A Generalized Formulation for Accurate and Robust Determination of Soil Shear Strength from Triaxial Tests

TL;DR

The paper addresses the challenge of estimating soil shear-strength envelopes from triaxial tests when a single common tangent to all Mohr circles is not achievable due to measurement noise. It extends the Least Squares with Virtual Displacements (LSVD) framework by introducing generalized envelope forms—linear, logarithmic, parabolic, power-law, and polynomial—each coupled with a virtual-displacement-based loss to locate a tangent envelope across $n$ circles. Through comparisons with p-q and CTPAC under synthetic noise, the work demonstrates LSVD’s greater robustness and flexibility, particularly for linear, logarithmic, and power-law envelopes, while highlighting practical considerations such as the number of samples (3–6) and potential overfitting in high-degree polynomial forms. The study positions LSVD as a versatile tool for geotechnical analysis, capable of modeling diverse soil behaviors and providing more reliable failure-envelope estimates in the presence of measurement uncertainty.

Abstract

This work presents an extended formulation of the Least Squares with Virtual Displacements (LSVD) method for estimating shear strength parameters from multiple soil samples under varying resistance conditions including cohesionless, frictional, and mixed types. LSVD is designed to identify a common tangent across n Mohr circles, even in the presence of measurement errors that render an exact solution infeasible. Beyond its original linear formulation, we introduce generalized LSVD variants like logarithmic, parabolic, polynomial, power law and generalized forms allowing the method to adapt to diverse failure envelope shapes observed in geotechnical materials. We benchmark these variants against established approaches such as the p-q method and CTPAC, analyzing performance under synthetic noise to simulate measurement uncertainty. This provides a comparative framework to assess each method's robustness, especially considering their differing selections of representative points on the Mohr circles. The results highlight LSVD's flexibility and reliability in modeling complex soil behavior and suggest its potential as a versatile tool for geomechanical analysis.

Figures (6)

• Figure 1: Scheme of stresses in a soil sample (left) and the virtual displacement by the $\sigma_3<\prescript{\theta}{}{\sigma_i}<\sigma_1$ to compute least square error (right).
• Figure 2: Failure envelopes with the polynomial LSVD and the results of calib and yuanming
• Figure 3: Failure envelopes computed with different methods. Top-left: CTPAC method. Top-right: LSVD method. Bottom-left: p-q method
• Figure 4: Variability computed with different methods. Top-left: linear methods. Top-right: parabolic methods. Bottom-left: logarithmic methods. Bottom-right: power methods.
• Figure 5: Plot of computed failure envelope.