英语文摘
英语文摘中英对照File
英语文摘中英对照File一、生活感悟英文原文：Life is like a camera. Just focus on what's important and capture the good times, develop from the negatives and if things don't work out, just take another shot.中文翻译：生活就像一台相机。
只需关注重要的事物，捕捉美好时光，从挫折中成长，如果事情不尽如人意，那就再试一次。
二、名人名言英文原文："The only way to do great work is to love what you do." – Steve Jobs中文翻译：“成就伟大事业的唯一途径，就是热爱你所做的事。
” ——史蒂夫·乔布斯三、趣味故事英文原文：Once upon a time, there was a fox who was very proud of his tail. One day, he got caught in a trap and had to sacrifice his tail to escape. Though he was free, he felt ashamed of his appearance. However, he soon realized that his life was more important than his tail.中文翻译：从前，有一只狐狸非常自豪自己的尾巴。
有一天，它不慎陷入了陷阱，为了逃脱，不得不牺牲自己的尾巴。
虽然它重获自由，但它为自己的外貌感到羞愧。
然而，它很快意识到，生命比尾巴更重要。
四、励志故事英文原文：Thomas Edison failed more than 10,000 times before he invented the light bulb. When asked about his failures, he replied, "I have not failed. I've just found 10,000 ways that won't work."中文翻译：托马斯·爱迪生在发明电灯泡之前失败了超过一万次。
英语文摘：自信的你最美丽
英语文摘：自信的你最美丽如果有人问你，什么时候的你最美丽，你可能会一头雾水，下面小编给大家分享一篇自信的你最美丽之7种方法教你自信满满，仅供参考。
自信的你最美丽：7种方法教你自信满满Are you good enough, clever enough, good looking enough? If you think not, would you consider your answer to be objective? Are you one of those people who has an inner critic that Satan would be jealous of? Well it’s time to see yourself as you really are; gifted, worthy and capable of anything you chose to be.你是不是足够优秀、足够聪明、足够美貌呢?如果觉得不是，你能否给出比较客观的回答?你是不是内心深处也有着色厉内荏的自责?好吧，那你该真正认识自己，做回那个渴望成为的聪明优秀而又能干的你了!Time to put an end to yourself criticism and look at yourself objectively.是时候停止自我批评、客观看待自己啦。
Follow these 7 steps below and you will be lacking in confidence no more.试试下面7个方法，你会一直自信满满!1. Monitor the Negative Voice留神消极声音Start by monitoring your negative voice. Notice when you are self-critical, and observe the conversations that go on in your head. When you become aware of the conversations, you can then work on changing them. Your job is to ensure that the voice in your head is positive and supportive at all times and not negative and critical.首先请留神自己的消极声音吧。
英语文摘 空中英语
英语文摘空中英语《空中英语教室》是一本非常受欢迎的英语学习杂志，以其独特的“听、说、读、写”综合英语学习法而著名。
以下是一篇从《空中英语教室》中摘录的文章，供您参考：The Power of PerseveranceIn life, we encounter countless obstacles and challenges that test our resolve and resilience. Some days, the going gets tough, and it seems like giving up is the easier path. But the truth is, perseverance is the key to unlocking our full potential and achieving our dreams.Perseverance is the ability to keep going despite difficulties and setbacks. It's about hanging in there, staying positive, and never giving up. When faced with adversity, the individual who perseveres ultimately prevails.The road to success is not always smooth. It's full of twists and turns, ups and downs. But it's these challenges that shape us and make us stronger. We learn from our mistakes, grow from our failures, and discover new strengths we didn't know we had.The secret to success is to never give up. Successful people don't see obstacles as insurmountable problems; they see them as opportunities for growth and learning. They believe in themselves, their abilities, and their dreams with unwavering faith.So the next time you hit a roadblock or face a challenge, remember this: Perseverance is power. With every step you take, you're getting closer to your goal. Hang in there, stay positive, and never give up. Your dreams are within reach—just keep pushing forward.。
经典英语文摘大全
经典英语文摘大全（经典版）编制人：__________________审核人：__________________审批人：__________________编制单位：__________________编制时间：____年____月____日序言下载提示：该文档是本店铺精心编制而成的，希望大家下载后，能够帮助大家解决实际问题。
文档下载后可定制修改，请根据实际需要进行调整和使用，谢谢!并且，本店铺为大家提供各种类型的经典范文，如演讲稿、总结报告、合同协议、方案大全、工作计划、学习计划、条据书信、致辞讲话、教学资料、作文大全、其他范文等等，想了解不同范文格式和写法，敬请关注!Download tips: This document is carefully compiled by this editor. I hope that after you download it, it can help you solve practical problems. The document can be customized and modified after downloading, please adjust and use it according to actual needs, thank you!In addition, this shop provides you with various types of classic sample essays, such as speech drafts, summary reports, contract agreements, project plans, work plans, study plans, letter letters, speeches, teaching materials, essays, other sample essays, etc. Want to know the format and writing of different sample essays, so stay tuned!经典英语文摘大全“兴趣是最好的老师”这句话放到英语学习上是千真万确。
英语文摘寻找属于自己的宁静
英语文摘寻找属于自己的宁静英语文摘寻找属于自己的宁静I’m an introvert—someone who prefers solitary[2] to social activities. Don’t misunderstand this as me being an awkward computer-nerd you see portrayed on televisions who can’t hold a decentconversation; instead, think of it as someone who simply needs to re-energize after spending the day in a crowd: like a battery with a low lifetime of sorts.[3]1. extrovert: 性格外向者;introvert: 性格内向者。
2. solitary: 单独，独处。
3. 别误会，不要把我想象成你在电视上看到的那种笨拙的电脑呆子，连正常的对话都应付不来;相反，你可以想象我只是个待机时间短的电池，在人群中熙熙攘攘一天之后，需要恢复能量。
awkward: 尴尬的，笨拙的;nerd: 书呆子;portray: 扮演，描绘;decent: 体面的，合适的。
My ideal day during the weekend would begin by getting nine hours of sleep and then lifting some weights in the morning after my breakfast has properly settled.[4] After a stress-relievingworkout, I would get my post-workout meal in whilst watching a few episodes of Parks & Recreationto get some good laughs in.[5] Next would be to dance, nap, listen to music, stretch/yoga,walk my dog, or some activity to pass time that I enjoy doing at the time. After spending the majority of the day alone doing these activities I would then sit down in my room and play videogames like League of Legends, or binge-watch on some anime that I’m currently obsessed with until I feel like it’s time to go to bed.”[6]4. lift weights: 举重;settle: 解决。
英语文摘_精品文档
英语文摘Introduction:The English language is spoken by millions of people worldwide and is considered the lingua franca of the modern era. As a result, there is a vast amount of written material available in English, ranging from books and news articles to academic papers and online blogs. In this English language digest, we will explore various aspects of the English language, including its history, grammar, vocabulary, and usage.Part 1: The History of the English LanguageThe English language traces its roots back to the Germanic languages spoken by tribes in the British Isles over 1,500 years ago. Over time, the English language evolved through various influences, including the Viking invasions, Latin and French borrowing during the Norman Conquest, and global colonization by the British Empire.During the Renaissance period, English underwent a significant transformation with the introduction of new wordsand ideas from classical languages such as Greek and Latin. The printing press also played a crucial role in standardizing the English language and making it accessible to the masses.Part 2: Grammar and SyntaxEnglish grammar can be a complex subject for learners due to its numerous rules and exceptions. However, understanding the basic concepts of grammar is essential for effective communication. This section will cover fundamental topics such as verb tenses, sentence structures, subject-verb agreement, and the correct usage of articles and prepositions.Additionally, we will explore common grammatical errors and provide tips on how to avoid them. By improving your understanding of English grammar, you can enhance your writing and speaking skills.Part 3: Vocabulary and IdiomsBuilding a strong vocabulary is crucial for expressing oneself eloquently in English. In this section, we will examine various methods for expanding your vocabulary, such as readingbooks, encountering new words in context, and using vocabulary learning apps.Moreover, we will delve into the world of idioms, which are expressions that cannot be understood by examining the individual words. Understanding and using idiomatic expressions can greatly enhance your fluency in English.Part 4: Common Writing and Speaking MistakesEven advanced English speakers often make mistakes when writing or speaking. This section will discuss some of the most common errors made by non-native English speakers, such as subject-verb agreement, word order, verb tense consistency, and pronunciation.Furthermore, we will provide practical tips to help you avoid these mistakes and improve your overall language skills. By becoming aware of these errors and working to correct them, you can communicate more effectively in English.Part 5: English in the Digital AgeThe rise of the internet and digital technology has greatly impacted the English language. In this section, we will explore how social media, texting, and online communication have influenced the way English is used today. We will discuss the use of abbreviations, emoticons, and emojis in digital communication and their implications for language evolution.Additionally, we will examine the role of English as a global language and the challenges and opportunities it presents in an interconnected world.Conclusion:This English language digest provides a comprehensive overview of the history, grammar, vocabulary, and usage of the English language. By understanding these aspects, learners can improve their language skills and become more proficient in English communication.Remember, mastering a language takes time and practice. Keep exploring different resources, engaging with native speakers, and immersing yourself in English-language environments to further enhance your abilities. With dedication and perseverance, you can achieve fluency inEnglish and unlock countless opportunities in the globalized world.。
英语文摘精选5篇
英语文摘精选5篇如果能够抄之前先好好读读，并且理解其意思，然后再抄完了之后是不是翻阅自己的摘抄本，那么效果又会更进一步！今天小编在这给大家整理了英语文摘大全，接下来随着小编一起来看看吧!英语文摘(一)给你一篇小情书You’re the one, It was you all the time.你一直都是我的最爱。
I love everything about you, except the fact that youre not with me.我爱你的一切，可事实是你并不爱我。
I wish that you were here or I were there or me and you we anywhere together..多么希望我们此刻能够紧紧相依。
I know its too much to ask for you to think of me as much as I think of you but I just hope that someday, somehow, you think of me too.但愿你哪天也会很想念我，正如我想念你一般。
My heart wont let you go, and I need you to know, I miss you. 我不舍得你离开我，我只想告诉你，我很想你。
When I miss you, I dont have to go far...I just have to look inside my heart because thats where Ill find you.其实，我的心里一直都有你。
Im waiting and hoping, and wishing for the time when we can be together again... I miss you so much.我等待着，期盼着，我们可以再次重逢，而你会重新爱上我…Even though we are far apart you will always be in my little heart.哪怕相距千里，你也依旧在我心里。
英语文摘
Bull Earthquake Eng(2008)6:645–675DOI10.1007/s10518-008-9078-1ORIGINAL RESEARCH PAPERNumerical analyses of fault–foundation interactionI.Anastasopoulos·A.Callerio·M.F.Bransby·M.C.R.Davies·A.El Nahas·E.Faccioli·G.Gazetas·A.Masella·R.Paolucci·A.Pecker·E.RossignolReceived:22October2007/Accepted:14July2008/Published online:17September2008©Springer Science+Business Media B.V.2008Abstract Field evidence from recent earthquakes has shown that structures can be designed to survive major surface dislocations.This paper:(i)Describes three differentfinite element(FE)methods of analysis,that were developed to simulate dip slip fault rupture propagation through soil and its interaction with foundation–structure systems;(ii)Validates the developed FE methodologies against centrifuge model tests that were conducted at the University of Dundee,Scotland;and(iii)Utilises one of these analysis methods to conduct a short parametric study on the interaction of idealised2-and5-story residential structures lying on slab foundations subjected to normal fault rupture.The comparison between nume-rical and centrifuge model test results shows that reliable predictions can be achieved with reasonably sophisticated constitutive soil models that take account of soil softening after failure.A prerequisite is an adequately refined FE mesh,combined with interface elements with tension cut-off between the soil and the structure.The results of the parametric study reveal that the increase of the surcharge load q of the structure leads to larger fault rupture diversion and“smoothing”of the settlement profile,allowing reduction of its stressing.Soil compliance is shown to be beneficial to the stressing of a structure.For a given soil depthH and imposed dislocation h,the rotation θof the structure is shown to be a function of:I.Anastasopoulos(B)·G.GazetasNational Technical University,Athens,Greecee-mail:ianast@civil.ntua.grA.Callerio·E.Faccioli·A.Masella·R.PaolucciStudio Geotecnico Italiano,Milan,ItalyM.F.BransbyUniversity of Auckland,Auckland,New ZealandM.C.R.Davies·A.El NahasUniversity of Dundee,Dundee,UKA.Pecker·E.RossignolGeodynamique et Structure,Paris,France123(a)its location relative to the fault rupture;(b)the surcharge load q;and(c)soil compliance.Keywords Fault rupture propagation·Soil–structure-interaction·Centrifuge model tests·Strip foundation1IntroductionNumerous cases of devastating effects of earthquake surface fault rupture on structures were observed in the1999earthquakes of Kocaeli,Düzce,and Chi-Chi.However,examples of satisfactory,even spectacular,performance of a variety of structures also emerged(Youd et al.2000;Erdik2001;Bray2001;Ural2001;Ulusay et al.2002;Pamuk et al.2005).In some cases the foundation and structure were quite strong and thus either forced the rupture to deviate or withstood the tectonic movements with some rigid-body rotation and translation but without damage(Anastasopoulos and Gazetas2007a,b;Faccioli et al.2008).In other cases structures were quite ductile and deformed without failing.Thus,the idea(Duncan and Lefebvre1973;Niccum et al.1976;Youd1989;Berill1983)that a structure can be designed to survive with minimal damage a surface fault rupture re-emerged.The work presented herein was motivated by the need to develop quantitative understan-ding of the interaction between a rupturing dip-slip(normal or reverse)fault and a variety of foundation types.In the framework of the QUAKER research project,an integrated approach was employed,comprising three interrelated steps:•Field studies(Anastasopoulos and Gazetas2007a;Faccioli et al.2008)of documented case histories motivated our investigation and offered material for calibration of the theoretical methods and analyses,•Carefully controlled geotechnical centrifuge model tests(Bransby et al.2008a,b)hel-ped in developing an improved understanding of mechanisms and in acquiring a reliable experimental data base for validating the theoretical simulations,and•Analytical numerical methods calibrated against the abovefield and experimental data offered additional insight into the nature of the interaction,and were used in developing parametric results and design aids.This paper summarises the methods and the results of the third step.More specifically: (i)Three differentfinite element(FE)analysis methods are presented and calibratedthrough available soil data.(ii)The three FE analysis methods are validated against four centrifuge experiments con-ducted at the University of Dundee,Scotland.Two experiments are used as a benchmark for the“free-field”part of the problem,and two more for the interaction of the outcrop-ping dislocation with rigid strip foundations.(iii)One of these analysis methods is utilised in conducting a short parametric study on the interaction of typical residential structures with a normal fault rupture.The problem studied in this paper is portrayed in Fig.1.It refers to a uniform cohesionless soil deposit of thickness H at the base of which a dip-slip fault,dipping at angle a(measured from the horizontal),produces downward or upward displacement,of vertical component h.The offset(i.e.,the differential displacement)is applied to the right part of the model quasi-statically in small consecutive steps.123hx O:“f o c u s ”O ’:“e p i c e n t e r ”Hanging wallFootwallyLW –LW hx O:“fo c u s ”O ’:“e p i c e n t e r ”Hanging wallFootwallyL W –LWq BStrip Foundation s(a )(b)Fig.1Definition and geometry of the studied problem:(a )Propagation of the fault rupture in the free field,and (b )Interaction with strip foundation of width B subjected to uniform load q .The left edge of the foundation is at distance s from the free-field fault outcrop2Centrifuge model testingA series of centrifuge model tests have been conducted in the beam centrifuge of the University of Dundee (Fig.2a)to investigate fault rupture propagation through sand and its in-teraction with strip footings (Bransby et al.2008a ,b ).The tests modelled soil deposits of depth H ranging from 15to 25m.They were conducted at accelerations ranging from 50to 115g.A special apparatus was developed in the University of Dundee to simulate normal and reverse faulting.A central guidance system and three aluminum wedges were installed to impose displacement at the desired dip angle.Two hydraulic actuators were used to push on the side of a split shear box (Fig.2a)up or down,simulating reverse or normal faulting,respectively.The apparatus was installed in one of the University of Dundee’s centrifuge strongboxes (Fig.2b).The strongbox contains a front and a back transparent Perspex plate,through which the models are monitored in flight.More details on the experimental setup can be found in Bransby et al.(2008a ).Displacements (vertical and horizontal)at different123Fig.2(a)The geotechnicalcentrifuge of the University ofDundee;(b)the apparatus for theexperimental simulation of faultrupture propagation through sandpositions within the soil specimen were computed through the analysis of a series of digital images captured as faulting progressed using the Geo-PIV software(White et al.2003).Soil specimens were prepared within the split box apparatus by pluviating dry Fontainebleau sand from a specific height with controllable massflow rate.Dry sand samples were prepared at relative densities of60%.Fontainebleau sand was used so that previously published laboratory element test data(e.g Gaudin2002)could be used to select drained soil parameters for thefinite element analyses.The experimental simulation was conducted in two steps.First,fault rupture propagation though soil was modelled in the absence of a structure(Fig.1a),representing the free-field part of the problem.Then,strip foundations were placed at a pre-specified distance s from the free-field fault outcrop(Fig.1b),and new tests were conducted to simulate the interaction of the fault rupture with strip foundations.3Methods of numerical analysisThree different numerical analysis approaches were developed,calibrated,and tested.Three different numerical codes were used,in combination with soil constitutive models ranging from simplified to more sophisticated.This way,three methods were developed,each one corresponding to a different level of sophistication:(a)Method1,using the commercial FE code PLAXIS(2006),in combination with a simplenon-associated elastic-perfectly plastic Mohr-Coulomb constitutive model for soil; 123Foundation : 2-D Elastic Solid Elements Elastic BeamElementsInterfaceElements hFig.3Method 1(Plaxis)finite element diecretisation(b)Method 2,utilising the commercial FE code ABAQUS (2004),combined with a modifiedMohr-Coulomb constitutive soil model taking account of strain softening;and(c)Method 3,making use of the FE code DYNAFLOW (Prevost 1981),along with thesophisticated multi-yield constitutive model of Prevost (1989,1993).Centrifuge model tests that were conducted in the University of Dundee were used to validate the effectiveness of the three different numerical methodologies.The main features,the soil constitutive models,and the calibration procedure for each one of the three analysis methodologies are discussed in the following sections.3.1Method 13.1.1Finite element modeling approachThe first method uses PLAXIS (2006),a commercial geotechnical FE code,capable of 2D plane strain,plane stress,or axisymmetric analyses.As shown in Fig.3,the finite element mesh consists of 6-node triangular plane strain elements.The characteristic length of the elements was reduced below the footing and in the region where the fault rapture is expected to propagate.Since a remeshing technique (probably the best approach when dealing with large deformation problems)is not available in PLAXIS ,at the base of the model and near the fault starting point,larger elements were introduced to avoid numerical inaccuracies and instability caused by ill conditioning of the element geometry during the displacement application (i.e.node overlapping and element distortion).The foundation system was modeled using a two-layer compound system,consisting of (see Fig.3):•The footing itself,discretised by very stiff 2D elements with linear elastic behaviour.The pressure applied by the overlying building structure has been imposed to the models through the self weight of the foundation elements.123Fig.4Method1:Calibration of constitutive model parameters utilising the FE code Tochnog;(a)oedometer test;(b)Triaxial test,p=90kPa•Beam elements attached to the nodes at the bottom of the foundation,with stiffness para-meters lower than those of the footing to avoid a major stiffness discontinuity between the underlying soil and the foundation structure.•The beam elements are connected to soil elements through an interface with a purely frictional behaviour and the same friction angleϕwith the soil.The interface has a tension cut-off,which causes a gap to develop between soil and foundation in case of detachment. Due to the large imposed displacement reached during the centrifuge tests(more than3m in several cases),with a relative displacement of the order of10%of the modeled soil height, the large displacement Lagrangian description was adopted.After an initial phase in which the geostatic stresses were allowed to develop,the fault displacement has been monotonically imposed both on the right side and the right bottom boundaries,while the remaining boundaries of the model have beenfixed in the direction perpendicular to the side(Fig.3),so as to reproduce the centrifuge test boundary conditions.3.1.2Soil constitutive model and calibrationThe constitutive model adopted for all of the analyses is the standard Mohr-Coulomb for-mulation implemented in PLAXIS.The calibration of the elastic and strength parameters of the soil had been conducted during the earlier phases of the project by means of the FEM code Tochnog(see the developer’s home page ),adopting a rather refined and user-defined constitutive model for sand.This model was calibrated with a set of experimental data available on Fontainebleau sand(Gaudin2002).Oedometer tests (Fig.4a)and drained triaxial compression tests(Fig.4b)have been simulated,and sand model parameters were calibrated to reproduce the experimental results.The user-defined model implemented in Tochnog included a yielding function at the critical state,which corresponds to the Mohr-Coulomb failure criterion.A subset of those parameters was then utilised in the analysis conducted using the simpler Mohr-Coulomb model of PLAXIS:•Angle of frictionϕ=37◦•Young’s Modulus E=675MPa•Poisson’s ratioν=0.35•Angle of Dilationψ=0◦123hFoundation : Elastic Beam ElementsGap Elements Fig.5Method 2(Abaqus)finite element diecretisationThe assumption of ψ=0and ν=0.35,although not intuitively reasonable,was proven to provide the best fit to experimental data,both for normal and reverse faulting.3.2Method 23.2.1Finite element modeling approachThe FE mesh used for the analyses is depicted in Fig.5(for the reverse fault case).The soil is now modelled with quadrilateral plane strain elements of width d FE =1m.The foun-dation,of width B ,is modelled with beam elements.It is placed on top of the soil model and connected through special contact (gap)elements.Such elements are infinitely stiff in compression,but offer no resistance in tension.In shear,their behaviour follows Coulomb’s friction law.3.2.2Soil constitutive modelEarlier studies have shown that soil behaviour after failure plays a major role in problems related to shear-band formation (Bray 1990;Bray et al.1994a ,b ).Relatively simple elasto-plastic constitutive models,with Mohr-Coulomb failure criterion,in combination with strain softening have been shown to be effective in the simulation of fault rupture propagation through soil (Roth et al.1981,1982;Loukidis 1999;Erickson et al.2001),as well as for modelling the failure of embankments and slopes (Potts et al.1990,1997).In this study,we apply a similar elastoplastic constitutive model with Mohr-Coulomb failure criterion and isotropic strain softening (Anastasopoulos 2005).Softening is introduced by reducing the mobilised friction angle ϕmob and the mobilised dilation angle ψmob with the increase of plastic octahedral shear strain:123ϕmob=ϕp−ϕp−ϕresγP fγP oct,for0≤γP oct<γP fϕres,forγP oct≥γP f(1)ψmob=⎧⎨⎩ψp1−γP octγP f,for0≤γP oct<γP fψres,forγP oct≥γP f⎫⎬⎭(2)whereϕp andϕres the ultimate mobilised friction angle and its residual value;ψp the ultimate dilation angle;γP f the plastic octahedral shear strain at the end of softening.3.2.3Constitutive model calibrationConstitutive model parameters are calibrated through the results of direct shear tests.Soil response can be divided in four characteristic phases(Anastasopoulos et al.2007):(a)Quasi-elastic behavior:The soil deforms quasi-elastically(Jewell and Roth1987),upto a horizontal displacementδx y.(b)Plastic behavior:The soil enters the plastic region and dilates,reaching peak conditionsat horizontal displacementδx p.(c)Softening behavior:Right after the peak,a single horizontal shear band develops(Jewelland Roth1987;Gerolymos et al.2007).(d)Residual behavior:Softening is completed at horizontal displacementδx f(δy/δx≈0).Then,deformation is accumulated along the developed shear band.Quasi-elastic behaviour is modelled as linear elastic,with secant modulus G S linearly incre-asing with depth:G S=τyγy(3)whereτy andγy:the shear stress and strain atfirst yield,directly measured from test data.After peak conditions are reached,it is assumed that plastic shear deformation takes placewithin the shear band,while the rest of the specimen remains elastic(Shibuya et al.1997).Scale effects have been shown to play a major role in shear localisation problems(Stone andMuir Wood1992;Muir Wood and Stone1994;Muir Wood2002).Given the unavoidableshortcomings of the FE method,an approximate simplified scaling method(Anastasopouloset al.2007)is employed.The constitutive model was encoded in the FE code ABAQUS(2004).Its capability toreproduce soil behaviour has been validated through a series of FE simulations of the directshear test(Anastasopoulos2005).Figure6depicts the results of such a simulation of denseFontainebleau sand(D r≈80%),and its comparison with experimental data by Gaudin (2002).Despite its simplicity and(perhaps)lack of generality,the employed constitutivemodel captures the predominant mode of deformation of the problem studied herein,provi-ding a reasonable simplification of complex soil behaviour.3.3Method33.3.1Finite element modeling approachThefinite element model used for the analyses is shown for the normal fault case in Fig.7.The soil is modeled with square,quadrilateral,plane strain elements,of width d FE=0.5m. 123Fig.6Method 2:Calibration ofconstitutive model—comparisonbetween laboratory direct sheartests on Fontainebleau sand(Gaudin 2002)and the results ofthe constitutive modelx D v3.3.2Soil constitutive ModelThe constitutive model is the multi-yield constitutive model developed by Prevost (1989,1993).It is a kinematic hardening model,based on a relatively simple plasticity theory (Prevost 1985)and is applicable to both cohesive and cohesionless soils.The concept of a “field of work-hardening moduli”(Iwan 1967;Mróz 1967;Prevost 1977),is used by defining a collection f 0,f 1,...,f n of nested yield surfaces in the stress space.V on Mises type surfaces are employed for cohesive materials,and Drucker-Prager/Mohr-Coulomb type surfaces are employed for frictional materials (sands).The yield surfaces define regions of constant shear moduli in the stress space,and in this manner the model discretises the smooth elastic-plastic stress–strain curve into n linear segments.The outermost surface f n represents a failure surface.In addition,accounting for experimental evidence from tests on frictional materials (de 1987),a non-associative plastic flow rule is used for the dilatational component of the plastic potential.Finally,the material hysteretic behavior and shear stress-induced anisotropic effects are simulated by a kinematic rule .Upon contact,the yield surfaces are translated in the stress space by the stress point,and the direction of translation is selected such that the yield surfaces do not overlap,but remain tangent to each other at the stress point.3.3.3Constitutive model parametersThe required constitutive parameters of the multi-yield constitutive soil model are summari-sed as follows (Popescu and Prevost 1995):a.Initial state parameters :mass density of the solid phase ρs ,and for the case of porous saturated media,porosity n w and permeability k .b.Low strain elastic parameters :low strain moduli G 0and B 0.The dependence of the moduli on the mean effective normal stress p ,is assumed to be of the following form:G =G 0 p p 0 n B =B 0 p p 0n (4)and is accounted for,by introducing two more parameters:the power exponent n and the reference effective mean normal stress p 0.c.Yield and failure parameters :these parameters describe the position a i ,size M i and plastic modulus H i ,corresponding to each yield surface f i ,i =0,1,...n .For the case of pressure sensitive materials,a modified hyperbolic expression proposed by Prevost (1989)and Griffiths and Prévost (1990)is used to simulate soil stress–strain relations.The necessary parameters are:(i)the initial gradient,given by the small strain shear modulus G 0,and (ii)the stress (function of the friction angle at failure ϕand the stress path)and strain,εmax de v ,levels at failure.Hayashi et al.(1992)improved the modified hyperbolic model by introducing a new parameter—a —depending on the maximum grain size D max and uniformity coefficient C u .Finally,the coefficient of lateral stress K 0is necessary to evaluate the initial positions a i of the yield surfaces.d.Dilation parameters :these are used to evaluate the volumetric part of the plastic potentialand consist of:(i)the dilation (or phase transformation)angle ¯ϕ,and (ii)the dilation parameter X pp ,which is the scale parameter for the plastic dilation,and depends basically on relative density and sand type (fabric,grain size).With the exception of the dilation parameter,all the required constitutive model parameters are traditional soil properties,and can be derived from the results of conventional laboratory 123Table1Constitutive model parameters used in method3Number of yield surfaces20Power exponent n0.5Shear modulus G at stress p1 (kPa)75,000Bulk modulus at stress p1(kPa)200,000Unit massρ(t.m−3) 1.63Cohesion0 Reference mean normal stressp1(kPa)100Lateral stress coefficient(K0)0.5Dilation angle in compression (◦)31Dilation angle in extension(◦)31Ultimate friction angle in compression(◦)41.8Ultimate friction angle inextension(◦)41.8Dilation parameter X pp 1.65Max shear strain incompression0.08Max shear strain in extension0.08Generation coefficient in compressionαc 0.098Generation coefficient inextensionαe0.095Generation coefficient in compressionαlc 0.66Generation coefficient inextensionαle0.66Generation coefficient in compressionαuc 1.16Generation coefficient inextensionαue1.16(e.g.triaxial,simple shear)and in situ(e.g.cone penetration,standard penetration,wave velocity)soil tests.The dilational parameter can be evaluated on the basis of results of liquefaction strength analysis,when available;further details can be found in Popescu and Prevost(1995)and Popescu(1995).Since in the present study the sand material is dry,the cohesionless material was modeled as a one-phase material.Therefore neither the soil porosity,n w,nor the permeability,k,are needed.For the shear stress–strain curve generation,given the maximum shear modulus G1,the maximum shear stressτmax and the maximum shear strainγmax,the following functional relationship has been chosen:For y=τ/τmax and x=γ/γr,withγr=τmax/G1,then:y=exp(−ax)f(x,x l)+(1−exp(−ax))f(x,x u)where:f(x,x i)=(2x/x i+1)x i−1/(2x/x i+1)x i+1(5)where a,x l and x u are material parameters.For further details,the reader is referred to Hayashi et al.(1992).The constitutive model is implemented in the computer code DYNAFLOW(Prevost1981) that has been used for the numerical analyses.3.3.4Calibration of model constitutive parametersTo calibrate the values of the constitutive parameters,numerical triaxial tests were simulated with DYNAFLOW at three different confining pressures(30,60,90kPa)and compared with the results of available physical tests conducted on the same material at the same confining pressures.The parameters are defined based on the shear stress versus axial strain curve and volumetric strain versus axial strain curve.Figure8illustrates the comparisons between numerical simulations and physical tests in terms of volumetric strain and shear stress versus123Table2Summary of main attributes of the centrifuge model testsTest Faulting B(m)q(kPa)s(m)g-Level a D r(%)H(m)L(m)W(m)h max(m) 12Normal Free—field11560.224.775.723.53.1528Reverse Free—field11560.815.175.723.52.5914Normal10912.911562.524.675.723.52.4929Reverse10919.211564.115.175.723.53.30a Centrifugal accelerationFig.9Test12—Free-field faultD r=60%Fontainebleau sand(α=60◦):Comparison ofnumerical with experimentalvertical displacement of thesurface for bedrock dislocationh=3.0m(Method1)and2.5m(Method2)[all displacements aregiven in prototype scale]Structure Interaction(FR-SFSI):(i)Test14,normal faulting at60◦;and(ii)Test29,reverse faulting at60◦.In this case,the comparison is conducted for all of the developed numerical analysis approaches.The main attributes of the four centrifuge model tests used for the comparisons are syn-opsised in Table2,while more details can be found in Bransby et al.(2008a,b).4.1Free-field fault rupture propagation4.1.1Test12—normal60◦This test was conducted at115g on medium-loose(D r=60%)Fontainebleau sand,simu-lating normal fault rupture propagation through an H=25m soil deposit.The comparison between analytical predictions and experimental data is depicted in Fig.9in terms of vertical displacement y at the ground surface.All displacements are given in prototype scale.While the analytical prediction of Method1is compared with test data for h=3.0m,in the case of Method2the comparison is conducted at slightly lower imposed bedrock displacement: h=2.5m.This is due to the fact that the numerical analysis with Method2was conducted without knowing the test results,and at that time it had been agreed to set the maximum displacement equal to h max=2.5m.However,when test results were publicised,the actually attained maximum displacement was larger,something that was taken into account in the analyses with Method1.As illustrated in Fig.9,Method2predicts almost correctly the location of fault out-cropping,at about—10m from the“epicenter”,with discrepancies limited to1or2m.The deformation can be seen to be slightly more localised in the centrifuge test,but the comparison between analytical and experimental shear zone thickness is quite satisfactory.The vertical displacement profile predicted by Method1is also qualitatively acceptable.However,the123Method 2Centrifuge Model TestR1S1Method 1(a )(b)(c)Fig.10Test 12—-Normal free-field fault rupture propagation through H =25m D r =60%Fontainebleau sand:Comparison of (a )Centrifuge model test image,compared to FE deformed mesh with shear strain contours of Method 1(b ),and Method 2(c ),for h =2.5mlocation of fault rupture emergence is a few meters to the left compared with the experimen-tal:at about 15m from the “epicenter”(instead of about 10m).In addition,the deformation predicted by Method 1at the ground surface computed using method 1is widespread,instead of localised at a narrow band.FE deformed meshes with superimposed shear strain contours are compared with an image from the experiment in Fig.10,for h =2.5m.In the case of Method 2,the comparison can be seen to be quite satisfactory.However,it is noted that the secondary rupture (S 1)that forms in the experiment to the right of the main shear plane (R 1)is not predicted by Method 2.Also,experimental shear strain contours (not shown herein)are a little more diffuse than the FE prediction.Overall,the comparison is quite satisfactory.In the case of Method 1,the quantitative details are not in satisfactory agreement,but the calculation reveals a secondary rupture to the right of the main shear zone,consistent with the experimental image.4.1.2Test 28—reverse 60◦This test was also conducted at 115g and the sand was of practically the same relative density (D r =61%).Given that reverse fault ruptures require larger normalised bedrock123Fig.11Test28—Reversepropagation through H=15mD r=60%Fontainebleau sand:Comparison of numerical withexperimental verticaldisplacement of the surface forbedrock dislocation h=2.0m(all displacements are given inprototype scale)displacement h/H to propagate all the way to the surface(e.g.Cole and Lade1984;Lade et al.1984;Anastasopoulos et al.2007;Bransby et al.2008b),the soil depth was set at H=15m.This way,a larger h/H could be achieved with the same actuator.Figure11compares the vertical displacement y at the ground surface predicted by the numerical analysis to experimental data,for h=2.0m.This time,both models predict correctly the location of fault outcropping(defined as the point where the steepest gradient is observed).In particular,Method1achieves a slightly better prediction of the outcropping location:−10m from the epicentre(i.e.,a difference of1m only,to the other direction). Method2predicts the fault outbreak at about−7m from the“epicenter”,as opposed to about −9m of the centrifuge model test(i.e.,a discrepancy of about2m).Figure12compares FE deformed meshes with superimposed shear strain contours with an image from the experiment,for h=2.5m.In the case of Method2,the numerical analysis seems to predict a distinct fault scarp,with most of the deformation localised within it.In contrast,the localisation in the experiment is clearly more intense,but the fault scarp at the surface is much less pronounced:the deformation is widespread over a larger area.The analysis with Method1is successful in terms of the outcropping location.However,instead of a single rupture,it predicts the development of two main ruptures(R1and R2),accompanied by a third shear plane in between.Although such soil response has also been demonstrated by other researchers(e.g.Loukidis and Bouckovalas2001),in this case the predicted multiple rupture planes are not consistent with experimental results.4.2Interaction with strip footingsHaving validated the effectiveness of the developed numerical analysis methodologies in simulating fault rupture propagation in the free-field,we proceed to the comparisons of experiments with strip foundations:one for normal(Test14),and one for reverse(Test29) faulting.This time,the comparison is extended to all three methods.4.2.1Test14—normal60◦This test is practically the same with the free-field Test12,with the only difference being the presence of a B=10m strip foundation subjected to a bearing pressure q=90kPa.The foundation is positioned so that the free-field fault rupture would emerge at distance s=2.9m from the left edge of the foundation.123。
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