A soil element in the field may go through various complicated stress paths during the lifetime of a geotechnical structure. It is sometimes possible to simulate these field conditions by advanced triaxial stress path testing, in which the axial and confining pressures are independently controlled and varied to achieve a desired stress path in the p'q space. This way, soil behavior can be predicted under more realistic field conditions. In this problem, we will investigate the influence of stress paths in producing the most damaging strains in a granular material undergoing consolidated drained triaxial testing. The following definitions of p' (mean normal effective stress) and q (deviatoric stress) is used in this study (Schofield and Wroth, 1968):

Task 1: Establishing the failure line in the p' q space
The following table shows the results of a series of consolidated-drained triaxial tests on a medium dense granular soil. Draw the stress paths for each test in the p'q space. Also, establish the failure line going through the origin and connecting the failure points (p'f, q'f).
σ3(kN/m2) (Δσd)f (kN/m2)
150...............................527
275...............................965
350.............................1225
450.............................1580
510.............................1800

Task 2: Loading the specimen through a specified stress path A soil specimen is loaded along the stress path O (0, 0), P (250, 0), and A (675, 1000) under drained conditions to reach point A close to the failure line established in Task 1 (Figure 12.58). Determine the combinations of confining pressure and deviator stresses applied to the triaxial specimen at O, P, and A in order to follow the stress path O-P-A.

Ure l Stress path O-P.A