Stability of slopes and passive earth structures in partially saturated soils by the method of characteristics.

Abstract

Stability analysis of slopes and passive earth pressures are problems of considerable economic importance and technical interest in geotechnical engineering. Efforts have continuously been made to improve the methods of analysis with the aim of achieving economy in construction and sophistication in design philosophy. With the increasing accessibility of computers, numerical methods are naturally gaining popularity. To this end, the method of characteristics is one of the most widely used. It is very well known that a vast area of land on earth consists of partially saturated soils. The shear strength of such soils is a function of effective stresses and is higher compared to dry soils because of enhanced effective stress due to negative pore water pressures (suction). The present work addresses the natural question of whether this reserve strength of the soil can be utilised to economise design. The investigations presented here deal with:

Stability analysis of a slope with a break in dry soils Stability analysis of a straight slope and a slope with a break in partially saturated soils Passive earth pressures in partially saturated soils

The work presented is nondimensionalised throughout. After a necessary introduction in Chapter 1, Chapter 2 presents a review of literature related to methods of analysis for slope stability, retaining wall pressures, and shear strength of partially saturated soils. A summary and discussion conclude the chapter.

Chapter 3 – Stability of Bilinear Slopes (Dry Soils) This chapter deals with the stability analysis of bilinear slopes with a horizontal top, considering dry, homogeneous, isotropic soil with both cohesion and internal friction. The new approach adopted is briefly discussed, and the derivation of characteristic equations from equilibrium is given in Appendix A. Unlike the conventional method of characteristics-which assumes the soil is at failure everywhere-the proposed method fully satisfies equilibrium and provides contours of mobilised internal friction angle for straight or bilinear slopes. Results are presented as stability charts for various mobilised friction angles ( ). A comparison with Taylor’s stability numbers for straight slopes shows that:

The proposed analysis predicts higher factors of safety (or lower stability numbers). The influence of the lower, flatter slope segment beneath the break is significant.

Chapter 4 – Slopes in Partially Saturated Soils This chapter considers stability analysis of slopes in partially saturated soils. Pore water pressure variation is assumed to follow Skempton’s pore pressure parameters A and B. Characteristic equations are derived for both straight and bilinear slopes. Results are provided as tables and stability charts for different values of:

Skempton’s parameters A and B Initial negative pore water pressure u Slope inclination

Key findings include:

For given geometry and initial suction, stability number increases as A and B increase. For fixed A and B, increasing suction increases stability (i.e., increases factor of safety). Partial saturation has a considerable positive effect compared to dry soil.

Chapter 5 – Passive Earth Pressures (Partially Saturated Soils) This chapter presents passive earth pressures on rough, rigid retaining walls supporting partially saturated soils. Results are given as nondimensional passive earth pressure coefficients KpK_pKp and Kp.cyK_{p.cy}Kp.cy . Negative pore water pressure at the top is treated as a surcharge. Change in pore pressure with depth is included in Kp.cyK_{p.cy}Kp.cy . Key observations:

For vertical retaining walls, K and KpcK_{pc}Kpc remain constant with depth, while K varies with wall height. Final pore water pressure profiles are plotted for representative cases. Passive earth pressures in partially saturated soils are higher than those in dry soils.

Chapter 6 – Summary of Conclusions A summary of the main conclusions drawn from the study is presented.