Formulation of ultimate bearing capacity for strip foundations based on the Meyerhof theory and unsaturated soil mechanics

Abstract

This study presents an ultimate bearing capacity formulation of strip foundations in unsaturated soils within the framework of the Meyerhof theory. The flowchart of calculation steps for this formulation is provided with a trial method according to suction distributions. The validity of the formulation obtained is demonstrated by two available theoretical solutions and experimental data. Comparisons are also performed between the results from the Meyerhof and the Terzaghi theories. It is found that the effects of matric suction and its distribution are significant; strength nonlinearity generates three types of the ultimate bearing capacity variation with respect to matric suction.

Introduction

Bearing capacity of shallow foundations is an important issue for classical soil mechanics and geotechnical engineering (Meyerhof, 1951, Terzaghi, 1943, Vesić, 1973); and its reasonable determination is critical for the safety and cost of engineering projects. Due to the wide application of waterproof-drainage measures in practice, the soil surrounding shallow foundations is mostly unsaturated. A shallow foundation can be in unsaturated conditions during the whole service life, particularly in arid and semi-arid areas. Yet, routine design of a shallow foundation is based on conventional saturated soil mechanics. Noticeable contributions from matric suction towards shear strength of unsaturated soils (and thus to the bearing capacity of shallow foundations resting on unsaturated soils) are then neglected (Costa et al., 2003, Garakani et al., 2020, Rojas et al., 2007, Tang et al., 2018, Vanapalli and Mohamed, 2013).

As matric suction was not explicitly considered in conventional bearing capacity theories, adjustments of overburden pressures or soil unit weight were made to reflect the influence of water table (Ausilio and Conte, 2005, Bowles, 1996, Meyerhof, 1955, Terzaghi and Peck, 1948, Vesić, 1973). Only a few investigations to date have been undertaken to address the ultimate bearing capacity of shallow foundations in unsaturated soils through theoretical analyses. For instance, the ultimate bearing capacity equation of strip foundations for saturated soils based on the Terzaghi theory was extended for unsaturated soils using the shear strength theory of two independent stress state variables (Fredlund and Rahardjo, 1993, Oloo et al., 1997, Xu, 2004). Within the framework of the Terzaghi theory, Oh and Vanapalli (2013) modified the total stress and the effective stress approaches for saturated soils to unsaturated soils considering the influence of matric suction. Vahedifard and Robinson (2016) and Tang et al. (2017) derived formulations of ultimate bearing capacity for strip foundations using the effective stress shear strength theory of unsaturated soils along with a complex numerical integration of average matric suction and a simply linear variation of the suction stress, respectively. On the other hand, Zhao et al. (2009) proposed the upper-bound solution for the ultimate bearing capacity of strip foundations in unsaturated soils in conjunction with the sequential quadratic program comprising many mathematical and geometrical restrictions. Jahanandish et al. (2010) introduced the zero extension line method to study the effect of matric suction on the ultimate bearing capacity of strip foundations for both associative and non-associative problems, whereas a computer code was required to solve complicated plasticity equations. Vo and Russell (2016) presented the ultimate bearing capacity equation of strip foundations in unsaturated soils based on the slip line theory by approximating the contribution of matric suction to the effective stress as a linearly varied function with depth, yet this equation was expressed in dimensionless forms rather than conventional superposition ones of three components.

Nonetheless, the soil weight above the foundation base level would be overestimated as an infinitely uniform surcharge by the Terzaghi theory. It may lead to an unsafe foundation design. Meanwhile, the results from the upper-bound theorem of plasticity, the zero extension line method, and the slip line theory, are too complicated or not in ordinary superposition forms for geotechnical engineers in practice. In fact, the Meyerhof theory of ultimate bearing capacity for saturated soils is commonly recommended by many regulations (Bowles, 1996, Motra et al., 2016). This is because the Meyerhof theory rationally makes use of the stress on an equivalent free surface to indirectly reflect the soil weight above the foundation base level. Accordingly, the classical Meyerhof theory should be extended for unsaturated soils to improve the infinitely uniform surcharge assumption of the Terzaghi theory. Two acquainted suction distributions (i.e., uniform suction with depth and linear suction with depth) are adopted to present a relatively simple approach in familiar superposition forms of three components for engineering applications.

This study aims to derive an ultimate bearing capacity formulation of strip foundations in unsaturated soils by extending the classical Meyerhof theory with an equivalent free surface. Some assumptions are made in consistent with the Meyerhof theory as well as the shear strength theory of two independent stress state variables. The limit equilibrium method and the superposition principle are employed in the derivation process of this conventional-form ultimate bearing capacity formulation. Calculation steps for the proposed formulation are discussed under uniform and linear suction distributions. Validations and comparisons are carried out between the formulation obtained and the results from the upper-bound theorem of plasticity, the effective stress shear strength theory, experimental researches, and the Terzaghi theory. A parametric study is also conducted to investigate the effects of matric suction and the friction angle related to matric suction in high suction regions.