction of shear wave velocity based on the earthquake level and ground strength. For the ratio of effective shear wave velocity to maximum shear wave velocity, FHWA-NHI-10-034 (Hung et al., 2009) recommends 1.0 for rock and 0.6 to 0.8 for stiff to very stiff soils. For softer soils, site-specific soil response analysis is recommended. Eurocode 8-5 (European Standard, 2004) presents recommendations for soils with shear velocity smaller than 360 m/s. For ground acceleration ratio between 0.1 to 0.3, reduction ratio decreases from 0.9 to 0.6. Since shear wave velocity level depends on the shear strain, effective velocity can be reasonably estimated using modulus reduction curves utilizing the relationship between shear wave velocity and shear modulus: To calculate the reduction of shear modulus and shear wave velocity for soils and rocks, an iterative approach is proposed based on the seismic shear strain. Darandeli (2001) curves can be used due to the validity of the approach for both sands and clays. In this equation, PI is the plasticity index (%), OCR is over-consolidation ratio and σ\u0026rsquo; is effective pressure (atm). For rocks, Schnabel (1973) curve can be approximated by the following equation with reasonable accuracy, R2=0.99. Since shear velocity depends on the square root of shear modulus, the following iterative approach can be used Iterative approach is used to calculate shear wave velocity reduction factors using both modulus reduction methods and presented as design charts in the following figures. These charts can be used in daily practice for estimation of reduction of shear wave velocity. It should be noted that Darendeli chart has been derived for OCR=1 and effective pressure = 2 atm. A simple Python code is also given in a Github repository to use to estimate effective shear wave velocity: https://github.com/berkdemir/Effective-Shear-Wave-Velocity Effective Peak Ground Velocity Peak ground velocity (PGV) is the main parameter to estimate seismic demand for underground structures since transient ground strains can be expressed using ratio of PGV to Vs based on the concept by Newmark (1968). Researches have shown that damage distribution of underground structures can be better correlated with PGV compared to PGA. (Kongar \u0026amp; Giovinazzi, 2015; Pineda-Porras \u0026amp; Najafi, 2010) Compared to other seismic parameters, there are very few methods to correlate PGV with other seismic parameters. Bommer and Alarcon (2006) have discussed a number of correlations available in literature. Aside from correlations, it is quite common for metro projects to take advantage of site-specific probabilistic seismic hazard assessment (PSHA) reports. However, in the absence of PSHA, several approaches from literature are proposed here due to ease of use with local codes and seismic maps. All parameters can be obtained after calculation of response spectrum which is standard practice for all projects. It should also be noted that Bommer and Alarcon (2006) have criticized the use of S1 for estimation of PGV based on their data, however, since FHWA (Hung et al., 2009) is widely accepted in practice, the proposed correlation of FHWA is included. The correlation by Paolucci and Smerzini (2018) includes both short and 1 sec spectral acceleration and the proposed correlation is also recommended by recent guideline on seismic design of tunnels published by Ministry of Transportation and Infrastructure of Turkey (2020). PGV/PGA ratio quoted by Hashash et. al. (2001) is also widely used, but not included in this study. Table below summarizes the recommended correlations for peak ground velocities. For underground structures, table below is recommended by FHWA (Hung et al., 2009) to reduce the earthquake demand based on the tunnel depth. FHWA-NHI-10-034 refers to Chang et. al. (1986) to support the reduction of ground motion parameters with depth, however, the referred study investigates the depth of nuclear reactors between 20 ft and 40 ft. Therefore, there is not clear information on how the recommendations are derived. To investigate this approach, nonlinear site response analyses are carried out using DeepSoil (Hashash et al., 2020) for a 250 m deep soil column with shear wave velocity increasing from 200 m/s to 800 m/s. Darendeli equation is used for modulus reduction and damping curves with PI=20, OCR=1. Selected earthquakes are summarized in Yee (2017). Nonlinear site response analysis results are presented in the left side of the figure below by normalizing the peak ground accelerations at each depth by accelerations at the ground surface which allows comparing the results with FHWA recommendations. Results show that except for four records, FHWA recommendations match the calculated reduction ratios reasonably. However, for Kobe, Loma Gilroy 2, Mammoth Lake, and Parkfield motions, ratio of PGA at surface to PGA at depth increases over 1 compared to values lower than 1 suggested by FHWA. To investigate this, equivalent linear analyses are also performed, and results are presented in right side of the figure below. Equivalent linear analyses result in closer values to FHWA recommendations compared to nonlinear analyses. The main reason behind the difference between the nonlinear and equivalent approach is the failure of soils closer to the surface. Due to the failure of soils closer to the surface in the nonlinear approach, ground motions are deamplified which results in higher ratios. Based on this comparison and available tools during the referred studies, it is reasonable to conclude that FHWA approach may have been developed based on equivalent linear or linear approaches. However, the outcomes of nonlinear analyses should not be disregarded. For high intensity, high PGA earthquakes, and low strength soils, the use of FHWA recommendations may be under-conservative. Finite Element Modelling of Pseudo-Static Deformation Method Deformations due to seismic loading should be applied to finite element model to simulate ovalling of underground structures due to seismic waves. However, the effects of imposed deformation should be carefully checked to validate that underground structures receive seismic loads. However, there are many factors that should be considered which will be detailed in the next chapter. In this part, the recommended procedure for imposing prescribed deformation on the finite element model will be presented. The recommendations will be given for Plaxis 2D V20, however, similar recommendations should apply to other FEM and FDM with small differences. Strains calculated using the procedures described before will be used to calculate the necessary amount of deformation to be imposed on the model. To properly simulate the earthquake deformations, Z-shaped or triangular prescribed deformations at vertical boundaries can be used (Fabozzi, 2017; Tsinidis, 2015). As long as a uniform total strain is obtained at the centre of the model, any deformation profile at vertical boundaries can be accepted such as “Z” shape with$\\gamma_{max}H/2$ at the top and $-\\gamma_{max}H/2$ at the bottom. However, it should be noted, in this case, uniform deformation profile should be applied in opposite direction to the top boundary too. It should also be noted that comparative analyses show that Z shape deformation profile results in shorter calculation time and lower number of calculation steps compared to triangular deformation profile. To properly “bend” the model in direction of applied deformation, it is suggested to fix the top boundaries at y direction. Figure below shows the recommended deformation profile in a finite element analysis. Due to shortcomings of some of available FEM codes, designers may choose to adapt different methods to simulate deformation. The methods to be chosen can be shaped based on the know-how of each designer as long as the imposed deformation profile is validated. Pescara et. al. (2011) uses rigid plates at vertical boundaries and iteratively determined force at the top and bottom of plates to bend the model. However, presented deformation profile in the paper shows that deformation is localized at the corners which may be unrealistic and resulting seismic forces may deviate from the “true” forces. Wang et. al. (2005) have recommended a detailed procedure for pseudo-static deformation on finite element models. Using similar approaches, the deformation profile at the centre of the model should be compared with the applied free field deformation before including the tunnel in the model. Similar recommendations can be applied to 3D models. In this case, prescribed deformations should be applied on all sides with same assumptions. Sensitivity of Pseudo-Static Deformation Method The behaviour of the model response depends strictly on the stiffness and strength of the medium. In case of a linear elastic soil, imposed deformations are uniformly distributed to all model regardless of the width, however, linear elastic soil behaviour assumption does not hold true for most soils and rock except very hard rocks. Boundary effects on finite element models are well investigated in literature for static and full-dynamic analyses. However, there are very few comments on pseudo-static deformation methods. Tsinidis (2015) compares the pseudo-static deformation method with full-dynamic analysis and finds that the simplified method underestimates the lining forces. Author, correctly, proposes that large distance between boundary and tunnel lining may act as an absorbent and “relieve” the strains on soils. Fabozzi (2017) uses 3D clear distance between lining and boundary for pseudo-static method and 8D for full-dynamic analysis. The relieving effect of soils between lining and boundary depends on, at least, the following factors: (For figures to compare the different properties of FE models, following notations are used: W – Width of the model (m), c: Drained cohesion (kPa), fi: Drained friction angle (deg), E: Drained elasticity modulus (kPa), D: Depth of model (m).)\nDistance between boundary and lining: With decreasing model with, deformation profiles at the centre are closer to the applied deformations as shown in following figure. However, it may not be possible to keep the boundary reasonably narrow since it will also affect the static forces due to boundary effects. Strength and stiffness of the soil Strength and stiffness affect the model behaviour significantly. Relieving effect on the free field deformation profile decreases with increasing strength. In case of linear elastic soil, there is no relieving effect. However, for softer soils, model width plays an important role on the deformations. Figure below shows the effect of these parameters on the deformation profile. Aspect ratio of the model The aspect ratio (Depth / Width) of the model is the primary property that can be easily manipulated to obtain correct free-field profile without affecting the static calculations and constitutive models. Based on a number of analyses in Plaxis 2D with softer soils which are summarized in Figure 8, it is recommended to keep the aspect ratio equal or above 2. It should also be noted that if the rock profile is below 1.4-2.2D below the tunnel (Möller, 2006), model can be extended to infinite depths using the same soil profile without affecting the results since the bedrock effect on the tunnels will be negligible. Overall Behaviour Summary of the conclusions from the three sensitivity analyses is presented in the following figure. As it can be observed from previous three chapters, overall behaviour of the model is similar to a beam. As the beam\u0026rsquo;s flexural rigidity increases, bending becomes more homogenous, as intended.\nComparison of Pseudo-Static Method with Analytical Methods A simple comparison between pseudo-static deformation method implement in FE and analytical method of Wang (1993) is presented in following figure. Due to limitation of space (which was important for WTC 2022), details of the model are not described in length. However, a simple comparison shows that using the recommended procedures, results of FE analyses agree with the analytical methods for circular linings. In cases where analytical methods fall short, pseudo-static methods provide an easy way to analyse tunnels in seismic conditions. As mentioned by Wang et. al. (2005), it is important to check the applied lateral deformation profile before the tunnel due to expected distortion of deformation profile with the inclusion of tunnel. Results of FE analysis in soft soil with and without the tunnel in shows the effect of tunnel on deformation profile. Conclusion Permanent linings of sprayed concrete lining (SCL) and TBM tunnels are designed to withstand both ground loadings, water loads and seismic loads in addition to temporary loads. Due to the symmetric nature of ground loads, in the seismic regions, seismic loads govern the tunnel design mostly. Seismic design of tunnels mainly based on the keystone papers in the literature with limited practical demonstration. This paper aims to close the gap between research and practice. Recommendations are given in the paper regarding the selection of seismic parameters as well as FEM models. Effective shear wave velocity and peak ground velocity are the main parameters to determine the demand on the structures. The ratio between effective and maximum shear wave velocity can be determined based on modulus reduction ratio curves in literature with an iterative approach. However, widely accepted rules for peak ground velocity reduction with depth should be re-evaluated for soft soils – high seismicity and 1D site response analysis should be used when needed. To apply pseudo-seismic deformation method in FEM and FDM, it is important to apply a quality control procedure to check if strains are applied at the centre of the model. Several recommendations are presented in the paper to obtain better strain profile along the model. These findings may improve the practice in tunnel designs in seismic regions while keeping the model complexity at sufficiently low levels.\nReferences Bommer, J. J., \u0026amp; Alarcon, J. E. (2006). The prediction and use of peak ground velocity. Journal of Earthquake Engineering, 10(01), 1–31. Celada, B., \u0026amp; Bieniawski, Z. T. (2019). Ground Characterization and Structural Analyses for Tunnel Design. CRC Press. Chang, C. Y., Power, M. S., Idriss, I. M., Somerville, P. G., Silva, W., \u0026amp; Chen, P. C. (1986). Engineering characterization of ground motion. Task II. Observational data on spatial variations of earthquake ground motion. Volume 3. Woodward-Clyde Consultants. Darendeli, M. B. (2001). Development of a new family of normalized modulus reduction and material damping curves. European Standard. (2004). Eurocode 8: Design of Structures for Earthquake Resistance (EN 1998-5). Fabozzi, S. (2017). Behaviour of segmental tunnel lining under static and dynamic loads. University of Naples Federico II. Hashash, Y. M. A., Hook, J. J., Schmidt, B., \u0026amp; I-Chiang Yao, J. (2001). Seismic design and analysis of underground structures. Tunnelling and Underground Space Technology, 16(4), 247–293. https://doi.org/10.1016/S0886-7798(01)00051-7 Hashash, Y. M. A., Musgrove, M. I., Harmon, J. A., Ilhan, O., Xing, G., Numanoglu, O., Groholski, D. R., Philips, C. A., \u0026amp; Park, D. (2020). DeepSoil 7 User Manual. Board of Trustees of University of Illinois at Urbana-Champaign. Hung, J. C., Monsees, J., Munfah, N., \u0026amp; Wisniewski, J. (2009). Technical Manual for Design and Construction of Road Tunnels (FHWA-NHI-10-034). U.S. Department of Transportation Federal Highway Administration. Kongar, I., \u0026amp; Giovinazzi, S. (2015). Damage to Infrastructure: Modeling. In M. Beer, I. A. Kougioumtzoglou, E. Patelli, \u0026amp; S.-K. Au (Eds.), Encyclopedia of Earthquake Engineering (pp. 524–536). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-35344-4_356 Kontoe, S., Zdravkovic, L., Potts, D. M., \u0026amp; Menkiti, C. O. (2008). Case study on seismic tunnel response. Canadian Geotechnical Journal, 45(12), 1743–1764. https://doi.org/10.1139/T08-087 Ministry of Transportation and Infrastructure of Republic of Turkey. (2020). Deprem Etkisi Altında Karayolu ve Demiryolu Tünelleri ile Diğer Zemin Yapılarının Tasarımı için Esaslar [in Turkish]. Möller, S. C. (2006). Tunnel induced settlements and structural forces in linings. IGS. Neuner, M., Cordes, T., Drexel, M., \u0026amp; Hofstetter, G. (2017). Time-Dependent Material Properties of Shotcrete: Experimental and Numerical Study. Materials, 10(9), 1067. https://doi.org/10.3390/ma10091067 Neuner, M., Gamnitzer, P., \u0026amp; Hofstetter, G. (2017). An Extended Damage Plasticity Model for Shotcrete: Formulation and Comparison with Other Shotcrete Models. Materials, 10(1), 82. https://doi.org/10.3390/ma10010082 Newmark, N. M. (1968). Problem in wave propagation in soil and rock. Proceedings of Int. Symp. Wave Propagation and Dynamic Properties of Earth Materials, 7–26. Paolucci, R., \u0026amp; Smerzini, C. (2018). Empirical evaluation of peak ground velocity and displacement as a function of elastic spectral ordinates for design. Earthquake Engineering \u0026amp; Structural Dynamics, 47(1), 245–255. https://doi.org/10.1002/eqe.2943 Pescara, M., Gaspari, G. M., \u0026amp; Repetto, L. (2011). Design of underground structures under seismic conditions: A long deep tunnel and a metro tunnel. ETH Zurich–2011 Colloquium on Seismic Design of Tunnels. Pineda-Porras, O., \u0026amp; Najafi, M. (2010). Seismic Damage Estimation for Buried Pipelines: Challenges after Three Decades of Progress. Journal of Pipeline Systems Engineering and Practice, 1(1), 19–24. https://doi.org/10.1061/(ASCE)PS.1949-1204.0000042 Roy, N., \u0026amp; Sarkar, R. (2017). A Review of Seismic Damage of Mountain Tunnels and Probable Failure Mechanisms. Geotechnical and Geological Engineering, 35(1), 1–28. https://doi.org/10.1007/s10706-016-0091-x Schädlich, B., \u0026amp; Schweiger, H. F. (2014). A new constitutive model for shotcrete. Numerical Methods in Geotechnical Engineering, 1, 103–108. Schädlich, B., Schweiger, H. F., Marcher, T., \u0026amp; Saurer, E. (2014, January 1). Application of a Novel Constitutive Shotcrete Model to Tunneling. ISRM Regional Symposium - EUROCK 2014. https://www.onepetro.org/conference-paper/ISRM-EUROCK-2014-130 Schnabel, P. B. (1973). Effects of local geology and distance from source on earthquake ground motions. University of California, Berkeley. Széchy, K. (1967). The Art of Tunnelling. Akademiai Kiado Budapest. Terzaghi, K. (1943). Theoretical Soil Mechanics. John Wiley \u0026amp; Sons. Tsinidis, G. (2015). On the seismic behaviour and design of tunnels. Aristotle University Of Thessaloniki (AUTH). Tsinidis, G., de Silva, F., Anastasopoulos, I., Bilotta, E., Bobet, A., Hashash, Y. M. A., He, C., Kampas, G., Knappett, J., Madabhushi, G., Nikitas, N., Pitilakis, K., Silvestri, F., Viggiani, G., \u0026amp; Fuentes, R. (2020). Seismic behaviour of tunnels: From experiments to analysis. Tunnelling and Underground Space Technology, 99, 103334. https://doi.org/10.1016/j.tust.2020.103334 Wang, J. N. (1993). Seismic Design of Tunnels (William Barclay Parsons Fellowship, p. 159). Wang, J. N., Erdik, M., \u0026amp; Otake, S. (2005). Seismic hazard assessment and earthquake resistant design considerations for the Bosphorus tunnel project Underground Space Use: Analysis of the Past and Lessons for the Future—Erdem \u0026amp; Solak. Wang, Z. Z., \u0026amp; Zhang, Z. (2013). Seismic damage classification and risk assessment of mountain tunnels with a validation for the 2008 Wenchuan earthquake. Soil Dynamics and Earthquake Engineering, 45, 45–55. https://doi.org/10.1016/j.soildyn.2012.11.002 Wood, A. M. M. (1975). The circular tunnel in elastic ground. Géotechnique, 25(1), 115–127. https://doi.org/10.1680/geot.1975.25.1.115 Yee, E. (2017). Preliminary estimation of fragility curves for the apr1400 turbine building under seismic loading. Zhang, X., Jiang, Y., \u0026amp; Sugimoto, S. (2018). Seismic damage assessment of mountain tunnel: A case study on the Tawarayama tunnel due to the 2016 Kumamoto Earthquake. Tunnelling and Underground Space Technology, 71, 138–148. https://doi.org/10.1016/j.tust.2017.07.019 ","permalink":"https://berkdemir.github.io/posts/recommendations-for-pseudo-static-deformation-for-seismic-analyses-of-tunnels/","summary":"\u003ch1 id=\"before-introduction\"\u003eBefore Introduction\u003c/h1\u003e\n\u003cp\u003eThis is the paper we have written with my dear wife Pinar Akdogan Demir, based on our experience from Istanbul tunnels. I was already considering uploading the paper here, but when I saw that my paper was not inside the proceedings USB due to a mistake (which also was almost preventing me from presenting - because they simply forgot us), it was a must. So, here it is. As always, get in touch if you have any comments.\u003c/p\u003e","title":"Recommendations for Pseudo-Static Deformation for Seismic Analyses of Tunnels"},{"content":"I have been working on StruSoft\u0026rsquo;s FEM-Design and Grasshopper connection for a trial case of a precast roof slab for a shaft. The results were great and even more than I expected! I was OK with some post-processing, but getting the results directly with a one-click from Grasshopper was amazing. It can handle shell connections, supports, load combinations and all I needed for this case. It is still improving a lot every day. ","permalink":"https://berkdemir.github.io/posts/roof-slab-with-grasshopper-and-femdesign/","summary":"\u003cp\u003eI have been working on \u003ca href=\"https://www.linkedin.com/company/strusoft/\"\u003eStruSoft\u003c/a\u003e\u0026rsquo;s FEM-Design and \u003ca href=\"https://www.linkedin.com/feed/hashtag/?keywords=grasshopper\u0026amp;highlightedUpdateUrns=urn%3Ali%3Aactivity%3A6957347171528527877\"\u003eGrasshopper\u003c/a\u003e connection for a trial case of a \u003cstrong\u003eprecast roof slab for a shaft\u003c/strong\u003e. The results were great and even more than I expected! I was OK with some post-processing, but getting the results directly with a one-click from Grasshopper was amazing. It can handle shell connections, supports, load combinations and all I needed for this case. It is still improving a lot every day.\n\u003cimg src=\"/posts/_assets/CoverSlab.gif\" alt=\"\"\u003e\n\n\u003cimg src=\"/posts/_assets/Untitled-23.png\" alt=\"\"\u003e\n\n\u003cimg src=\"/posts/_assets/Untitled-24.png\" alt=\"\"\u003e\n\n\u003cimg src=\"/posts/_assets/Untitled-25.png\" alt=\"\"\u003e\n\u003c/p\u003e","title":"Roof Slab with Grasshopper and FemDesign"},{"content":"A new paper from Tatone et. al. is published here. Using the data of the authors, following violin graph is drawn to estimate Modulus Ratio (MR = E / UCS) of the different rocks. Update: Aly Abdelaziz has proposed an update on the code and graph. Thanks to him, it looks better now. Code and data are in the Github Gist.\n# Data from Tatone, B. S., Abdelaziz, A., \u0026amp; Grasselli, G. (2022). Novel Mechanical Classification Method of Rock Based on the Uniaxial Compressive Strength and Brazilian Disc Strength. Rock Mechanics and Rock Engineering, 1-5. import pandas as pd import seaborn as sns # Rock Category rock_type = {\u0026#34;Sedimentary\u0026#34;: [\u0026#34;SL\u0026#34;, \u0026#34;SSh\u0026#34;, \u0026#34;SS\u0026#34;, \u0026#34;SC\u0026#34;], \u0026#34;Metamorphic\u0026#34;: [\u0026#34;MG\u0026#34;, \u0026#34;MS\u0026#34;, \u0026#34;MQ\u0026#34;, \u0026#34;MM\u0026#34;], \u0026#34;Igneous\u0026#34;: [\u0026#34;IG\u0026#34;, \u0026#34;IF\u0026#34;, \u0026#34;ID\u0026#34;]} ordered_box_list = [] for i, v in rock_type.items(): ordered_box_list += v df = pd.read_csv(\u0026#34;data.csv\u0026#34;) df = df[df.E != \u0026#34;-\u0026#34;] df = df.astype({\u0026#34;E\u0026#34;: float, \u0026#34;UCS\u0026#34;: float}) df[\u0026#34;MR\u0026#34;] = df[\u0026#34;E\u0026#34;] / df[\u0026#34;UCS\u0026#34;] * 1000 sns.set(rc={\u0026#34;figure.figsize\u0026#34;: (20, 8.27), \u0026#34;figure.dpi\u0026#34;: 300}) ax = sns.violinplot(x=\u0026#34;Type\u0026#34;, y=\u0026#34;MR\u0026#34;, data=df, order=ordered_box_list) ax.set_ylim(0) The data.csv file can be saved from here or from Gist. [[Notion/Quick Note/BDEM (1)/Blog Posts/_assets/data.csv]]\n","permalink":"https://berkdemir.github.io/posts/mr-data-from-tatone-et-al-2022/","summary":"\u003cp\u003eA new paper from Tatone et. al. is published \u003ca href=\"https://link.springer.com/article/10.1007/s00603-021-02759-7\"\u003ehere\u003c/a\u003e.\nUsing the data of the authors, following violin graph is drawn to estimate \u003cstrong\u003eModulus Ratio (MR = E / UCS)\u003c/strong\u003e of the different rocks.\nUpdate: \u003ca href=\"https://github.com/alicarlos\"\u003eAly Abdelaziz\u003c/a\u003e has proposed an update on the code and graph. Thanks to him, it looks better now.\n\u003cimg src=\"/posts/_assets/MRTatoneetal2022.png\" alt=\"\"\u003e\n\nCode and data are in the \u003ca href=\"https://gist.github.com/berkdemir/2799253491835776555e36c3a5b09ddd\"\u003eGithub Gist\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv class=\"highlight\"\u003e\u003cpre tabindex=\"0\" style=\"color:#f8f8f2;background-color:#272822;-moz-tab-size:4;-o-tab-size:4;tab-size:4;-webkit-text-size-adjust:none;\"\u003e\u003ccode class=\"language-python\" data-lang=\"python\"\u003e\u003cspan style=\"display:flex;\"\u003e\u003cspan\u003e\u003cspan style=\"color:#75715e\"\u003e# Data from Tatone, B. S., Abdelaziz, A., \u0026amp; Grasselli, G. (2022). Novel Mechanical Classification Method of Rock Based on the Uniaxial Compressive Strength and Brazilian Disc Strength. Rock Mechanics and Rock Engineering, 1-5.\u003c/span\u003e\n\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display:flex;\"\u003e\u003cspan\u003e\u003cspan style=\"color:#f92672\"\u003eimport\u003c/span\u003e pandas \u003cspan style=\"color:#66d9ef\"\u003eas\u003c/span\u003e pd\n\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display:flex;\"\u003e\u003cspan\u003e\u003cspan style=\"color:#f92672\"\u003eimport\u003c/span\u003e seaborn \u003cspan style=\"color:#66d9ef\"\u003eas\u003c/span\u003e sns\n\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display:flex;\"\u003e\u003cspan\u003e\n\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display:flex;\"\u003e\u003cspan\u003e\u003cspan style=\"color:#75715e\"\u003e# Rock Category\u003c/span\u003e\n\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display:flex;\"\u003e\u003cspan\u003erock_type \u003cspan style=\"color:#f92672\"\u003e=\u003c/span\u003e {\u003cspan style=\"color:#e6db74\"\u003e\u0026#34;Sedimentary\u0026#34;\u003c/span\u003e: [\u003cspan style=\"color:#e6db74\"\u003e\u0026#34;SL\u0026#34;\u003c/span\u003e, \u003cspan style=\"color:#e6db74\"\u003e\u0026#34;SSh\u0026#34;\u003c/span\u003e, \u003cspan style=\"color:#e6db74\"\u003e\u0026#34;SS\u0026#34;\u003c/span\u003e, \u003cspan style=\"color:#e6db74\"\u003e\u0026#34;SC\u0026#34;\u003c/span\u003e],\n\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display:flex;\"\u003e\u003cspan\u003e             \u003cspan style=\"color:#e6db74\"\u003e\u0026#34;Metamorphic\u0026#34;\u003c/span\u003e: [\u003cspan style=\"color:#e6db74\"\u003e\u0026#34;MG\u0026#34;\u003c/span\u003e, \u003cspan style=\"color:#e6db74\"\u003e\u0026#34;MS\u0026#34;\u003c/span\u003e, \u003cspan style=\"color:#e6db74\"\u003e\u0026#34;MQ\u0026#34;\u003c/span\u003e, \u003cspan style=\"color:#e6db74\"\u003e\u0026#34;MM\u0026#34;\u003c/span\u003e],\n\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display:flex;\"\u003e\u003cspan\u003e             \u003cspan style=\"color:#e6db74\"\u003e\u0026#34;Igneous\u0026#34;\u003c/span\u003e: [\u003cspan style=\"color:#e6db74\"\u003e\u0026#34;IG\u0026#34;\u003c/span\u003e, \u003cspan style=\"color:#e6db74\"\u003e\u0026#34;IF\u0026#34;\u003c/span\u003e, \u003cspan style=\"color:#e6db74\"\u003e\u0026#34;ID\u0026#34;\u003c/span\u003e]}\n\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display:flex;\"\u003e\u003cspan\u003e\n\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display:flex;\"\u003e\u003cspan\u003eordered_box_list \u003cspan style=\"color:#f92672\"\u003e=\u003c/span\u003e []\n\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display:flex;\"\u003e\u003cspan\u003e\u003cspan style=\"color:#66d9ef\"\u003efor\u003c/span\u003e i, v \u003cspan style=\"color:#f92672\"\u003ein\u003c/span\u003e rock_type\u003cspan style=\"color:#f92672\"\u003e.\u003c/span\u003eitems():\n\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display:flex;\"\u003e\u003cspan\u003e    ordered_box_list \u003cspan style=\"color:#f92672\"\u003e+=\u003c/span\u003e v\n\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display:flex;\"\u003e\u003cspan\u003e\n\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display:flex;\"\u003e\u003cspan\u003edf \u003cspan style=\"color:#f92672\"\u003e=\u003c/span\u003e pd\u003cspan style=\"color:#f92672\"\u003e.\u003c/span\u003eread_csv(\u003cspan style=\"color:#e6db74\"\u003e\u0026#34;data.csv\u0026#34;\u003c/span\u003e)\n\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display:flex;\"\u003e\u003cspan\u003e\n\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display:flex;\"\u003e\u003cspan\u003edf \u003cspan style=\"color:#f92672\"\u003e=\u003c/span\u003e df[df\u003cspan style=\"color:#f92672\"\u003e.\u003c/span\u003eE \u003cspan style=\"color:#f92672\"\u003e!=\u003c/span\u003e \u003cspan style=\"color:#e6db74\"\u003e\u0026#34;-\u0026#34;\u003c/span\u003e]\n\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display:flex;\"\u003e\u003cspan\u003edf \u003cspan style=\"color:#f92672\"\u003e=\u003c/span\u003e df\u003cspan style=\"color:#f92672\"\u003e.\u003c/span\u003eastype({\u003cspan style=\"color:#e6db74\"\u003e\u0026#34;E\u0026#34;\u003c/span\u003e: float, \u003cspan style=\"color:#e6db74\"\u003e\u0026#34;UCS\u0026#34;\u003c/span\u003e: float})\n\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display:flex;\"\u003e\u003cspan\u003e\n\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display:flex;\"\u003e\u003cspan\u003edf[\u003cspan style=\"color:#e6db74\"\u003e\u0026#34;MR\u0026#34;\u003c/span\u003e] \u003cspan style=\"color:#f92672\"\u003e=\u003c/span\u003e df[\u003cspan style=\"color:#e6db74\"\u003e\u0026#34;E\u0026#34;\u003c/span\u003e] \u003cspan style=\"color:#f92672\"\u003e/\u003c/span\u003e df[\u003cspan style=\"color:#e6db74\"\u003e\u0026#34;UCS\u0026#34;\u003c/span\u003e] \u003cspan style=\"color:#f92672\"\u003e*\u003c/span\u003e \u003cspan style=\"color:#ae81ff\"\u003e1000\u003c/span\u003e\n\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display:flex;\"\u003e\u003cspan\u003e\n\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display:flex;\"\u003e\u003cspan\u003esns\u003cspan style=\"color:#f92672\"\u003e.\u003c/span\u003eset(rc\u003cspan style=\"color:#f92672\"\u003e=\u003c/span\u003e{\u003cspan style=\"color:#e6db74\"\u003e\u0026#34;figure.figsize\u0026#34;\u003c/span\u003e: (\u003cspan style=\"color:#ae81ff\"\u003e20\u003c/span\u003e, \u003cspan style=\"color:#ae81ff\"\u003e8.27\u003c/span\u003e), \u003cspan style=\"color:#e6db74\"\u003e\u0026#34;figure.dpi\u0026#34;\u003c/span\u003e: \u003cspan style=\"color:#ae81ff\"\u003e300\u003c/span\u003e})\n\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display:flex;\"\u003e\u003cspan\u003e\n\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display:flex;\"\u003e\u003cspan\u003eax \u003cspan style=\"color:#f92672\"\u003e=\u003c/span\u003e sns\u003cspan style=\"color:#f92672\"\u003e.\u003c/span\u003eviolinplot(x\u003cspan style=\"color:#f92672\"\u003e=\u003c/span\u003e\u003cspan style=\"color:#e6db74\"\u003e\u0026#34;Type\u0026#34;\u003c/span\u003e, y\u003cspan style=\"color:#f92672\"\u003e=\u003c/span\u003e\u003cspan style=\"color:#e6db74\"\u003e\u0026#34;MR\u0026#34;\u003c/span\u003e, data\u003cspan style=\"color:#f92672\"\u003e=\u003c/span\u003edf, order\u003cspan style=\"color:#f92672\"\u003e=\u003c/span\u003eordered_box_list)\n\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display:flex;\"\u003e\u003cspan\u003eax\u003cspan style=\"color:#f92672\"\u003e.\u003c/span\u003eset_ylim(\u003cspan style=\"color:#ae81ff\"\u003e0\u003c/span\u003e)\n\u003c/span\u003e\u003c/span\u003e\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\u003cp\u003eThe data.csv file can be saved from here or from Gist.\n[[Notion/Quick Note/BDEM (1)/Blog Posts/_assets/data.csv]]\u003c/p\u003e","title":"MR Data from Tatone et. al. (2022)"},{"content":"Topology optimization is very similar to sculpting. You give a bulk volume to the algorithm and some constraints, it gives you the best shape that it can find. It is possible to use this in any software, as long as you can calculate the stresses - or any other criteria that you can use to eliminate the unnecessary volumes. I have been planning to try this in Plaxis for a long time. Using a couple of hours of coding and trials, it turns out Plaxis - Python connection works pretty well for topology optimization. This code lacks too much such as unstable volume check (stiffness matrix errors) or stop-criteria. But it was fun. ","permalink":"https://berkdemir.github.io/posts/topology-optimization-in-plaxis/","summary":"\u003cp\u003eTopology optimization is very similar to sculpting. You give a bulk volume to the algorithm and some constraints, it gives you the best shape that it can find.\nIt is possible to use this in any software, as long as you can calculate the stresses - or any other criteria that you can use to eliminate the unnecessary volumes.\nI have been planning to try this in Plaxis for a long time. Using a couple of hours of coding and trials, it turns out Plaxis - Python connection works pretty well for topology optimization. This code lacks too much such as unstable volume check (stiffness matrix errors) or stop-criteria. But it was fun.\n\u003cvideo controls style=\"max-width:100%\"\u003e\u003csource src=\"_assets/TopologyOptimization.mp4\" type=\"video/mp4\"\u003e\u003c/video\u003e\u003c/p\u003e","title":"Topology Optimization in Plaxis"},{"content":"Crack propogation during three point bending beam test using Concrete model in Plaxis. In this case, we have tried to capture the behavior of steel fibre reinforced concrete and results are really promising. The actual photo of the 3 point bending beam test is shown below from Buttignol et. al. (2008). ","permalink":"https://berkdemir.github.io/posts/plaxis-and-steel-fibre-reinforced-concrete/","summary":"\u003cp\u003eCrack propogation during three point bending beam test using Concrete model in Plaxis. In this case, we have tried to capture the behavior of steel fibre reinforced concrete and results are really promising.\n\u003cvideo controls style=\"max-width:100%\"\u003e\u003csource src=\"_assets/Bending_Beam_Test.mp4\" type=\"video/mp4\"\u003e\u003c/video\u003e\nThe actual photo of the 3 point bending beam test is shown below from \u003ca href=\"https://www.scielo.br/j/riem/a/3FH99MRnvSLHXrBY5Rg8j9p/?lang=en\"\u003eButtignol et. al. (2008)\u003c/a\u003e.\n\u003cimg src=\"/posts/_assets/Untitled-26.png\" alt=\"\"\u003e\n\u003c/p\u003e","title":"Plaxis and Steel Fibre Reinforced Concrete"},{"content":"Recently, I have prepared a Moment-Axial Force Interaction Diagram that fetches the structural forces from Plaxis automatically. Using the amazing Streamlit module, I have created a simple GUI for MN diagram and published its video in Linkedin. The response was amazing and I got a lot of questions regarding the procedure, Python-Plaxis connection and Streamlit. You can see the video here. I will not publish the code since it will require me to check every aspect of the code, do extensive tests and prepare a documentation. Instead, I want to give some insights on the methods that I have used in the code. I had to try and fail too many times and contacted Plaxis support several times. Since this is a gray area still with lot to develop, it is not easy to find discussions on the internet, so even a brain-storming with Plaxis support is really valuable. (Thanks to Stefanos) So, to create a record of these functions, I will share small gists (a little code snippets sharing tool by Github.)\nHow to Get the Loads From Plaxis? I have though about this a lot: What would be the best user experience? The best would be to know which plates user selected and get the loads for that plates. However, it is not possible with our current tools. So, I have created two options:\nGroups: User may group the plates beforehand. For example, 35_cm_shotcretes and 25_cm_shotcretes can be grouped together to seperately evaluate the structural capacity of these linings. Disadvantage: Tunnels designed in tunnel designer cannot be grouped in Plaxis (at least for now.) So, you will have to create the tunnel manually to use this option. Plates: This is not ideal, but it became the one I use mostly. All plates are listed to the user and user can select the plates that s/he want to plot. Disadvantage: Number of plates for complex geometries may increase to 10s, 20s with the intersection of temporary stages with the permanent wall. So, selecting too many plates can be inconvenient. We can fetch groups and plates from Plaxis. In my procedure, I create two list:\nGroup or Plate List: Group or plate objects of Plaxis. They are not readable by user but instead they are called Entities with long codes. However, we have to use these objects to make necessary processes. Group or Plate Names: Names of groups or plates as seen in Plaxis GUI. An example output of group_list_func() given below. ([\u0026lt;Entity {073DA50B-22A0-4D85-B9B1-E6470DC89EC4}\u0026gt;], ['RetainingWall'])\nDisclaimer I am not a coder, software engineer. So, there are many don\u0026rsquo;t-dos in the codes below. For example, no proper error handling is used. The proposed codes\u0026rsquo; runtime can be decreased significantly. You should rewrite everything given below to have a proper code. If you do not know Plaxis-Python connection but you are experienced in Python, you can find clever ways to rewrite the code, but this article will help you to get started. If you find a better way to write these codes, please let me know and I can edit the Gist and post by thanking you.\nBefore the Codes There are several ways to contact with Plaxis using Python. One of them is using the interpreter coming built-in with Plaxis for short codes. You can reach this by Expert - Python - Interpreter menu. This is already connected to Plaxis without a need for boilerplate code that calls for the plxscripting. It uses Jupyter QtConsole and works great. However, for longer codes, you will need to call for plxscripting.easy and you should start a new server with s_o, g_o = new_server(\u0026quot;localhost\u0026quot;, localhostport_o, password=password). This is pretty standard although it seems complicated. See the tutorials on the Bentley Plaxis website for boilerplate codes. When we performed all these steps, we have four keys:\ns_i, g_i for Plaxis Input applications. s_o, g_o for Plaxis Output applications. You will see that g_o is frequently used in the codes below since I mainly interact with output to fetch the results.\nFetching Groups Following function can be used to fetch the group list. Note that, no error handling is used, so if your model does not have groups, it will just print \u0026ldquo;Error.\u0026rdquo;\ndef group_list_func(): \u0026#34;\u0026#34;\u0026#34; Plaxis group list fetcher by Berk Demir / https://github.com/berkdemir Returns (group_list, group_names) as a tuple from Plaxis. If no group is defined in the model, it will print an error and will not return a value. \u0026#34;\u0026#34;\u0026#34; group_list = [] group_names = [] try: for i in g_o.Groups: group_list.append(i) group_names.append(i.Name.value) return group_list, group_names except: print(\u0026#34;Error. No group is defined.\u0026#34;) Fetching Plates Same procedure can be adapted to plates too.\ndef plate_list_func(): \u0026#34;\u0026#34;\u0026#34; Plaxis plate list fetcher by Berk Demir / https://github.com/berkdemir Returns (plate_list, plate_names) as a tuple from Plaxis. No error handling is present assuming user will not run the function without plates present in the model. \u0026#34;\u0026#34;\u0026#34; plate_list = [] plate_names = [] for i in g_o.Plates: plate_list.append(i) plate_names.append(i.Name.value) return plate_list, plate_names Phase List You should also create a phase list to select the phases that you will get the loads from Plaxis. A simple for loop can be used or you can modify this code to select certain phases:\nPhase_list = [] Phase_names = [] for i in g_o.Phases: Phase_list.append(i) Phase_names.append(i.Identification.value) Fetching Loads Now that we have everything (list of plates/groups and phases), we can ask for the loads from Plaxis. Notice that, when the results are called using g_o.getresults( object , phase,g_o.ResultTypes.Plate.M2D , \u0026quot;node\u0026quot;), we have a list of forces that should be flattened using a simple list comprehension.\ndef group_forces(plate_list, plate_names, phase_list): \u0026#34;\u0026#34;\u0026#34; Plaxis group forces fetcher by Berk Demir / https://github.com/berkdemir Returns (M, N) as a tuple from Plaxis. If no group is defined in the model, it will return None. \u0026#34;\u0026#34;\u0026#34; select_group_obj = [] for i, j in enumerate(group_names): # In my original code, I offer user the list of group_names and user select the groups. Returned selected_group_names is used to enumerate here. This is why code is structured the way it is. select_group_obj.append( group_list[group_names.index(j)] ) # Selected group names mapped in the group list to create a list of Plaxis objects. Results_M = [] Results_N = [] for i, j in enumerate(select_group_obj): for k, l in enumerate(phase_list): try: m = g_o.getresults(j, l, g_o.ResultTypes.Plate.M2D, \u0026#34;node\u0026#34;) Results_M.append([x for x in m]) n = g_o.getresults(j, l, g_o.ResultTypes.Plate.Nx2D, \u0026#34;node\u0026#34;) Results_N.append([-x for x in n]) except: pass return Results_M, Results_N def plate_forces(plate_list, plate_names, phase_list): \u0026#34;\u0026#34;\u0026#34; Plaxis plate forces fetcher by Berk Demir / https://github.com/berkdemir Returns (M, N) as a tuple from Plaxis. \u0026#34;\u0026#34;\u0026#34; select_plate_obj = [] for _, j in enumerate(plate_names): # In my original code, I offer user the list of plate_names and user select the plates. Returned selected_plate_names is used to enumerate here. This is why code is structured the way it is. select_plate_obj.append( plate_list[plate_names.index(j)] ) # Selected plate names mapped in the plate list to create a list of Plaxis objects. Results_M = [] Results_N = [] for _, j in enumerate(select_plate_obj): for _, l in enumerate(phase_list): try: m = g_o.getresults(j, l, g_o.ResultTypes.Plate.M2D, \u0026#34;node\u0026#34;) Results_M.append([x for x in m]) n = g_o.getresults(j, l, g_o.ResultTypes.Plate.Nx2D, \u0026#34;node\u0026#34;) Results_N.append([-x for x in n]) except: pass return Results_M, Results_N Note that resulting M and N lists are nested list due to incoming list types. I am 100% sure there are better ways to do it, mine was just to save the day. I used a flattener to re-write the list with something like flatten = lambda t: [item for sublist in t for item in sublist]. You can modify the code above to get a proper list. That\u0026rsquo;s it! Now that you have a list of M and N, so you can create your interaction diagram in another function and combine them!\n","permalink":"https://berkdemir.github.io/posts/plaxis-python-mn-interaction/","summary":"\u003cp\u003eRecently, I have prepared a Moment-Axial Force Interaction Diagram that fetches the structural forces from Plaxis automatically. Using the amazing Streamlit module, I have created a simple GUI for MN diagram and published its video in Linkedin. The response was amazing and I got a lot of questions regarding the procedure, Python-Plaxis connection and Streamlit.\nYou can see the video here.\n\u003cvideo controls style=\"max-width:100%\"\u003e\u003csource src=\"_assets/1614513616521.mp4\" type=\"video/mp4\"\u003e\u003c/video\u003e\nI will not publish the code since it will require me to check every aspect of the code, do extensive tests and prepare a documentation. Instead, I want to give some insights on the methods that I have used in the code. I had to try and fail too many times and contacted Plaxis support several times. Since this is a gray area still with lot to develop, it is not easy to find discussions on the internet, so even a brain-storming with Plaxis support is really valuable. (Thanks to Stefanos)\nSo, to create a record of these functions, I will share small gists (a little code snippets sharing tool by Github.)\u003c/p\u003e","title":"Plaxis-Python  MN Interaction"},{"content":"If you will use Hoek-Brown in your Python code, you may want to recommend some constants based on rock type. There is a widely used table in literature by Hoek and others that we use to select Modulus Ratio and material constant (mi) in the absence of high quality laboratory tests. I have done the manual labour, don\u0026rsquo;t write it all again. A dictionary called RockDict is given in the following Gist. Rock types are given as keys of dict and a sub-dictionary with:\nMR: Modulus Ratio MRSTD: Modulus Ratio Deviation Type: Rock Type (Igneous, Metamorphic, Sedimentary) mi: Material Constant miSDT: Material Constant Deviation \u0026#34;\u0026#34;\u0026#34; Hoek-Brown parameters in literature by Berk Demir This is a simple dictionary called \u0026#34;RockDict\u0026#34; for different rock types and their mi and MR values. Deviations (± from the average) are also stored as miSTD and MRSTD. Keys: Rock Types. Sub-dictionary keys: * \u0026#34;MR\u0026#34;: Modulus Ratio - int * \u0026#34;MRSTD\u0026#34;: Deviation of Modulus Ratio - int * \u0026#34;Type\u0026#34;: Rock type - str * \u0026#34;mi\u0026#34;: Hoek-Brown constant * \u0026#34;mi\u0026#34;: Deviation of mi. Prepared using Plaxis Reference Manual. \u0026#34;\u0026#34;\u0026#34; RockDict = { \u0026#34;Agglomerate\u0026#34;: { \u0026#34;MR\u0026#34;: 500, \u0026#34;MRSTD\u0026#34;: 100, \u0026#34;Type\u0026#34;: \u0026#34;Igneous\u0026#34;, \u0026#34;mi\u0026#34;: 19, \u0026#34;miSTD\u0026#34;: 3, }, \u0026#34;Amphibolites\u0026#34;: { \u0026#34;MR\u0026#34;: 450, \u0026#34;MRSTD\u0026#34;: 50, \u0026#34;Type\u0026#34;: \u0026#34;Metamorphic\u0026#34;, \u0026#34;mi\u0026#34;: 26, \u0026#34;miSTD\u0026#34;: 6, }, \u0026#34;Andesite\u0026#34;: { \u0026#34;MR\u0026#34;: 400, \u0026#34;MRSTD\u0026#34;: 100, \u0026#34;Type\u0026#34;: \u0026#34;Igneous\u0026#34;, \u0026#34;mi\u0026#34;: 25, \u0026#34;miSTD\u0026#34;: 5, }, \u0026#34;Anhydrite\u0026#34;: { \u0026#34;MR\u0026#34;: 350, \u0026#34;MRSTD\u0026#34;: 0, \u0026#34;Type\u0026#34;: \u0026#34;Sedimentary\u0026#34;, \u0026#34;mi\u0026#34;: 12, \u0026#34;miSTD\u0026#34;: 2, }, \u0026#34;Basalt\u0026#34;: { \u0026#34;MR\u0026#34;: 350, \u0026#34;MRSTD\u0026#34;: 100, \u0026#34;Type\u0026#34;: \u0026#34;Igneous\u0026#34;, \u0026#34;mi\u0026#34;: 25, \u0026#34;miSTD\u0026#34;: 5, }, \u0026#34;Breccia-I\u0026#34;: { \u0026#34;MR\u0026#34;: 500, \u0026#34;MRSTD\u0026#34;: 0, \u0026#34;Type\u0026#34;: \u0026#34;Igneous\u0026#34;, \u0026#34;mi\u0026#34;: 19, \u0026#34;miSTD\u0026#34;: 5, }, \u0026#34;Breccia-S\u0026#34;: { \u0026#34;MR\u0026#34;: 290, \u0026#34;MRSTD\u0026#34;: 60, \u0026#34;Type\u0026#34;: \u0026#34;Sedimentary\u0026#34;, \u0026#34;mi\u0026#34;: 19, \u0026#34;miSTD\u0026#34;: 5, }, \u0026#34;Chalk\u0026#34;: { \u0026#34;MR\u0026#34;: 1000, \u0026#34;MRSTD\u0026#34;: 0, \u0026#34;Type\u0026#34;: \u0026#34;Sedimentary\u0026#34;, \u0026#34;mi\u0026#34;: 7, \u0026#34;miSTD\u0026#34;: 2, }, \u0026#34;Claystones\u0026#34;: { \u0026#34;MR\u0026#34;: 250, \u0026#34;MRSTD\u0026#34;: 50, \u0026#34;Type\u0026#34;: \u0026#34;Sedimentary\u0026#34;, \u0026#34;mi\u0026#34;: 4, \u0026#34;miSTD\u0026#34;: 2, }, \u0026#34;Conglomerates\u0026#34;: { \u0026#34;MR\u0026#34;: 350, \u0026#34;MRSTD\u0026#34;: 50, \u0026#34;Type\u0026#34;: \u0026#34;Sedimentary\u0026#34;, \u0026#34;mi\u0026#34;: 21, \u0026#34;miSTD\u0026#34;: 3, }, \u0026#34;Dacite\u0026#34;: { \u0026#34;MR\u0026#34;: 400, \u0026#34;MRSTD\u0026#34;: 50, \u0026#34;Type\u0026#34;: \u0026#34;Igneous\u0026#34;, \u0026#34;mi\u0026#34;: 25, \u0026#34;miSTD\u0026#34;: 3, }, \u0026#34;Diabase\u0026#34;: { \u0026#34;MR\u0026#34;: 325, \u0026#34;MRSTD\u0026#34;: 25, \u0026#34;Type\u0026#34;: \u0026#34;Igneous\u0026#34;, \u0026#34;mi\u0026#34;: 15, \u0026#34;miSTD\u0026#34;: 5, }, \u0026#34;Diorite\u0026#34;: { \u0026#34;MR\u0026#34;: 325, \u0026#34;MRSTD\u0026#34;: 25, \u0026#34;Type\u0026#34;: \u0026#34;Igneous\u0026#34;, \u0026#34;mi\u0026#34;: 25, \u0026#34;miSTD\u0026#34;: 5, }, \u0026#34;Dolerite\u0026#34;: { \u0026#34;MR\u0026#34;: 350, \u0026#34;MRSTD\u0026#34;: 50, \u0026#34;Type\u0026#34;: \u0026#34;Igneous\u0026#34;, \u0026#34;mi\u0026#34;: 12, \u0026#34;miSTD\u0026#34;: 3, }, \u0026#34;Dolomites\u0026#34;: { \u0026#34;MR\u0026#34;: 425, \u0026#34;MRSTD\u0026#34;: 75, \u0026#34;Type\u0026#34;: \u0026#34;Sedimentary\u0026#34;, \u0026#34;mi\u0026#34;: 9, \u0026#34;miSTD\u0026#34;: 3, }, \u0026#34;Gabbro\u0026#34;: { \u0026#34;MR\u0026#34;: 450, \u0026#34;MRSTD\u0026#34;: 50, \u0026#34;Type\u0026#34;: \u0026#34;Sedimentary\u0026#34;, \u0026#34;mi\u0026#34;: 27, \u0026#34;miSTD\u0026#34;: 3, }, \u0026#34;Gneiss\u0026#34;: { \u0026#34;MR\u0026#34;: 525, \u0026#34;MRSTD\u0026#34;: 225, \u0026#34;Type\u0026#34;: \u0026#34;Metamorphic\u0026#34;, \u0026#34;mi\u0026#34;: 28, \u0026#34;miSTD\u0026#34;: 5, }, \u0026#34;Granite\u0026#34;: { \u0026#34;MR\u0026#34;: 425, \u0026#34;MRSTD\u0026#34;: 125, \u0026#34;Type\u0026#34;: \u0026#34;Igneous\u0026#34;, \u0026#34;mi\u0026#34;: 32, \u0026#34;miSTD\u0026#34;: 3, }, \u0026#34;Granodiorite\u0026#34;: { \u0026#34;MR\u0026#34;: 425, \u0026#34;MRSTD\u0026#34;: 125, \u0026#34;Type\u0026#34;: \u0026#34;Igneous\u0026#34;, \u0026#34;mi\u0026#34;: 29, \u0026#34;miSTD\u0026#34;: 3, }, \u0026#34;Greywackes\u0026#34;: { \u0026#34;MR\u0026#34;: 350, \u0026#34;MRSTD\u0026#34;: 0, \u0026#34;Type\u0026#34;: \u0026#34;Sedimentary\u0026#34;, \u0026#34;mi\u0026#34;: 18, \u0026#34;miSTD\u0026#34;: 3, }, \u0026#34;Gypsum\u0026#34;: { \u0026#34;MR\u0026#34;: 350, \u0026#34;MRSTD\u0026#34;: 0, \u0026#34;Type\u0026#34;: \u0026#34;Sedimentary\u0026#34;, \u0026#34;mi\u0026#34;: 8, \u0026#34;miSTD\u0026#34;: 2, }, \u0026#34;Hornfels\u0026#34;: { \u0026#34;MR\u0026#34;: 550, \u0026#34;MRSTD\u0026#34;: 150, \u0026#34;Type\u0026#34;: \u0026#34;Metamorphic\u0026#34;, \u0026#34;mi\u0026#34;: 19, \u0026#34;miSTD\u0026#34;: 4, }, \u0026#34;Limestone (Crystalline)\u0026#34;: { \u0026#34;MR\u0026#34;: 500, \u0026#34;MRSTD\u0026#34;: 100, \u0026#34;Type\u0026#34;: \u0026#34;Sedimentary\u0026#34;, \u0026#34;mi\u0026#34;: 12, \u0026#34;miSTD\u0026#34;: 3, }, \u0026#34;Limestone (Micritic)\u0026#34;: { \u0026#34;MR\u0026#34;: 900, \u0026#34;MRSTD\u0026#34;: 100, \u0026#34;Type\u0026#34;: \u0026#34;Sedimentary\u0026#34;, \u0026#34;mi\u0026#34;: 9, \u0026#34;miSTD\u0026#34;: 2, }, \u0026#34;Limestone (Sparitic)\u0026#34;: { \u0026#34;MR\u0026#34;: 700, \u0026#34;MRSTD\u0026#34;: 100, \u0026#34;Type\u0026#34;: \u0026#34;Sedimentary\u0026#34;, \u0026#34;mi\u0026#34;: 10, \u0026#34;miSTD\u0026#34;: 2, }, \u0026#34;Marble\u0026#34;: { \u0026#34;MR\u0026#34;: 850, \u0026#34;MRSTD\u0026#34;: 150, \u0026#34;Type\u0026#34;: \u0026#34;Metamorphic\u0026#34;, \u0026#34;mi\u0026#34;: 9, \u0026#34;miSTD\u0026#34;: 3, }, \u0026#34;Marls\u0026#34;: { \u0026#34;MR\u0026#34;: 175, \u0026#34;MRSTD\u0026#34;: 25, \u0026#34;Type\u0026#34;: \u0026#34;Sedimentary\u0026#34;, \u0026#34;mi\u0026#34;: 7, \u0026#34;miSTD\u0026#34;: 2, }, \u0026#34;Metasandstones\u0026#34;: { \u0026#34;MR\u0026#34;: 250, \u0026#34;MRSTD\u0026#34;: 50, \u0026#34;Type\u0026#34;: \u0026#34;Metamorphic\u0026#34;, \u0026#34;mi\u0026#34;: 19, \u0026#34;miSTD\u0026#34;: 3, }, \u0026#34;Migmatite\u0026#34;: { \u0026#34;MR\u0026#34;: 375, \u0026#34;MRSTD\u0026#34;: 25, \u0026#34;Type\u0026#34;: \u0026#34;Metamorphic\u0026#34;, \u0026#34;mi\u0026#34;: 29, \u0026#34;miSTD\u0026#34;: 3, }, \u0026#34;Norite\u0026#34;: { \u0026#34;MR\u0026#34;: 375, \u0026#34;MRSTD\u0026#34;: 25, \u0026#34;Type\u0026#34;: \u0026#34;Igneous\u0026#34;, \u0026#34;mi\u0026#34;: 20, \u0026#34;miSTD\u0026#34;: 5, }, \u0026#34;Peridotite\u0026#34;: { \u0026#34;MR\u0026#34;: 275, \u0026#34;MRSTD\u0026#34;: 25, \u0026#34;Type\u0026#34;: \u0026#34;Igneous\u0026#34;, \u0026#34;mi\u0026#34;: 25, \u0026#34;miSTD\u0026#34;: 5, }, \u0026#34;Phyllites\u0026#34;: { \u0026#34;MR\u0026#34;: 550, \u0026#34;MRSTD\u0026#34;: 250, \u0026#34;Type\u0026#34;: \u0026#34;Metamorphic\u0026#34;, \u0026#34;mi\u0026#34;: 7, \u0026#34;miSTD\u0026#34;: 3, }, \u0026#34;Porphyries\u0026#34;: { \u0026#34;MR\u0026#34;: 400, \u0026#34;MRSTD\u0026#34;: 0, \u0026#34;Type\u0026#34;: \u0026#34;Igneous\u0026#34;, \u0026#34;mi\u0026#34;: 20, \u0026#34;miSTD\u0026#34;: 5, }, \u0026#34;Quartzites\u0026#34;: { \u0026#34;MR\u0026#34;: 375, \u0026#34;MRSTD\u0026#34;: 75, \u0026#34;Type\u0026#34;: \u0026#34;Metamorphic\u0026#34;, \u0026#34;mi\u0026#34;: 20, \u0026#34;miSTD\u0026#34;: 3, }, \u0026#34;Rhyolite\u0026#34;: { \u0026#34;MR\u0026#34;: 400, \u0026#34;MRSTD\u0026#34;: 100, \u0026#34;Type\u0026#34;: \u0026#34;Igneous\u0026#34;, \u0026#34;mi\u0026#34;: 25, \u0026#34;miSTD\u0026#34;: 5, }, \u0026#34;Sandstones\u0026#34;: { \u0026#34;MR\u0026#34;: 275, \u0026#34;MRSTD\u0026#34;: 75, \u0026#34;Type\u0026#34;: \u0026#34;Sedimentary\u0026#34;, \u0026#34;mi\u0026#34;: 17, \u0026#34;miSTD\u0026#34;: 4, }, \u0026#34;Schists\u0026#34;: { \u0026#34;MR\u0026#34;: 675, \u0026#34;MRSTD\u0026#34;: 425, \u0026#34;Type\u0026#34;: \u0026#34;Metamorphic\u0026#34;, \u0026#34;mi\u0026#34;: 12, \u0026#34;miSTD\u0026#34;: 3, }, \u0026#34;Shales\u0026#34;: { \u0026#34;MR\u0026#34;: 200, \u0026#34;MRSTD\u0026#34;: 50, \u0026#34;Type\u0026#34;: \u0026#34;Sedimentary\u0026#34;, \u0026#34;mi\u0026#34;: 6, \u0026#34;miSTD\u0026#34;: 2, }, \u0026#34;Siltstones\u0026#34;: { \u0026#34;MR\u0026#34;: 375, \u0026#34;MRSTD\u0026#34;: 25, \u0026#34;Type\u0026#34;: \u0026#34;Sedimentary\u0026#34;, \u0026#34;mi\u0026#34;: 7, \u0026#34;miSTD\u0026#34;: 2, }, \u0026#34;Slates\u0026#34;: { \u0026#34;MR\u0026#34;: 500, \u0026#34;MRSTD\u0026#34;: 100, \u0026#34;Type\u0026#34;: \u0026#34;Metamorphic\u0026#34;, \u0026#34;mi\u0026#34;: 7, \u0026#34;miSTD\u0026#34;: 4, }, \u0026#34;Tuff\u0026#34;: {\u0026#34;MR\u0026#34;: 300, \u0026#34;MRSTD\u0026#34;: 100, \u0026#34;Type\u0026#34;: \u0026#34;Igneous\u0026#34;, \u0026#34;mi\u0026#34;: 13, \u0026#34;miSTD\u0026#34;: 5,}, } ","permalink":"https://berkdemir.github.io/posts/hoek-brown-parameters-database/","summary":"\u003cp\u003eIf you will use Hoek-Brown in your Python code, you may want to recommend some constants based on rock type. There is a widely used table in literature by Hoek and others that we use to select Modulus Ratio and material constant (mi) in the absence of high quality laboratory tests.\nI have done the manual labour, don\u0026rsquo;t write it all again. A dictionary called \u003ccode\u003eRockDict\u003c/code\u003e is given in the following Gist. Rock types are given as keys of dict and a sub-dictionary with:\u003c/p\u003e","title":"Hoek-Brown Parameters Database"},{"content":"There was a question regarding Plaxis in Bentley forum: A user asked the following question -paraphrased-:\nWhen we changed the plate parameters to simulate long term stiffness, there is no change in deformations. Is there something wrong?\nI have tried my best to explain this in the forum, but it is not an isolated case. In fact, there are many examples of design reports that do not take this into account. For example, changing the plate parameters from shotcrete to final lining is not a correct approach to simulate long-term degradation of the temporary lining. Why are deformations not changed when we changed the stiffness of structural elements? There is a clear explanation for that: Because finite element method does not work that way. As can be seen below or in Appendix of Scientific Manual of Plaxis, the incremental deformations are caused by unbalanced load. If there is no unbalanced load, the deformations will not increase since the equation results in 0. But let\u0026rsquo;s consider a tunnel. As you can see below, the real case is in first row. If we want the ground loads to act on the permanent lining, we can\u0026rsquo;t just change the material properties and hope for the best. We have to simulate the degradation of the temporary lining. There are several methods for this such as gray rock or assuming a certain thickness of shotcrete thickness is degraded. However, some project requirements do not allow for the consideration of temporary lining for permanent lining analyses at all. This is the case for subway projects in Turkey. In the second row, you see the wrong way of using plates for tunnel design. If we use this method, structural forces will be less than actual. Why? Let\u0026rsquo;s remember few things and consider the above case of wrong use of plates:\nIn soil-structure interaction, the stresses around the structures are affected by the stiffness of the structure and structural loads on these elements will be affected by the stresses and lining stiffness. Stresses to lining forces! Stresses are calculated based on the unbalanced forces. So if there is no unbalanced force, stresses will be the same and will be based on the black plate above. Lining forces? They depend on two things: Stresses and lining stiffness. Stresses are same but stiffness changed from black to red lining. So structural forces are changed. But is it correct? No. Because stresses used to calculate these forces are not true, they are based on black lining! They are based on previous soil-structure interaction analysis and not recalculated since there is no unbalanced force. See the example below for assuming temporary lining is 25 cm and the permanent lining is 35 cm. Let me be clear: I do not recommend applying permanent lining directly, I have never used this method in design. What should we do is TRANSFERRING THE GROUND LOADS FROM TEMPORARY LINING TO PERMANENT LINING. To do that, the methodology should be revised to model both at the same time and degrading the temporary lining in long term. One can use a combination of volume elements and plate elements so that volume elements are deactivated in long term and only plates are left in place. When can be changing plate properties a good idea? When we know that plate properties are changing in time and ground loads will be acting on different plate properties: Shotcrete vs. time analysis! You can use different properties for wet and dry shotcrete if you want to model the staged loading of temporary lining. For example, 50% of the soil loads will be relaxed until we reach the excavation, additional 20% will act on the wet shotcrete and remaining will act on the dry shotcrete. Do deformations change if we change the strength of soils? There is a really nice explanation by Plaxis for this. Assume that you have soil under a constant load. You change the initial c = 10 kPa and fi = 25 deg to c = 9 kPa and fi = 25 deg. Will there be any deformation? If there is a plastic failure caused by an additional decrease of strength parameters, Plaxis will try to redistribute the forces in the soil volume until equilibrium is reached. Therefore, we will see additional displacements. However, if none of the soils reached the failure due to a decrease in strength, there will be no additional displacements even if we change the material properties significantly. We can see that in the stage of forming the reaction vector. There is an option in Rocscience\u0026rsquo;s RS2 for changing materials that allow users to select the soil volume\u0026rsquo;s stress state. If we select the initial element loading as none, it will recalculate the stress when a certain material model is introduced to the model. If we create a small unbalanced load to tweak the settings? No, it will not work. Notice that in the equations above, displacement increment is calculated, not the total displacements all over again. So your less stiff model (or stiffer) will not resist against all existing loads but only to unbalanced loads.\n","permalink":"https://berkdemir.github.io/posts/plaxis-and-plate-properties-a-look-into-the-fe-adaptation-of-long-term-stiffness-changes/","summary":"\u003cp\u003eThere was a \u003ca href=\"https://communities.bentley.com/products/geotech-analysis/f/plaxis-soilvision-forum/209838/diaphragm-wall-movement-due-to-reduction-of-stiffness/636050#636050\"\u003equestion\u003c/a\u003e regarding Plaxis in Bentley forum: A user asked the following question -paraphrased-:\u003c/p\u003e\n\u003cblockquote\u003e\n\u003cp\u003eWhen we changed the plate parameters to simulate long term stiffness, there is no change in deformations. Is there something wrong?\u003c/p\u003e\n\u003c/blockquote\u003e\n\u003cp\u003eI have tried my best to explain this in the forum, but it is not an isolated case. In fact, there are many examples of design reports that do not take this into account. For example, changing the plate parameters from shotcrete to final lining is not a correct approach to simulate long-term degradation of the temporary lining.\n\u003cstrong\u003eWhy are deformations not changed when we changed the stiffness of structural elements?\u003c/strong\u003e\nThere is a clear explanation for that: Because finite element method does not work that way. As can be seen below or in Appendix of Scientific Manual of Plaxis, the incremental deformations are caused by unbalanced load. If there is no unbalanced load, the deformations will not increase since the equation results in 0.\n\u003cimg src=\"/posts/_assets/1614286024541-1619901469706.png\" alt=\"\"\u003e\n\nBut let\u0026rsquo;s consider a tunnel. As you can see below, the real case is in first row. If we want the ground loads to act on the permanent lining, we can\u0026rsquo;t just change the material properties and hope for the best. We have to \u003cstrong\u003esimulate the degradation of the temporary lining.\u003c/strong\u003e There are several methods for this such as gray rock or assuming a certain thickness of shotcrete thickness is degraded. However, some project requirements do not allow for the consideration of temporary lining for permanent lining analyses at all. This is the case for subway projects in Turkey.\n\u003cimg src=\"/posts/_assets/1614287907556.png\" alt=\"\"\u003e\n\nIn the second row, you see the \u003cstrong\u003ewrong way\u003c/strong\u003e of using plates for tunnel design. If we use this method, structural forces will be less than actual. Why?\nLet\u0026rsquo;s remember few things and consider the above case of wrong use of plates:\u003c/p\u003e","title":"Plaxis and Plate Properties - A Look into the FE Adaptation of Long Term Stiffness Changes"},{"content":"For underground structures, a rough but reasonable simplification is pseudo-static deformation method. In this method, we apply seismic strain which can be calculated as the ratio of effective PGV (Peak Ground Velocity) to effective shear wave velocity. $$ \\gamma = \\frac{PGV_e}{VS_e} $$ Effective PGV can be multiplied with depth dependent reduction factors (see FHWA-NHI-10-034) and maximum shear wave velocity obtained from geophysical tests with almost zero strain can be converted to effective shear wave velocity based on recommendations of FHWA or Eurocode 8. A simple Python code can be written to implement lateral deformation profile in Plaxis to simulate seismic loading. If you locate this Python file inside the Bentley folder (\u0026lt; PLAXIS installation folder \u0026gt;\\pytools\\input) this can be directly called from Plaxis Input.\n\u0026#34;\u0026#34;\u0026#34; Seismic Deformations for Plaxis by Berk Demir / https://github.com/berkdemir Locate this file in \u0026lt;PLAXIS installation folder\u0026gt;\\pytools\\input and call it from Plaxis - Expert - Run Python tool \u0026#34;\u0026#34;\u0026#34; import easygui from plxscripting.easy import * # If script is used OUTSIDE of Plaxis. \u0026#34;\u0026#34;\u0026#34; localhostport_i = 10000 # Local host port id can be different. password = \u0026#34;password\u0026#34; # Your password should be here. s_i, g_i = new_server(\u0026#34;localhost\u0026#34;, localhostport_i, password=password) \u0026#34;\u0026#34;\u0026#34; # If we use the script as a Plaxis tool. s_i, g_i = new_server() def get_borehole_layers(borehole): \u0026#34;\u0026#34;\u0026#34; reads the borehole information to collect soillayer thickness information and returns a dictionary per layer top-down \u0026#34;\u0026#34;\u0026#34; borehole_layers = [] for soillayer in g_i.Soillayers: for zone in soillayer.Zones: if (zone.Borehole.value) == borehole: borehole_layers.append({\u0026#34;name\u0026#34;: soillayer.Name.value, \u0026#34;top\u0026#34;: zone.Top.value, \u0026#34;bottom\u0026#34;: zone.Bottom.value, \u0026#34;thickness\u0026#34;: zone.Thickness.value } ) return borehole_layers def get_xmin_xmax(): \u0026#34;\u0026#34;\u0026#34; gets the xmax and xmin of the model.\u0026#34;\u0026#34;\u0026#34; point_list = [] for i in g_i.SoilContour: point_list.append(i) xmin = point_list[0].x.value xmax = point_list[1].x.value return xmin, xmax bh = g_i.Boreholes[0] borehole_layers = get_borehole_layers(bh) top = borehole_layers[0][\u0026#34;top\u0026#34;] bottom = borehole_layers[-1][\u0026#34;bottom\u0026#34;] depth = top-bottom title = \u0026#34;Seismic Deformation Application by Berk Demir\u0026#34; msg = \u0026#34;Please enter seismic parameters.\u0026#34; fieldNames = [ \u0026#34;Peak Ground Velocity (cm/sec)\u0026#34;, \u0026#34;Reduction in PGV due to depth\u0026#34;, \u0026#34;Maximum Shear Wave Velocity (m/s)\u0026#34;, \u0026#34;Ratio of Effective to Maximum Shear Wave Velocity\u0026#34; ] fieldValues = easygui.multenterbox(msg, title, fieldNames) def_choice = [\u0026#34;Triangular\u0026#34;,\u0026#34;Z-Shape\u0026#34;] select_def_type = easygui.buttonbox(\u0026#34;Select deformation type\u0026#34;, \u0026#34;Seismic Deformation Type\u0026#34;, def_choice) PGV, PGV_Red, VS, VS_Red = [float(item) for item in fieldValues] xmin, xmax = get_xmin_xmax() strain = PGV * PGV_Red * 0.01 / (VS*VS_Red) if select_def_type == \u0026#34;Triangular\u0026#34;: deformation = strain * depth LD_Left = g_i.linedispl((xmin,top),(xmin,bottom))[-1] LD_Right = g_i.linedispl((xmax,top),(xmax,bottom))[-1] LD_Top = g_i.linedispl((xmin,top),(xmax,top))[-1] LD_Left.setproperties(\u0026#34;Displacement_x\u0026#34;,\u0026#34;Prescribed\u0026#34;,\u0026#34;Displacement_y\u0026#34;,\u0026#34;Free\u0026#34;,\u0026#34;Distribution\u0026#34;,\u0026#34;Linear\u0026#34;,\u0026#34;ux_start\u0026#34;,deformation,\u0026#34;ux_end\u0026#34;,0) LD_Right.setproperties(\u0026#34;Displacement_x\u0026#34;,\u0026#34;Prescribed\u0026#34;,\u0026#34;Displacement_y\u0026#34;,\u0026#34;Free\u0026#34;,\u0026#34;Distribution\u0026#34;,\u0026#34;Linear\u0026#34;,\u0026#34;ux_start\u0026#34;,deformation,\u0026#34;ux_end\u0026#34;,0) LD_Top.setproperties(\u0026#34;Displacement_x\u0026#34;,\u0026#34;Prescribed\u0026#34;,\u0026#34;Displacement_y\u0026#34;,\u0026#34;Fixed\u0026#34;,\u0026#34;Distribution\u0026#34;,\u0026#34;Uniform\u0026#34;,\u0026#34;ux_start\u0026#34;,deformation) elif select_def_type == \u0026#34;Z-Shape\u0026#34;: deformation = strain * depth * 0.5 LD_Left = g_i.linedispl((xmin,top),(xmin,bottom))[-1] LD_Right = g_i.linedispl((xmax,top),(xmax,bottom))[-1] LD_Top = g_i.linedispl((xmin,top),(xmax,top))[-1] LD_Bottom = g_i.linedispl((xmin,bottom),(xmax,bottom))[-1] LD_Left.setproperties(\u0026#34;Displacement_x\u0026#34;,\u0026#34;Prescribed\u0026#34;,\u0026#34;Displacement_y\u0026#34;,\u0026#34;Free\u0026#34;,\u0026#34;Distribution\u0026#34;,\u0026#34;Linear\u0026#34;,\u0026#34;ux_start\u0026#34;,deformation,\u0026#34;ux_end\u0026#34;,-deformation) LD_Right.setproperties(\u0026#34;Displacement_x\u0026#34;,\u0026#34;Prescribed\u0026#34;,\u0026#34;Displacement_y\u0026#34;,\u0026#34;Free\u0026#34;,\u0026#34;Distribution\u0026#34;,\u0026#34;Linear\u0026#34;,\u0026#34;ux_start\u0026#34;,deformation,\u0026#34;ux_end\u0026#34;,-deformation) LD_Top.setproperties(\u0026#34;Displacement_x\u0026#34;,\u0026#34;Prescribed\u0026#34;,\u0026#34;Displacement_y\u0026#34;,\u0026#34;Fixed\u0026#34;,\u0026#34;Distribution\u0026#34;,\u0026#34;Uniform\u0026#34;,\u0026#34;ux_start\u0026#34;,deformation) LD_Bottom.setproperties(\u0026#34;Displacement_x\u0026#34;,\u0026#34;Prescribed\u0026#34;,\u0026#34;Displacement_y\u0026#34;,\u0026#34;Fixed\u0026#34;,\u0026#34;Distribution\u0026#34;,\u0026#34;Uniform\u0026#34;,\u0026#34;ux_start\u0026#34;,-deformation) To determine the effective shear wave velocity, I have developed a simple methodology and will present this as a part of a paper in the near future (hopefully in WTC 2022). I will not go into detail too much, but you can understand from the code that it is a iterative process.\nCalculate seismic shear strain using reduced PGV based on the depth of tunnel and maximum shear wave velocity. Ignoring any static strain, calculate the G/Gmax based on either one of the presented approaches. Calculate shear modulus reduction ratio as square root of the G/Gmax. Using the calculated ratio, calculate effective shear wave velocity. Calculate new seismic shear strain using reduced PGV and new effective shear wave velocity. Continue until reasonable difference is obtained between Vsi+1 and Vsi. Here is the simple code that calculates the effective shear wave velocity:\ndef EFS(Ground_Type, PGV, PGV_Red, VS, PI=20, OCR=1, Eff_Pressure=300): \u0026#34;\u0026#34;\u0026#34; Effective Shear Wave Velocity Using Darendeli (2001) and Schnabel (1973) by Berk Demir / https://github.com/berkdemir Inputs: Ground_Type: Either \u0026#34;Soil\u0026#34; or \u0026#34;Rock\u0026#34; PGV: Peak Ground Velocity (cm/sec) PGV_Red: PGV reduction ratio with depth VS: Maximum shear wave velocity (m/s) PI: Plasticity index in percent. (For Soil only.) OCR: Overconsolidation Ratio. (For Soil only.) Eff_Pressure: Effective pressure (kPa) (For Soil only) Returns: VS_Red: Reduction ratio for maximum shear wave velocity. Notes: Also prints a sentence with reduction ratio and effective shear wave velocity. Example: For Soils: Vs_Red = EFS(Ground_Type = \u0026#34;Soil\u0026#34;, PGV = 70, PGV_Red = 0.8, VS = 300, PI=20, OCR=1, Eff_Pressure=300) For Rocks: Vs_Red = EFS(Ground_Type = \u0026#34;Rock\u0026#34;, PGV = 70, PGV_Red = 0.8, VS = 800) \u0026#34;\u0026#34;\u0026#34; PGV_eff = PGV * PGV_Red * 0.01 # m/s Shear_Modulus_Reaction = 0.7 # initial value VS_Red = pow(Shear_Modulus_Reaction, 0.5) if Ground_Type == \u0026#34;Soil\u0026#34;: Strain_Ref = (0.0352 + 0.001 * PI * pow(OCR, 0.3246)) * \\ pow(Eff_Pressure / 100, 0.3483) / 100 VS_Red = pow(Shear_Modulus_Reaction, 0.5) for i in range(0, 20): seismic_shear_strain = PGV_eff / (VS_Red * VS) Shear_Modulus_Reaction = 1 / \\ (1 + pow(seismic_shear_strain / Strain_Ref, 0.919)) VS_Red = pow(Shear_Modulus_Reaction, 0.5) print(\u0026#34;Reduction ratio of shear wave velocity is\u0026#34;, round(VS_Red, 2), \u0026#34;and effective shear wave velocity is\u0026#34;, round( VS*VS_Red, 0), \u0026#34;m/s using Darandeli (2001) G/Gmax curves for soils.\u0026#34;) elif Ground_Type == \u0026#34;Rock\u0026#34;: for i in range(0, 20): seismic_shear_strain = PGV_eff / (VS_Red * VS) Shear_Modulus_Reaction = -3.642 * \\ pow(seismic_shear_strain, 0.02553) + 3.784 VS_Red = pow(Shear_Modulus_Reaction, 0.5) print(\u0026#34;Reduction ratio of shear wave velocity is\u0026#34;, round(VS_Red, 2), \u0026#34;and effective shear wave velocity is\u0026#34;, round( VS*VS_Red, 0), \u0026#34;m/s using Schnabel (1973) G/Gmax curve for rocks.\u0026#34;) return VS_Red if __name__ == \u0026#34;__main__\u0026#34;: VS_Red = EFS(Ground_Type, PGV, PGV_Red, VS, PI, OCR, Eff_Pressure) VS_eff = VS * VS_Red ","permalink":"https://berkdemir.github.io/posts/plaxis-python-seismic-deformation/","summary":"\u003cp\u003eFor underground structures, a rough but reasonable simplification is pseudo-static deformation method. In this method, we apply seismic strain which can be calculated as the ratio of effective PGV (Peak Ground Velocity) to effective shear wave velocity.\n$$\n\\gamma = \\frac{PGV_e}{VS_e} \n$$\nEffective PGV can be multiplied with depth dependent reduction factors (see FHWA-NHI-10-034) and maximum shear wave velocity obtained from geophysical tests with almost zero strain can be converted to effective shear wave velocity based on recommendations of FHWA or Eurocode 8.\nA simple Python code can be written to implement lateral deformation profile in Plaxis to simulate seismic loading. If you locate this Python file inside the Bentley folder (\u0026lt; PLAXIS installation folder \u0026gt;\\pytools\\input) this can be directly called from Plaxis Input.\u003c/p\u003e","title":"Plaxis-Python  Seismic Deformation"},{"content":"Estimating damage level on the existing buildings due to tunnelling is a tricky business which depend on many factors and cannot be over-simplified. But one of the simplifications that has been used commonly is equivalent beam method. Equivalent beam method allows us to simplify the rigidity of buildings in a simple Mindlin beam. Why do we need the rigidity of the building to come into our numerical models? We have many evidences that show us greenfield deformations (which are deformations due to tunnelling on level ground without any structure.) are much higher and narrower than building deformations caused by tunnelling. One evidence is given my Frischman et. al. (1994) and reported by Mair, Taylor and Burland (1996). So, we need the rigidity of the structure to be modelled and we need it as close as possible to the reality. How? We can model the structure every time we model a tunnel problem, this is an option of course, but an option for people with lot of time. We need a simpler solution. The simpler solution is equivalent beam method. To determine the EI and EA of the beam, we have to come up with a methodology that allows us to simplify the building. Potts and Addenbrooke (1997) have proposed calculating moment of inertia of the building with respect to neutral axis, considering only slabs using parallel axis theorem. (If you forget: Moment of inertia of a beam at point P at a distance y to its neutral axis is I_P=I+Ay². As authors state, this is an over-estimation since this assumption holds true only for rigidly framed structures. But they also summarize another method which is also described in CIRIA report 200 by Mair and Taylor (2001). Using this method, authors have predicted the deformations before the construction (Class A prediction) and results are very close to measurements. In this method, moment of inertia of each slab is summed up by neglecting Ay² term. Note that in both methods equivalent area of the beam can be calculated using sum of the area of each slab. Goh and Mair (2014) developed a third approach which adds column stiffening factor, C of Meyerhof to approach given in Mair and Taylor (2001). However, calculation of C requires detailed information on column and beam positions which may not be readily available in every project. But, to make a note, I should state that, if you will perform a detailed analysis for a significant building, you should definitely use this paper (if you will not model the building in full detail.)s Goh and Mair (2014) states that parallel axis method is over-estimation of the building rigidity while algebraic sum of moment of inertias is under-estimation. To be honest, parallel axis method was looking better for me. However, a very very simple experiment proved me wrong. I have modelled a building in almost-full detail. Of course, there are still many simplifications such as connections of slabs and columns, but it is a simple trial, so this should do. I have created three models using Plaxis 2D 2019:\nFull structural model with beams and columns modelled explicitly. Equivalent beam model using parallel axis theorem. Equivalent beam model with algebraic sum of moment of inertias of slabs and raft. Views of full structural model and equivalent beam model are given below: Results are very surprising for me: What do we see here? First of all, due to very high EI and EA calculated using parallel axis theorem resulted in a rigid beam rotation without significant bending of the beam. But full structural model does not behave like this. In fact, vertical deformations calculated using full structural model and equivalent beam using algebraic sum of inertias practically same. Same conclusion applies to lateral deformations too. So, this simple work-out tells us that algebraic sum method is much more suitable for framed buildings. What is your opinion and experience on this topic? What is your daily practice when assessing tunnel-induced damages on buildings?\nReferences: Potts, D. M., \u0026amp; Addenbrooke, T. I. (1997, April). A structure\u0026rsquo;s influence on tunnelling-induced ground movements. In Proceedings of the Institution of Civil Engineers: Geotechnical Engineering (Vol. 125, No. 2). Mair, R. J., \u0026amp; Taylor, R. N. (2001). 14 Elizabeth House: settlement predictions. Building Response to Tunnelling: Case Studies from Construction of the Jubilee Line Extension, London, 1, 195. Goh, K. H., \u0026amp; Mair, R. J. (2014). Response of framed buildings to excavation-induced movements. Soils and Foundations, 54(3), 250-268. ","permalink":"https://berkdemir.github.io/posts/comparison-of-building-rigidity-calculation-approaches-to-estimate-tunnelling-induced-deformations/","summary":"\u003cp\u003eEstimating damage level on the existing buildings due to tunnelling is a tricky business which depend on many factors and cannot be over-simplified. But one of the simplifications that has been used commonly is \u003cem\u003eequivalent beam method.\u003c/em\u003e\n\u003cimg src=\"/posts/_assets/BuildingRigidity-1.png\" alt=\"\"\u003e\n\n\u003cem\u003eEquivalent beam method\u003c/em\u003e allows us to simplify the rigidity of buildings in a simple Mindlin beam. Why do we need the rigidity of the building to come into our numerical models? We have many evidences that show us \u003cem\u003egreenfield deformations\u003c/em\u003e (which are deformations due to tunnelling on level ground without any structure.) are much higher and narrower than building deformations caused by tunnelling. One evidence is given my Frischman et. al. (1994) and reported by Mair, Taylor and Burland (1996).\nSo, we need the rigidity of the structure to be modelled and we need it as close as possible to the reality. How? We can model the structure every time we model a tunnel problem, this is an option of course, but an option for people with lot of time. We need a simpler solution.\nThe simpler solution is equivalent beam method. To determine the EI and EA of the beam, we have to come up with a methodology that allows us to simplify the building. Potts and Addenbrooke (1997) have proposed calculating moment of inertia of the building with respect to neutral axis, considering only slabs using parallel axis theorem. (If you forget: Moment of inertia of a beam at point P at a distance y to its neutral axis is I_P=I+A\u003cem\u003ey².\nAs authors state, this is an over-estimation since this assumption holds true only for rigidly framed structures. But they also summarize another method which is also described in CIRIA report 200 by Mair and Taylor (2001). Using this method, authors have predicted the deformations before the construction (Class A prediction) and results are very close to measurements. In this method, moment of inertia of each slab is summed up by neglecting A\u003c/em\u003ey² term.\n\u003cimg src=\"/posts/_assets/BuildingRigidity-2.png\" alt=\"\"\u003e\n\nNote that in both methods equivalent area of the beam can be calculated using sum of the area of each slab.\nGoh and Mair (2014) developed a third approach which adds column stiffening factor, C of Meyerhof to approach given in Mair and Taylor (2001). However, calculation of C requires detailed information on column and beam positions which may not be readily available in every project. But, to make a note, I should state that, if you will perform a detailed analysis for a significant building, you should definitely use this paper (if you will not model the building in full detail.)s\nGoh and Mair (2014) states that parallel axis method is over-estimation of the building rigidity while algebraic sum of moment of inertias is under-estimation. To be honest, parallel axis method was looking better for me. However, a \u003cstrong\u003every very simple experiment\u003c/strong\u003e proved me wrong.\nI have modelled a building in almost-full detail. Of course, there are still many simplifications such as connections of slabs and columns, but it is a simple trial, so this should do. I have created three models using Plaxis 2D 2019:\u003c/p\u003e","title":"Comparison of Building Rigidity Calculation Approaches to Estimate Tunnelling-induced Deformations"}]