基坑工程的应力路径
小应变下基坑开挖应力路径对剪切模量的影响
中图 分 类 号 ： Ｕ４ １ ３ Ｔ １． 文 献 标识 码 ：Ａ
的初始 值 与有 效 球 应 力 之 间存 在 着 幂 函数 关 系 ， 主 动 区 内幂 函数 的 理 论 值 与 试 验 值 间 的符 合 度 要 比 但 被 动 区 内 的高 ； 切 应 变 处 于 ０ ０ ％ ～ １ 内 表 现 出很 强 的 非 线 性 ， 时 具 有 很 高 的 剪 切 模 量 ； 同 一 剪 ．１ ％ 同 在 应 变水 平 下 ， 同应 力 路 径 ， 切 模 量 的 数 值 不 同 ， 剪 切 模 量 随 剪 切 应 变增 加而 衰 减 的规 律 一 致 ； 切 不 剪 但 剪
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摘
要 ： 粉质 黏 土 重 塑 土经 等压 固结 形 成 的试 样 为 试 验 对 象 ， 究 了 在 小 应 变 范 围 内 深 基 坑 开 挖 应 以 研
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STRESS PATHS IN RELATION TO DEEP EXCAVATIONS
D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y T o n g j i U n i v e r s i t y o n 12/04/12. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .FIG. 1.Idealized Stress Path Associated with Stress Relief:(a)Effective-Stress Path;(b)T otal StressPathFIG. 2.Instrumented PanelIn contrast to element P ,the total stress change experienced by element A results from a reduction in horizontal stress.Changes in vertical stress are comparatively small.The total stress path A 2A 3will move toward the K f compression line with a gradient of 45Њin s Ϫt space,i.e.,⌬t /⌬s =Ϫ1.If the soil is unloaded rapidly so that undrained conditions are main-tained,the corresponding effective-stress path A 2ЈA 3Јwill be vertical.The induced pore-water pressure is negative.As the excess pore-water pressure disspates,the effective-stress path will shift toward the K f compression line.TOP-DOWN CONSTRUCTION AT LION Y ARDThe Lion Yard site is located in the city center of Cam-bridge,U.K.and it is approximately 65ϫ45m on plan.The site was developed as a three-level underground car park be-neath a five-story hotel above ground.The 10-m-deep under-ground car park is retained by a 17-m-deep perimeter rein-forced concrete diaphragm wall that is 0.6m thick (Fig.2).The initial stiffness of the uncracked concrete wall is estimated to be 580MN иm 2/m run.The car park floors,which prop the diaphragm wall,are supported by steel columns connected to the tops of bored piles.The design of the supporting system was fairly conservative and a K 0value of 3was adopted to calculate the design earth pressures for gault clay.The ground conditions comprise approximately 3m of fill and gravel over 38m of gault clay.The gault clay is over-consolidated heavily and consists of stiff-to-hard silty grey fis-sured clay of high plasticity.The ground-water table was at approximately 3m below ground surface before construction.To speed up the construction and to minimize ground de-formations during excavation,the top-down construction method was adopted.For providing a working platform,the ground floor slab (level 4)was cast as soon as the diaphragm wall and bored piles and associated steel columns had been completed.Soil then was excavated from beneath it by me-chanical plants down to the next level (level 3)and removedthrough an opening left in the slab.Similar operations were repeated for subsequent stages of construction until the bottom level (level 1)was reached.Erection of the superstructure was carried out simultaneously.Other details of the construction are given by Ng (1998).For providing vehicle access to each underground parking level after construction,there was a 3.5-m-wide and 19-m-long rectangular opening left in the slabs,adjacent to an instru-mented panel shown in Fig.2.The selected instrumented panel was located near the center of one long side of the site.Tem-porary steel props (152ϫ152ϫ23universal steel columnsD o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y T o n g j i U n i v e r s i t y o n 12/04/12. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .TABLE1.Key Construction StagesStage(1)Construction operation(2)Week number(3)I Construction of diaphragm wall 1–7II Excavation to level 318–20III Excavation to level 223–25IV Excavation to level 129–32V 9months after casting level 1slab 78VI25months after casting level 1slab150FIG. teral Displacement of Diaphragm WallFIG. 3.T otal Lateral Pressures during and after Constructionat level 4and 203ϫ203ϫ60universal steel columns at levels 2and 3)were installed at 1.7m spacing (on plan)across these 3.5-m-wide openings at each level to support the dia-phragm wall (including the instrumented panel)during exca-vation.The props were not prestressed,but the ends were grouted after installation.After completion of the level 1slab,the vehicle access ramps were constructed from the lowest level upward and the temporary props were removed once all the concrete ramps had been completed.Key excavation stages,which are relevant to this paper,are summarized in Table 1.During the course of construction,comprehensive instru-ments were installed to monitor the performance of the mul-tipropped excavation.At the instrumented panel shown in Fig.2,seven total earth pressure cells (EPCs)(Glo ¨tzl)and seven pneumatic piezometers were installed on both faces of the di-aphragm wall panel.Each total pressure cell consisted of a sensitive pad (150ϫ250mm),formed by joining two thin plates of steel at their edges.The space between the plates was filled with mercury.The pressure applied by the surrounding ground was transmitted through the mercury to an integral pneumatic diaphragm similar to those used in pneumatic pi-ezometers.The mercury pressure was measured with a pneu-matic readout unit as used for reading piezometers.The cells were designed to operate to a maximum pressure of 1,500kPa.The seven pneumatic piezometers were positioned 150mm below the EPCs to measure the pore-water pressures on the faces of the wall.Hence the effective horizontal stresses can be determined.The surface contact tips of the piezometers were fitted with flat flush stones,which were pushed approx-imately 5mm into the excavated clay surface.The pneumatic piezometer system selected had been developed to measure positive pore pressures only.This imposed a limitation on measuring negative pore-water pressures caused by stress re-lief.In fact,one of the piezometers (PP 1)went to zero during the final stage of excavation (level 1)and so changes of ef-fective stress were not known at that location.Details of other instrumentation and interpreted results including wall deflec-tions,prop forces,and ground deformations are given by Ng (1998).FIELD STRESS P ATHST otal Earth Pressures at Soil-Wall InterfaceInitial stresses in the ground are very difficult to measure and determine accurately.At Lion Yard,initial stresses in the ground were estimated using a self-boring pressuremeter,Schmidt’s (1966)semiempirical rules allowing for reloading,and numerical simulations of the geological processes.Simp-son’s (1992)nonlinear Brick model was used for the numerical simulations.Based on results obtained from these methods,it was concluded that the initial K 0values varied somewhere be-tween 1.0and 2.0for the top 10m of the clay (Ng 1998).The measured lateral pressures on both sides of the wall are shown in Fig.3.A constant initial K 0=1.5with depth is provided for reference.Reduction in lateral stresses at the soil-wall interface following the construction of the diaphragm wall was observed.The reduction in total horizontal stress wassubstantially larger during wall installation than during any subsequent stage of construction.During the subsequent ex-cavation stages,all EPCs excluding EPC7,showed consistent reduction in lateral stresses until the deepest basement level was reached.This observed reduction in lateral stresses was consistent with gradual inward deflections of the wall (Fig.4).In the long-term,there was a general trend of increasing in lateral stresses with time following excavation,except at EPC3.At stage VI (25months after casting level 1slab),four EPCs,EPC4–7(those still functioning properly),recorded an increase in total earth pressure,compared with measurements made before the main excavation.The increase in pressure probably resulted from general swelling of the clay.More de-tails are discussed later in this paper.When considering the measured earth pressures in the ground,it is important to check that equilibrium requirements are satisfied.From beam bending theory,it is well known that there are relationships between applied net pressure,shear force,bending moment,wall curvature,rotation,and deflec-tion.At the instrumented diaphragm wall panel (Fig.2),the field data recorded including measured prop forces (Table 2)and wall rotations measured by electrolevels,enabled an in-ternal check to be carried out on the measured earth pressures if some boundary conditions and wall stiffness were known.This was done by constructing net earth pressure diagrams,which in conjunction with measured prop forces,satisfied the requirements of horizontal force and moment equilibrium,and after triple integration showed agreement with measured wallD o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y T o n g j i U n i v e r s i t y o n 12/04/12. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .TABLE2.Summary of Measured Prop ForcesProp force(1)Measured(2)Average L4prop forces (kN/m)14Average L3prop forces (kN/m)119Average L2prop forces (kN/m)144FIG. 5.Interpreted Field Effective-Stress Pathrotations.These deduced earth pressure diagrams then were compared with the measured values of earth pressure (Ling et al.1993).Reasonable consistency was obtained,with an ex-ception at EPC3,which underrecorded lateral stress by ap-proximately 50kPa at the final stage of excavation based on the equilibrium analysis.The continuous decrease of total earth pressure at EPC3probably was caused by the softening of the clay.The EPC1recorded abnormal high stress at stage V (9months after casting level 1slab),and subsequently both EPC1and EPC2ceased functioning.Effective-Stress Paths at Soil-Wall InterfaceChanges in effective stress at the soil-wall interface are pre-sented in Fig.5in the form of stress paths.Four limiting pressure lines also are plotted,which represent Rankine’s ac-tive and passive pressures with and without wall friction.The limiting pressures have been calculated using the results of laboratory tests on intact specimens trimmed from block sam-ples obtained from the site.Details of the laboratory tests on gault clay are given in a subsequent section in the paper later on.Horizontal effective stresses shown in the figure were cal-culated from measured total earth pressures and pore-water pressures at the seven locations of a vertical section at the soil-wall interface.The measured total earth and pore-water pres-sures were very likely to represent the localized behavior at the soil-wall interface only.Vertical effective stresses were cal-culated by assuming that total vertical stresses were equivalent to overburden pressures remote from the wall.The calculated horizontal and vertical effective stresses did not take wall fric-tion into account.The presence of wall friction (or shear stress)at the soil-wall interface would reduce the actual mag-nitude of the vertical stress.However,this reduction is likely to be small and will not affect any conclusions drawn in this paper.As the total vertical stress is assumed to be constant,any change of pore-water pressure thus is reflected by a change of vertical effective stress.The initial state of stress corresponding to the location of each EPC has been determined using the varying K 0profile with depth predicted by the nonlinear brick model.Reloading from gravel on the site has been taken into account (Ng 1992).Immediate after the installation of the instrumented panel,there were substantial reductions in horizontal effective stress at the soil-wall interface at all seven EPCs.Pore-water pres-sures at the soil-wall interface returned to their initial condi-tions within 10days later (Lings et al.1991;Ng 1992).If similar total stress and pore pressure reductions occurred in the soil farther away from the wall,then it would be expected that subsequent equalization of pore pressures would have been accompanied by swelling of the clay during the 3-month period after the construction of the wall.This would be ex-pected to result in an increase in total horizontal stress.On the contrary,all the earth pressure cells registered a decrease rather than an increase in total earth pressures (Fig.3).The recorded decrease in the total earth pressures could be caused by the gradual contraction of the EPCs as the temperature in the ground had decreased continuously after concrete curing.During the main excavation,three effective-stress paths (EPC2,4,and 6)behind the wall moved almost vertically up-ward,as a result of reducing pore pressures accompanied by a small increase in horizontal effective stress.The states of stress behind the wall at the soil-wall interface reached,or were close to,the assumed active condition.After stage V (9months after casting level 1slab),there was a continuous in-crease in horizontal effective stress accompanied by a decrease in vertical effective stress behind the wall.The increase in horizontal effective stress in the long-term is a result of an increase of total earth pressure,which is greater than the rise of pore-water pressure.The increase in the total earth pressure might be caused by long-term swelling of the clay behind the wall.In front of the wall,all three stress paths show an increase in horizontal effective stress with a decrease in vertical effec-tive stress during the period of the main excavation.The soil at EPC3appears to have reached passive failure at stage V as illustrated by the abrupt change of direction of the stress path toward the origin.In contrast,the lowest two EPCs show a continuation of the same stress paths and do not appear to have reached passive failure.D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y T o n g j i U n i v e r s i t y o n 12/04/12. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .The field-observed effective-stress paths behind the wall clearly are very different from the idealized conceptual model shown in Fig.2.The idealization of constant mean effective stress (s Ј)during each excavation stage does not hold (not an undrained behavior)for the stiff fissured clay at the soil-wall interface.This discrepancy could be caused by a number of factors such as observed rapid equilibrium of pore-water pres-sures at the interface during and after each stage of excavation as reported by Lings et al.(1991).‘‘Opening up’’fissures in the clay caused by lateral stress relief or the formation of a ‘‘bleed channel’’at the soil-wall interface during diaphragm wall construction could result in the observed rapid rise of pore-water pressure.On the contrary,the field-observed effec-tive-stress paths in front of the wall can be represented rea-sonably by the idealized conceptual model during the main excavation stages.It can be deduced that the mean effective stress holds approximately constant (an undrained behavior)probably as a result of inward movement of the diaphragm wall during the main excavation.This inward movement could suppress the opening up of fissures in the clay caused by ver-tical stress relief and closing up the bleed channel at the in-terface.LABORATORY STRESS P ATHSDuring the last two stages of excavation at Lion Yard,300ϫ300mm intact block samples were taken using an electric chain saw.They were covered immediately with cling film and nonshrinkable wax and stored in a humidity-controlled room.All the samples used in the tests were from the elevation of ϩ4.8m above ordinary datum (OD)outside diameter,i.e.,approximately 5m below the original ground surface and 2–3m below the clay surface.At that depth,the estimated over-consolidation ration was 25–50.Very few laboratory tests on gault clay have been performed using stress paths and stress levels that are relevant to deep excavations,during which the soil is subjected to unloading either vertically or horizontally at relatively low stress levels.Therefore,a laboratory program was carried out to investigate the response of gault clay related to the excavation at Lion Yard.T est ProgramNatural specimens were reconsolidated isotropically to var-ious preshearing pressures,which were relevant to the stress conditions around the excavation,and then loaded or unloaded along specified stress paths.The K 0reconsolidation was not carried out because zero lateral strains were difficult to achieve even in a computer-controlled triaxial stress path apparatus.In the following,the first and second letters of each set of ab-breviations are used to denote the drainage condition and the shearing mode.1.Drained compression (DC)tests in triaxial cell •DC1:undisturbed,constant p Ј•DC2:undisturbed,constant axial stress but with de-creasing radial stress•DC3:undisturbed,⌬q /⌬p Ј=Ϫ12.Drained extension (DE)tests in triaxial cell •DE1:undisturbed,constant p Ј•DE2:undisturbed,⌬q /⌬p Ј=13.Undrained compression (UC)tests in triaxial cell•UC1:undisturbed,constant radial total stress but with increasing total axial stress•UC2:undisturbed,constant axial total stress but with decreasing total radial stress4.Undrained extension (UE)tests in triaxial cell•UE1:undisturbed,constant radial total stress but withdecreasing total axial stress•UE2:undisturbed,constant axial total stress but with increasing total radial stressAll the tests were conducted under a constant room tem-perature of 24ЊC using a computer-controlled triaxial stress path apparatus.Sample Preparation and T est ProcedureFor the triaxial tests,each block sample was divided into four specimens using a thin wire.Each specimen then was mounted in a soil lathe and trimmed carefully to the required size (150mm long and 75mm in diameter)using various sharp blades.Great care was taken because the clay was fis-sured highly and very apt to fall apart.Small hard nodules frequently were found during the preparation process.The nodules were removed carefully and the cavities were filled with fine material from the parings.For all triaxial tests,the specimens initially were consoli-dated isotropically unless stated otherwise to various pressures before shearing.No side drains were used.The consolidation was carried out against an elevated back-pressure of 200kPa (Atkinson et al.1989)to ensure complete saturation of the specimen.During the shearing stage,the loading or unloading rate was applied slowly at 1.0–1.5kPa/h in drained tests and 5–10kPa/h in undrained tests.On completion of a test,the specimen was removed from the cell.It then was weighed and measured with venier cali-pers,and its water content was determined.Observed Stress Paths and Measured Shear Strength The applied or observed stress paths for the natural speci-mens are shown in Fig.6.The stress paths are expressed in the (s Ј,t )stress space to compare field observations that are likely to be under plane strain conditions.For clarity,only a single stress path is used to denote each series of tests.The critical state line shown in the figure was obtained from tests on reconstituted samples,which possess a critical state friction angle of 26Њ.Details of the tests are given by Ng (1992).All the test results for both reconstituted and natural specimens are summarized in Fig.7,which shows the end points of the stress paths based on the maximum deviator stress failure cri-terion.Although the specimens were subjected to various stress paths,the failure points lie on two common failure en-velopes for each type of material.It is evident that the failure envelopes are different in compression and in extension for both reconstituted and natural samples.For all tests on natural samples,failure took place abruptly along a single slip surface.It was not possible to ascertain whether failure occurred along a preexisting discontinuity,al-though all specimens contained numerous fissures.A higher shear strength was mobilized in extension than in compression.Similar results were found by Tedd and Charles (1985)from tests on natural London clay from Bell Common.Slightly dif-ferent Mohr-Coulomb parameters were found in compression (c Ј=3kPa and Ј=32Њ)and in extension (c Ј=2kPa and Ј=34Њ).COMP ARISON OF FIELD AND LABORATORY STRESS P ATHSFour representative field stress paths monitored at the soil-wall interface are compared with four corresponding stress paths measured in the laboratory in Fig.8.The stress path of UE1terminated a long way from the average passive pressure line probably because the specimen was noted to be extremely fissured during sample preparation and failure took place along a preexisting fissure.D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y T o n g j i U n i v e r s i t y o n 12/04/12. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .FIG. 6.Effective-Stress Path for NaturalSpecimensFIG.7.Failure Points of All SpecimensThe stress paths followed in the UE tests are similar to the field stress paths in front of the wall.There is no obvious difference between a test with constant radial total stress but with decreasing total axial stress (UE1)and an experiment with constant axial total stress but with increasing total radial stress (UE2).This seems to suggest that the stress changes in front of the wall can be represented reasonably by UE tests in the laboratory.In contrast,neither type of compression tests (UC1and UC2)modeled the field conditions behind the wall particularly well,except when the stress state approached ac-tive failure.This is not surprising because the soil at the soil-wall interface had already been reached or was close to the active condition after wall installation,resulting from a sub-stantial horizontal stress relief during the wall construction.Details of a three-dimensional numerical analysis of the dia-phragm wall panel construction at Lion Yard are given by Ng and Yan (1998).Thus it would be consistent to compare the field and laboratory stress paths only in the region near the active condition.It can be seen that the field and laboratory stress paths compare favorably during the main excavation stages.Based on the comparisons of field and laboratory stress paths,practicing engineers may realize that stiff clays locatedbehind a diaphragm wall may easily reach the active condi-tions locally after wall installation.Experimental results from undrained triaxial compression tests (i.e.,reducing radial but keeping axial stress constant)and an undrained assumption only may be used with caution when analyzing and design-ing retaining-wall systems in stiff clays.On the contrary,an undrained assumption inside excavations and the use of un-drained triaxial extension stress path tests (i.e.,reducing axial but keeping radial stress constant)seem to be relevant for en-gineers to derive design parameters for excavations in stiff clays.CONCLUSIONSHorizontal earth and pore-water pressures at the soil-wall interface during the construction of a deep excavation in the stiff fissured clay (gault clay)at Lion Yard,Cambridge,U.K.were measured locally using seven total EPCs and seven pneu-matic piezometers,respectively.Effective-stress changes as-sociated with the vertical and horizontal stress relief during the excavation were obtained from these measurements and expressed in terms of stress paths.The field stress paths were compared with an idealized conceptual model and laboratory measured stress paths.Because the field measurements wereD o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y T o n g j i U n i v e r s i t y o n 12/04/12. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .parison of Laboratory and Field Stress Pathstaken locally behind the wall,the conclusions drawn in this paper should be considered carefully for general applications.Based on the local field-observed effective-stress paths be-hind the wall,the theoretical concept of constant mean effec-tive stress during each excavation stage does not hold in the stiff fissured clay,i.e.,the response of the clay was not un-drained at the interface.On the contrary,the field effective-stress paths in front of the wall seem to support the conven-tional assumption about undrained behavior of the clay (constant mean effective stress)inside the excavation.The field effective-stress paths in front of the wall were similar to those stress paths observed in the UE tests in the laboratory.There is no obvious difference between a test with constant radial total stress but with decreasing total axial stress and an experiment with constant axial total stress but with increasing total radial stress in terms of effective-stress path and shear strength.However,for the stress paths behind the wall the field observations did not correspond particularly well with those from laboratory undrained tests on natural speci-mens in compression,except when the stress state approached active failure.ACKNOWLEDGMENTSThe writer would like to thank the financial support from JT Design Build and the Science and Engineering Research Council,and the co-operation of site staff of JT Design Build.The writer also thanks Dr.B.Simpson of Arup Geotechnics and M.Lings and D.Nash of Bristol Uni-versity,U.K.for their useful discussions and comments on the field mon-itoring results.APPENDIX I.REFERENCESAtkinson,J.H.,Lau,W.H.W.,Powell,J.J.M.(1989).‘‘Determination of soil stiffness parameters in stress path probing tests.’’Proc.,12th Int.Conf.on Soil Mech.and Found.Engrg.,Rio de Janeiro ,V ol.1,Balkema,Rotterdam,The Netherlands,7–10.Lambe,T.W.(1967).‘‘Stress path method.’’J.Geotech.Engrg.Div.,ASCE,93(6),309–331.Lings,M.L.,Nash,D.F.T.,and Ng,C.W.W.(1993).‘‘Reliability of earth pressure measurements adjacent to a multi-propped diaphragm wall.’’Retaining structures ,Thomas Telford,London,258–269.Lings,M.L.,Nash,D.F.T.,Ng,C.W.W.,and Boyce,M.D.(1991).‘‘Observed behavior of a deep excavation in Gault clay:A preliminary appraisal.’’Proc.,10th Eur.Conf.on Soil Mech.and Found.Engrg.,Florence ,V ol.2,Balkema,Rotterdam,The Netherlands,467–470.Ng,C.W.W.(1992).‘‘An evaluation of soil-structure interaction asso-ciated with a multi-propped excavation,’’PhD thesis,University of Bristol,U.K.Ng,C.W.W.(1998).‘‘Observed performance of multipropped excavation in stiff clay.’’J.Geotech.and Geoenvir.Engrg.,ASCE,124(9),889–905.Ng,C.W.W.,and Yan,W.M.(1998).‘‘Stress transfer and deformation mechanisms around a diaphragm wall panel.’’J.Geotech.and Geoen-vir.Engrg.,ASCE,124(7),638–648.Schmidt,R.(1966).‘‘Discussions.’’Can.Geo.J.,Ottawa,3(4),239–242.Simpson,B.(1992).‘‘Thirty-second Rankine lecture:Retaining struc-tures:Displacement and design.’’Ge ´otechnique ,42(4),541–576.Tedd,P.,and Charles,J.A.(1985).‘‘The strength of London Clay in relation to the design of embedded retaining walls.’’Ge ´otechnique ,35,199–204.APPENDIX II.NOTATIONThe following symbols are used in this paper:c Ј=effective cohesion;h =subscript h means horizontal direction;K 0=coefficient of earth pressure at rest;K f -line=failure line in s ЈϪt stress space;p Ј=ϩ;(Ј2Ј)/313q =Ϫ;(ЈЈ)13s =(v ϩh )/2;s Ј=ϩ(ЈЈ)/2;v h t =t Ј=(v Ϫh )/2;v =subscript v means vertical direction;u =pore pressure;⌬=increment;1,3=major and minor principal total stresses;Ј,Ј13=major and minor principal effective stresses;h =total horizontal stress;v =total vertical stress;Јh =horizontal effective stress;Јv =vertical effective stress;and Ј=effective angle of friction.D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y T o n g j i U n i v e r s i t y o n 12/04/12. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .。
三向应力状态下应力路径对土体的变形特性的影响
三向应力状态下应力路径对土体的变形特性的影响作者：朱志政庄心善何世秀来源：《科教导刊》2010年第21期摘要对粉质粘土进行固结不排水真三轴剪切试验,探讨了三向应力状态下应力路径对土体的变形特性的影响,研究结果表明:土体在三向受力状态下,应力路径土体的变形特性的影响显着,平面应变加载试验试样在整个剪切过程中表现为剪缩性,平面应变卸荷试验试样在固结压力较低时表现为剪胀性,在固结压力较高时试样表现为先剪缩再剪胀。
关键词应力路径真三轴试验三向应力中图分类号:TU4文献标识码:A0 引言应力路径对土体的变形特性的影响是一个十分复杂的课题。
大量的试验研究表明,土的应力-应变关系是非线性的,应力路径不同则土体的变形也不同,且与其受的应力状态密切相关。
基于这种认识,我们利用真三轴仪,分别就同一种土在不同的应力路径下,对土体进行固结不排水的平面应变加荷与平面应变卸荷两种不同系列的试验研究,来探讨三向应力状态下应力路径对土体的变形特性的影响。
1 不同应力路径试验1.1 开挖过程中土体的应力路径在软土中进行基坑开挖,由于开挖卸荷改变了原位土体的应力场及地下水等环境因素的变化,土体中平均正应力下降,偏应力则大增,其应力释放及变形过程是十分复杂的,为了便于分析,我们将开挖过程中土体的应力路径做一定的简化。
由于开挖卸荷,支挡结构在两边土压力作用下,将产生水平变位,因此土体的应力状态可简化为是竖向应力基本保持不变,水平向应力在静止侧压力与主动土压力水平分量之间变化;同时基坑底部会产生隆起,应力状态是竖向卸荷量大于横向卸荷量,总体上可简化为竖向卸荷,横向荷载保持不变。
1. 2 试验方案在真三轴仪上,我们进行了两种应力路径试验。
一是对基坑周边为主动区土体的卸荷应力路径进行模拟,其应力状态是竖向荷载不变,横向卸荷,即1不变,3减小,并控制2方向上的应变为零;二是为了对比分析的加载应力路径,应力状态为竖向加荷,横向荷载保持不变,1即增加,3不变,并控制2方向上的应变为零。
基坑开挖卸载过程中考虑应力路径的抗剪强度指标的确定 (1)
表 2 侧向分级卸荷方案
土样 编号 X1 X2 X3
取土深度 （ m）
4. 5 ～ 4. 7 6. 5 ～ 6. 7 8. 5 ～ 8. 7
固结应力状态 （ kPa）
σ1 = 90 ，σ3 = 60 σ1 = 120 ，σ3 = 90 σ1 = 160 ，σ3 = 120
侧向分级卸荷应力路径 （ kPa）
2. 2 模拟试样 K0 固结应力状态 基坑开挖之前，现 场 土 体 一 般 已 经 在 自 重 应 力
作用下完成了排 水 固 结。 故 一 般 认 为，天 然 状 态 的 土体是在 K0 条件下进行固结，土体内任意点的应力 状态为：σ1 = γh，σ2 = σ3 = k0 σ1 = k0 γh。而土样 从 原 位取出后其初始应 力 均 为 零，不 符 合 土 体 实 际 的 应 力状态。同时，试验 取 土 及 运 输 过 程 难 免 会 对 土 样 造 成 一 定 程 度 的 扰 动 ，会 改 变 孔 隙 水 压 力 ，影 响 试 样 剪前有效固结压 力，从 而 影 响 试 样 不 排 水 强 度。 因 此 ，进 行 卸 荷 试 验 前 ，应 首 先 恢 复 土 体 原 有 的 应 力 状 态，进行固结过程 的 模 拟，受 实 验 条 件 的 限 制，本 实 验不模拟 K0 固结过程，只模拟 K0 固结的应力状态。 即在围压 σ3 下固 结，然 后 再 轴 向 加 荷 至 K0 应 力 状 态 ，等 待 固 结 变 形 稳 定 后 进 行 卸 荷 过 程 模 拟 。
基坑开挖卸载过程中考虑应力路径的抗剪强度指标的确定崔宏环张立群河北建筑工程学院土木系河北张家口075024针对基坑支护设计所采用的抗剪强度指标忽略了开挖卸载这一应力路径造成的影响本文通过三轴实验以及数值计算探讨分析不同应力路径条件下土体的抗剪强度指标的变化
第二节应力路径分析
图2-12 均匀压缩
∆σc σc σc
u=0
ESP
A σc′ σc′+∆ σc′ p B u=us
σc′
ESP
第二节 应力路径分析方法
应力路径的概念:
土体受力发生.发展和变化的过程.
τ
D C B σ
ቤተ መጻሕፍቲ ባይዱτ b
A
a
σ
图2-5不同应力路径
K0,Kf和f线的基本概念
• 一，K0线 • K0线的特点： • （１）．若应力变化条 件是沿K0线走，标志着 土样的变形只有单向压 缩而无側向变形 • （２）若应力沿K0线发 展，土样不会发生强度 破坏 • （３）K0线代表静止土 压力状态，即天然土的 自重压力状态，K0线也 就是土层的天然条件 q D2 D2 D1 p′
σc
u=us
p
• 结论： • （1）均匀加载,显然凡是平形P轴的应力路径均 • 指均匀加载 （2）按比例加载：α=arctg(1-K/1+K),K可正可 • 负，K=－1 时，是一条垂直于P的直线 • • 1.单向压缩试验的应力路径分析 2. 三轴压缩试验的应力路径分析
q kf
应力路径
(4)
(1)
(2)
(3)
图2-9 三轴试验应力路径
p
• 土样破坏时的标准容易 判别，土样破坏时，应 力点的走向发生变化
q
q
向上转折 停滞 向上转折 向下转折
126
8
1.7 p
OCR=1 p 图2-11 土样破坏时三种情况
应力路径课件ppt
研究复合材料在复杂应力状态下的力学行为，为复合材料的优化设 计提供依据。
生物材料的应力路径模拟
研究生物材料在不同应力路径下的力学行为，为生物材料的优化设 计提供依据。
04
应力路径在工程中的应用
Chapter
岩土工程
岩土工程是研究岩体和土体工程的科学，应力路径在岩 土工程中有着广泛的应用。
在结构工程中，应力路径用于描述结构在各种载荷作用下的响应，包括静载、动载 、温度载荷等。
通过应力路径分析，可以评估结构的强度、刚度和稳定性，优化结构设计，提高结 构的可靠性和安全性。
环境工程
环境工程是研究环境保护和治理的科 学，应力路径在环境工程中也有着一 定的应用。
例如，在土壤污染治理中，通过应力 路径分析可以评估土壤的渗透性和流 动性，优化土壤修复方案，提高治理 效果。
应力路径的表示方法
应力路径通常用应力-应变曲线来表示，横坐标为 应变，纵坐标为应力。根据不同的受力条件和材料 特性，应力-应变曲线会有不同的形状和特征。
应力路径的重要性
指导材料加工和产品设计
促进新材料和技术的研发
通过了解材料的应力路径，可以更好 地指导材料加工和产品设计，优化材 料的性能和使用寿命。
在环境工程中，应力路径可以用于描 述土壤和地下水在应力作用下的流动 和变形规律，对于土壤污染治理和地 下水保护具有重要的意义。
05
应力路径的未来发展
Chapter
应力路径理论的发展
应力路径理论在岩石力学、土壤 力学和结构工程等领域的应用将 进一步深化，为解决复杂工程问
题提供更有效的理论支持。
随着数值模拟技术的发展，应力 路径理论将与数值模拟技术结合 ，实现更精确、更高效的数值模
基坑开挖应力路径试验与有限元变形分析的研究的开题报告
基坑开挖应力路径试验与有限元变形分析的研究的开题报告一、研究背景及意义基坑开挖是土木工程中常见的一项工作，将要施工的建筑物下部所需的土壤、岩石等物质从地下部分中挖掘出来。
开挖土体会承受来自上部建筑物及周边土体的水平和竖向荷载，因此施工中应考虑基坑土体的稳定性，充分评估基坑开挖所产生的不同形式的内力和变形特征，以及不断调整支护结构，确保施工安全和环保。
近年来，伴随着计算机技术的发展和数值模拟方法的成熟，在理论研究和数值计算方面，已经取得了许多趋近于实际的成果。
最新技术的广泛应用为有效地保护人类生命和财产的安全提供了支持和补充。
二、研究内容和目标本文旨在从实验和数值模拟两方面入手，对基坑开挖过程中产生的应力路径影响及其成因进行深入探究，刻画其反射至上方建筑物结构的影响程度，并通过有限元数值模拟技术，为基坑开挖设计及施工提供理论参考。
研究内容包括以下几个方面：1.通过现场实验掌握基坑开挖过程中土体应力路径的变化规律，重点研究基坑开挖时土体受到的竖向荷载和水平荷载的影响，以及不同土壤类型的应力路径差异。
2.将实验结果输入到有限元分析软件中，根据现场实际条件建立基坑开挖的三维数值模型，进行应力与变形分析。
通过有限元方法追踪基坑开挖引起的地面变形，识别变形类型、分析特点和模拟过程，并进一步掌握地面变形的规律和变化规律，预测基坑开挖过程中沉降量、应力变化规律以及裂缝产生原因。
3.基于地面变形及裂缝的精确分析，开展结构响应分析，以解决基坑开挖对上部工程建筑物的影响问题。
三、研究方法1.现场实验法：在现有基础条件下建立基坑开挖实验模型，并通过测量土体体变、沉降、裂缝发生情况等指标，对基坑开挖后土体应力路径的变化规律进行观测和测试，收集实验资料，为数值模拟提供数据支撑。
2.数值分析法：采用有限元分析方法，根据实验数据制定三维地下空间的数学模型，对考虑不同土体类型、不同开挖方法及支护措施的基坑开挖问题进行仿真计算。
计算结果包括基坑开挖影响下的土体变形量、沉降量、塑性区域及应力分布情况等参数，进一步解决结构响应分析问题。
深基坑开挖过程中二维应力路径分析与研究
深基坑开挖过程中二维应力路径分析与研究梁志松【摘要】The changes of stress path in the process of deep excavation are systematically analyzed. 2-D finite element method is used to simulate a real example of deep excavation. The changes of stress path in the various parts of deep excavation are studied in the process of construction. The results show that stress path of soil around deep excavation is in unloaded state, and the degree of unloading is significantly different in different directions. Deep excavation can be clearly divided into three regions, while the stress state of soil around deep excavation is closely related to the displacement of supporting structure.% 系统分析深基坑开挖过程中土体的应力路径变化，对具体基坑工程实例进行二维有限元分析，分析基坑在开挖施工过程中的各部位的应力路径的变化。
分析结果表明：基坑开挖过程中周围土体的应力路径整体表现为卸载状态，不同方向的卸荷程度存在明显不同，可以明显区分为三种不同的区域，基坑土体的应力状态与支护结构的位移密切相关。
【期刊名称】《广东水利电力职业技术学院学报》【年(卷),期】2013(000)001【总页数】8页(P44-51)【关键词】应力路径;基坑;卸载【作者】梁志松【作者单位】广东水利电力职业技术学院，广东广州 510635【正文语种】中文【中图分类】TU470随着大规模城市地下空间的开发与利用，深基坑工程日益增多，且规模和深度也在逐渐加大。
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不固结不排水(UU)与固结不排水 (CU)强度指标的选用
• cu(UU)，由于不排水强度是随着土层的深
度增加的，基坑土的深度变化很大; • 基坑土压力计算采用固结不排水强度指标
是合理的; • 但饱和软黏土属于欠固结土，墙后地面超
载q以及新建的相邻建筑物，应当cu(UU)，
202.0
1001.8
54.3 156.3
400.5 353.5
207.7
305.0
979.8
919.5
方法１：水土合算 ； 方法２：渗流的平均水力梯度为
i H 10 0.556 H 2hd 10 2 4
方法３：通过绘制流网确定沿墙壁各点的水力梯度ii，用朗肯土 压力理论计算有效土压力
方法４：绘制流网，＝０，根据库伦土压力理论
时间 变形
挡土墙后砂土的液化
杭州地铁－灵敏性土
东侧地墙移动
坑内土体受挤压向上抬起 立柱移动、倾斜
地面下沉 西侧坑外土体进入 西侧坑外土体进入
桩断裂 西侧地墙移动、坑外土体进入
支撑体 系失效 土体整 体滑移
预估滑移面
坑内扰动后土体静探锥尖阻力最小值仅为原 状土的35%，
事故后勘察的灵敏度
地层 层序
墙上水土压力计算表
水压力kN
被动侧 (左)Ewp
122.3
主动侧(右) Ewa
422.6
153.4
579.3
153.4
579.3
153.4
579.3
土压力kN
总压力kN
被动侧 (左)Ep
79.4
主动侧(右) Ea
460.3
被动侧 (左)Ep
388
201.7
主动侧(右) Ea
747
882.9
48.6
422.5
• （1）它所支挡的原状土，不是重塑土，存在着 结构强度，非饱和土的吸力；
• （2）天然土层在空间的变化很大； • （3）地下水的分布、赋存形式和时空变化复杂，
水土之间呈十分复杂的相互耦合的关系。 • （4）土压力与挡土结构变形之间的耦合，与刚
性挡墙不同，很难达到全断面的极限状态。
2.基坑工程中土水压力的特点
(qKa 2c Ka )
KaH
梯形
Ea
1 2
KaH 2
H (qKa
2c
Ka )
(qKa 2c Ka )
库伦土压力理论 砂土
Ka
sin2
sin(
sin2( ) )[1 sin(
)sin(
)
ቤተ መጻሕፍቲ ባይዱ]2
sin( )sin( )
E
W
E
R
=+-- R
-
W
黏土＋地面超载q
Ka
sin2
45.0/7.5 54.2/8.0 28.5/3.7
4. 土压力的计算与分布
• 主动土压力与被动土压力； • 朗肯与库伦土压力理论； • 任意位移状态下的土压力计算； • 局部超载下的土压力。
朗肯土压力理论（砂土）
z
H
KaH
Ka tan2 (45 / 2)
pa Ka v Kaz
Ea
1 2
④2 11.0 0.2 25.34(47.9) 28.4(23.71) 8.1 6.1(3.2) 15.8 11.9 17.1 9.7
⑥
1
9.0
0.4 24.06(51.9) 34.1(32.42) 7.1 8.3(3.3) 13.8 13.6 17.8 13.2
不排水强度指标 cu
土层④1和⑥2层土的平均不排水强度指标 cu（kPa）
(45
2
)]
z
(A=2/3)
墙后土的应力路径的影响
• 三轴试验的K0固结与等压减载的固结不排水试验。
q
总应力路 径
Mcu M
有效应力路径
K0线
取样后的三轴试验
p p
墙后土体的减载应力路径
h=30
墙前土的应力路径的影响
正常固结土的强度线
q 超固结土的强度线
b
z
q
常规压缩三轴(CU)
试验
b2
a
bu
K0
基坑支挡结构上的水土压力
清华大学 岩土工程研究所 李广信
目录
• 1.设计理论与荷载组合； • 2.基坑工程中土水压力的特点； • 3.墙体的位移与土压力； • 4.墙后土压力的计算与分布； • 5.土中水与土水压力； • 6.土压力计算与土的抗剪强度指标 • 7.水土分算与合算。
岩土工程的不确定性
砂土分算
z z jz ( w)z sat z
pa z Ka sat zKa
黏性土合算
坑内排水对挡土结构物上的水土压力的影响
水压力分布
(a)达不透水层 (b)均匀水头损失 (c)不计渗流 (d)开挖很快，非稳 定渗流 (e)用流网计算
水、土压力
计算方法
方法１ 方法２ 方法３ 方法４ 方法５
DAC：三轴CU试验；
预固结D
q
有效应力路 径
C
A
M 总应力路径
K0
P
o
D D
p B
某基坑土的强度指标
三轴不固结不 土层 排水
土层④ 和⑥ 层土的不同试验的强度指标
1
2
无测限抗压 十字板试
强度
验
快剪
固结快剪 固结不排水
cu(kPa u qc（kPa） cu（kPa） cq q
ccq cq ccu cu
• RH —抗力分项系数；
• s—作用分项系数，取1.0；
• 这实际上与安全系数等效；
• 不能将一个随机变量的不确定性， 放入另一个随机变量之中；
• 安全系数：包含所有的不确定性。
• 同样数值的安全系数与抗力分项 系数所表现的安全度是无法相比 的。其中差一个荷载分项系数。
s Esk
1
RH
ERk
2.基坑工程中土水压力的特点
A
a2
b0
z
au
a0
B
a a1
b1 b p
1.体积不变，其有效应力路径为a0a1a2，b0b1b2, 2.完全排水固结应力路径为a0aa，b0bb ，成为超固结土； 3.常规三轴的压缩试验应力路径：aau, bbu。
考虑墙后负孔压的水土压力分布图
5m
50kPa
-5kPa 16.6kPa
61.6kPa
太沙基的土压力分布
砂土
软粘土
中-硬粘土
太沙基土压力分布的说明
•
管路基坑，浅层支撑：主要是针对以绕支挡结构顶部转动为主的；
•
它是通过实测各个横向支撑构件上的轴向力，假设它平均分布在该
支撑所承担的面积中，是“表观”的土压力；
•
它是基于实测的所有同一排水平支撑构件上的最大值；反算的表观
土压力强度包络线，也不是开挖到坑底状态时的土压力分布线；
在有效自重压力下的预固结不排水强度
三轴不固 无测限抗 十字板试 土层 结不排水 压强度 验
快剪
经预固结 经预固结
后固结快 后固结不
剪
排水
④2⑥1 10.4
12.3
31.2
17.7
32.8
33.6
十字板剪切试验在基坑中的应用
cu
2M
D(H D / 3)
b
fh Ut z tancu ccu fv Ut K0 z tancu ccu
Kq
1
2q sin cos H sin( )
2c H
墙后地面上的局部荷载
弹性力学解（布辛尼 斯克解）：
pH
2q (
sin
cos2 )
其他计算方法
q
pa
b1
q
b
z
pa
b1
b
q
45
pa 45
土压力的分布
不同墙体运动形式的土压力分布
(a)绕墙底旋转；(b)平移；( c) 绕墙顶旋转。
KaH 2
朗肯土压力理论（黏土）
2cKa
无地面超载
H
z0
z
pa Kaz 2c Ka
z0
2c Ka
Ea
1 2
Ka
(H
z0 )2
1 2
KaH 2
2c
Ka H 2c2 /
KaH
2cKa
有地面超载 H
q
z0
z
三角形
z0
1
(
2c Ka
q)
pa Ka (z q) 2c Ka
Ea
1 2
Ka
(H
z0 )2
3 (Ka K0 ) z
(1 3 ) (K0 Ka ) z
u B[3 A(1 3)]
各类土的孔压系数A的数值范
土类 高灵敏度土 正常固结黏土 轻超固结黏土 重超固结黏土
孔压系数 A
0.75-1.5 0.5-1.0
0-0.5 -0.5-0
u
1 3
(K0
Ka
)
z
1 3
[1
sin
tan2
• 开挖引起支挡构件的前移，使墙后土体的小主应力减 少，也会在饱和黏土中产生负孔压，从而减少了荷载， 也有利于基坑稳定。。
饱和黏土地基中的基坑
地面超载q=30kPa引起的超静孔隙水压力
加载瞬时
sat=19kN/m3 =30,
完全固结 一段时间以后
墙后土的应力路径与的负孔隙水压力
1 z z 0,
基坑工程具有更多的不确定性。
• 地层土水分布不确定性； • 现场与实验室岩土指标的不确定性； • 现场原位应力与孔隙水压力的不确定性； • 外加荷载及其分布的不确定性； • 岩土材料性质的复杂性； • 计算理论和方法的不确定性； • 参数的相关性。