1、 路徑：某物通過或移動的路線 Path：The route or course along which something travels or moves。XY 應力路徑：加載過程中應力點的軌跡。 Stress Path: Trajectory of stress points during loading.Pq應力路徑表示方法1） 直角坐標系統2） 直角坐標系統3） 直角坐標系統4） 直角坐標系統13pqst1()a 3()r o31 坐標系統中的應力路徑三軸壓縮試驗（排水）破壞線13o4513坐標系統中的應力路徑1313三軸壓縮試驗（排水）破壞線12313233ppqo13q131332

2、3qp qppq 坐標系統中的應力路徑破壞線1313三軸壓縮試驗（排水）Mean normal stress平均正應力Deviatoric stress偏應力132ssto132t1313212tstsst 坐標系統中的應力路徑破壞線1313三軸壓縮試驗（排水）三軸試驗的應力路徑三軸壓縮（Triaxial Compression）三軸拉伸（Triaxial Extension）排水試驗（Drained Test）不排水試驗（Undrained Test）三軸試驗加載方式排水條件總應力路徑（Total Stress Path）有效應力路徑（Effective Stress Path）應力路徑12

3、313233p13qpqo1313323qp qp13三軸壓縮（排水）pqo1313 2()2()33uuppu1313()()quuq u有效應力原理：( , )A p q三軸壓縮（不排水）u( , )A p qpqo3112313233p13q1313323qp qp三軸拉伸（排水）例題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(反壓力) 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)例題2對一個砂土試樣做三軸壓縮試驗，先在排水條件下對土樣施加固結壓力至200 kN/m2。然后在不排水條件下增加三軸室的壓力至350 kN/m2。這時量測到的孔隙水壓力u = 144 kN/m2。然后在不排水條件下增加軸向壓力直到土樣破壞。試驗數據如下表。1. 繪制偏應力和軸向應變的關系；2.

5、在pq空間繪制總應力和有效應力路徑；3. 在 空間繪制破壞時的總應力和有效應力摩爾圓以及摩爾庫倫強度包線，計算該砂土的剪切強度參數（內摩擦角）；5. 確定孔隙水壓力系數B的數值，繪制孔隙水壓力系數A隨軸向應變變化的關系，確定土樣破壞時孔隙水壓力系數A的數值。軸向應變 e1 (%)0246810軸向壓力差 1-3 (kN/m2)0201252275282283孔隙水壓力 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相對于起點相對于上一級荷載 Anisotropic consolidation 各向異性固結1113332221213hrvarararaararakqkpk k0 consolidation k0 固結0000113332221213hrvarararaararakkqpkNo lateral deformation Anisotropic consolidation and K0 consolidation 各向異性固結與K0固結pIsotropic Consolidation q/p=0qAnisotropic Consolidation (

7、q/p=0, K0 Condition, no lateral strain)Anisotropic Consolidationq/p=各向同性壓縮各向異性壓縮一維壓縮k0壓縮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三軸壓縮Triaxial Extension三軸拉伸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例題 一個粘性土樣本受一維壓縮從O狀態變化到A狀態（如圖所示）。在此一維