# Stress Path | Stress (Mechanics) | Geotechnical Engineering

View again

All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
PDF
8 pages
0 downs
6 views
Share
Description
Stress Path
Tags

## Physics

Transcript
NPTEL- Advanced Geotechnical Engineering Dept. of Civil Engg. Indian Institute of Technology, Kanpur 1   Module 6 Lecture 40 Evaluation of Soil Settlement - 6 Topics 1.5   STRESS-PATH METHOD OF SETTLEMENT CALCULATION 1.5.1 Definition of Stress Path  1.5.2 Stress and Strain Path for Consolidated Undrained Undrained Triaxial Tests  1.5.3 Calculation of Settlement from Stress Point 1.5   STRESS-PATH METHOD OF SETTLEMENT CALCULATION Lambe (1964) proposed a technique for calculation of settlement in clay which takes into account both the immediate and the primary consolidation settlements. This is called the  stress-path method. 1.5.1 Definition of Stress Path In order to understand what a stress path is, consider a normally consolidated clay specimen subjected to a consolidated drained triaxial test ( Figure 6.31a ). At any time during the test, the stress condition in the specimen can be represented  by a Mohr’s circle ( Figure 6.31b ). Note here that, in a drained test, total stress is equal to effective stress. So,  3 = ′ 3  (minor principal stress)    1 =  3 + ∆ = ′ 1  (major principal stress)    NPTEL- Advanced Geotechnical Engineering Dept. of Civil Engg. Indian Institute of Technology, Kanpur 2   At failure, the Mohr’s circle will touch a line that is the Mohr  -Coulomb failure envelope; this makes an angle ∅  with the normal stress axis ( ∅  is the soil friction angle). We now consider another concept; without drawing the M ohr’s circles, we may represent each one by a  point defined by the coordinates  ′ = ′ 1 + ′ 3 2  (59) And ′ = ′ 1 −′ 3 2  (60) This is shown in Figure 6.31b   for the smaller of the Mohr’s circles. If the points with  ′    ′  coordinates of all the Mohr’s circles are joined, this will result in the line  AB . This line is called a  stress path . The straight line joining the srcin and the point  B  will be defined here as the     line. The     line makes an angle   with the normal stress axis. Now, tan  =  = (  ′ 1   − ′ 3   )/2(  ′ 1   +  ′ 3   )/2  (61) Where  ′ 1    and  ′ 3    are the effective major and minor principal stresses at failure. Similarly, sin ∅ =  = (  ′ 1   − ′ 3   )/2(  ′ 1   +  ′ 3   )/2  (62) From equations (61 and 62), we obtain tan α = sin∅  (63) Figure 6. 31  Definition of stress path  NPTEL- Advanced Geotechnical Engineering Dept. of Civil Engg. Indian Institute of Technology, Kanpur 3  Again let us consider a case where a soil specimen is subjected to an oedometer (one-dimensional consolidation) type of loading ( Figure 6.32 ). For this case, we can write ′ 3 =   ′ 1  (64) Where    is the at-rest earth pressure coefficient and can be given by the expression (Jaky, 1944)   =1 − sin ∅  (65) For the Mohr’s circle shown in Figure 6. 32 , the coordinates of point  E   can be given by  ′ = ′ 1 −′ 3 2 =  ′ 1 (1 −  )2    ′ = ′ 1 + ′ 3 2 =  ′ 1 (1+   )2  Thus,  =  − 1  ′′  =  − 1  1 −  1+     (66) Where ,   is the angle that the line   (    line)  makes with the normal stress axis. For purposes of comparison, the    line  is also shown in Figure 6. 31b . In any particular problem, if a stress path is given in a  ′  . ′  plot, we should be able to determine the values of the major and minor principal stresses for any given point on the stress path. This is demonstrated in Figure 6. 33 , in which  ABC   is an effective stress path. Figure 6.32  Determination of the slope of    line  NPTEL- Advanced Geotechnical Engineering Dept. of Civil Engg. Indian Institute of Technology, Kanpur 4   1.5.2 Stress and Strain Path for Consolidated Undrained Triaxial Tests Consider a clay specimen consolidated under an isotropic stress  3 = ′ 3  in a triaxial test. When a deviator stress ∆  is applied on the specimen and drainage is not permitted there will be an increase in the pore water  pressure, ∆  ( Figure 6. 34a ). ∆ =     ∆  (67) Figure 6. 33  Determination of major and minor principal stresses for a point on a stress path Figure 6. 34  Stress path for consolidation undrained triaxial test
Related Search
Similar documents

View more...