三轴试验与应力路径

1、 路径：某物通过或移动的路线 Path：The route or course along which something travels or moves。XY 应力路径：加载过程中应力点的轨迹。 Stress Path: Trajectory of stress points during loading.Pq应力路径表示方法1） 直角坐标系统2） 直角坐标系统3） 直角坐标系统4） 直角坐标系统13pqst1()a 3()r o31 坐标系统中的应力路径三轴压缩试验（排水）破坏线13o4513坐标系统中的应力路径1313三轴压缩试验（排水）破坏线12313233ppqo13q131332

2、3qp qppq 坐标系统中的应力路径破坏线1313三轴压缩试验（排水）Mean normal stress平均正应力Deviatoric stress偏应力132ssto132t1313212tstsst 坐标系统中的应力路径破坏线1313三轴压缩试验（排水）三轴试验的应力路径三轴压缩（Triaxial Compression）三轴拉伸（Triaxial Extension）排水试验（Drained Test）不排水试验（Undrained Test）三轴试验加载方式排水条件总应力路径（Total Stress Path）有效应力路径（Effective Stress Path）应力路径12

3、313233p13qpqo1313323qp qp13三轴压缩（排水）pqo1313 2()2()33uuppu1313()()quuq u有效应力原理：( , )A p q三轴压缩（不排水）u( , )A p qpqo3112313233p13q1313323qp qp三轴拉伸（排水）例题1 A consolidated-undrained triaxial test on a specimen of saturated clay was carried out under an all-round pressure of 600 kN/m2. Consolidation took plac

4、e against a back pressure(反压力) of 200 kN/m2. The following results were recorded during the test. Draw the stress paths 323ararqp A(626.7,80)A(397.7,80)例题2对一个砂土试样做三轴压缩试验，先在排水条件下对土样施加固结压力至200 kN/m2。然后在不排水条件下增加三轴室的压力至350 kN/m2。这时量测到的孔隙水压力u = 144 kN/m2。然后在不排水条件下增加轴向压力直到土样破坏。试验数据如下表。1. 绘制偏应力和轴向应变的关系；2.

5、在pq空间绘制总应力和有效应力路径；3. 在 空间绘制破坏时的总应力和有效应力摩尔圆以及摩尔库伦强度包线，计算该砂土的剪切强度参数（内摩擦角）；5. 确定孔隙水压力系数B的数值，绘制孔隙水压力系数A随轴向应变变化的关系，确定土样破坏时孔隙水压力系数A的数值。轴向应变 e1 (%)0246810轴向压力差 1-3 (kN/m2)0201252275282283孔隙水压力 u (kN/m2)14424424022221220900.10.20.30.40.50.6024681012Axial Strain (%)A Value-3.5-3-2.5-2-1.5-1-0.500.51024681012

6、Axial Strain (%)A Value相对于起点相对于上一级荷载 Anisotropic consolidation 各向异性固结1113332221213hrvarararaararakqkpk k0 consolidation k0 固结0000113332221213hrvarararaararakkqpkNo lateral deformation Anisotropic consolidation and K0 consolidation 各向异性固结与K0固结pIsotropic Consolidation q/p=0qAnisotropic Consolidation (

7、q/p=0, K0 Condition, no lateral strain)Anisotropic Consolidationq/p=各向同性压缩各向异性压缩一维压缩k0压缩aaaakakak0kk1k 01kk0kk00000Maak材料：各向同性k11312kk pqM00M0000kk01kk0kkMohr-Coulomb Failure Envelope in p-q Spacetanffc13131313cos2tansin222fff13213() 231c(,)ffMohr-Coulomb Failure Envelope in p-q Space Substituting E

8、qs. 2 and 3 into Eq. 1 yields131313cossintan222c13131313tancos2tansin222fffffc(1)(2)(3)(4)Mohr-Coulomb Failure Envelope in p-q SpaceRearrange Eq. 4 givesNote here 1 is the major principal stress and 3 is the minor principal stress.13cos1sin21sin1sincMohr-Coulomb Failure Envelope in p-q SpaceFor tria

9、xial compression,Therefore, we haveSubstituting Eq. 5 into Eq. 4 results in13,ar132/3/3pqpq1313(2)/3(2)/3ararpq( )6sin()3sintanfccqp(5)(6)Mohr-Coulomb Failure Envelope in p-q SpaceFor triaxial extension,Therefore, we haveSubstituting Eq. 7 into Eq. 4 results in13,ra13/32/3pqpq3131(2)/3(2)/3ararpq( )

10、6sin()3sintanfecqp (7)(8)Mohr-Coulomb Failure Envelope in p-q Spaceacar3f1f3f1ff(e)f(c)f(e)f(c)Triaxial Compression三轴压缩Triaxial Extension三轴拉伸Mohr-Coulomb Failure Envelope in p-q Space Therefore, the Mohr-Coulomb failure envelope in the p-q space is as followsq6sin3sincMp6sin3sineM11TCTEMohr-Coulomb

11、Failure Envelope in p-q Space The failure stress ratio M=|q/p| under triaxial compression is different from that under triaxial extension:3sin3sinceMMMohr-Coulomb Failure Envelope in p-q Space If c=0 (sand or normally consolidated clay), the failure envelope is as follows:q6sin3sincMp6sin3sineM11例题 一个粘性土样本受一维压缩从O状态变化到A状态（如图所示）。在此一维