An attempt to apply the kinematic method of rigid solids in the study of bearing capacity of shallow foundations

In the geotechnical engineering field, shallow foundations are frequently needed to ensure good fieldwork stability. They are also intended to permanently and uniformly transmit all load pressure on the seating floor. However, numerous mechanical constraints, such as bearing capacity of foundations, durability, stability, design of shallow foundations, lead, unfortunately, to a serious realization challenge. Finding an adequate solution presents the main goal and effort of both scholars and professionals. Indeed, the corresponding drawback is observed through the high number of reported damages that occurred in the structure of foundations and the punching failure. The failure mechanisms of shallow foundations, verified in full size or on scale models, show “sliding surfaces” and rigid (solid) blocks, which can be described with the kinematic method of rigid solids. The main objective of this study is the application of the kinematic method of rigid solids in the study of the stability of shallow foundations with respect to punching, the purpose of which is to determine the bearing capacity factors Nc, N γ, and the passive earth pressure coefficient Kp of foundations. In this context, two mechanical models have been proposed with 5 and 7 rigid solids, and a program developed via the MathCAD environment is applied to check the validity of the two previous models. The kinematic method of rigid solids gives results very close and comparable with that of Caquot/Kerisel for the factors of the bearing capacity and passive earth pressure coefficient - the ratio Kp - according to the five- and seven-solid model.

Earth Pressure on Retaining Wall with Surface-Inclined Cohesive Fill Based on Principal Stress Rotation

When considering the friction and bonding force between the back of the retaining wall and the horizontal fill behind the wall, the principal stress of the soil element near the vertical back of the retaining wall is no longer vertical and horizontal but deflects to a certain extent. When the surface of the backfill becomes inclined, the principal stress of the soil behind the wall deflects in a more complicated way. In this paper, the cohesion of the soil element in the fill with an inclined surface is assumed, and the formulas for calculating the active and passive earth pressures of the retaining wall with inclined cohesive backfill are derived by rotating the principal stress of the soil element behind the wall. The proposed method is compared with the existing algorithm, and the influences of the inclination and the cohesion of the fill are analyzed. The results show that the proposed method is more universal. Both the active and passive earth pressures increase rapidly with the increase of the inclination of the fill. The active earth pressure and its horizontal component decrease with the increase of the cohesion of the fill, while the passive earth pressure and its horizontal component increase with the increase of the cohesion of the fill.

Earth Pressure of Three-Dimensional Stress States under Different Strength Criteria and Its Application

To solve the Earth pressure problems in practical engineering, such as retaining walls and foundation pits, we derive active and passive Earth pressure formulas in accordance with the relationship between intermediate principal stress and excavation under three-dimensional stress states. The formulas are derived on the basis of the Mohr–Coulomb, spatially mobilized plane (SMP), σ 3 SMP, Lade–Duncan, axisymmetric compression- (AC-) SMP strength, and generalized Mises (Gen-Mises) criteria and then extended to clay. We also compare the calculated Earth pressure with the measured data. Results indicate that the Earth pressure considering medium principal stress contribution under a three-dimensional stress state is consistent with the actual engineering. The calculated active Earth pressure in the Mohr–Coulomb strength criterion is larger, and the passive Earth pressure is smaller than the practical one because the intermediate principal stress effect is not considered. The calculated results of the SMP, σ 3 SMP, Lade–Duncan, AC-SMP strength, and Gen-Mises criteria are close to the measured data, among which the result of the Gen-Mises criterion is closer. The Earth pressure calculated using the Lade–Duncan criterion is no longer appropriate to describe the Earth pressure under medium principal stress condition in this study. The results of this study have theoretical significance for retaining structure design under a three-dimensional stress state.

Significance of flow rule for the passive earth pressure problem

Determination of earth pressures is one of the fundamental tasks in geotechnical engineering. Although many different methods have been utilized to present passive earth pressure coefficients, the influence of non-associated plasticity on the passive earth pressure problem has not been discussed intensively. In this study, finite-element limit analysis and displacement finite-element analysis are applied for frictional materials. Results are compared with selected data from literature in terms of passive earth pressure coefficients, shape of failure mechanism and robustness of the numerical simulation. The results of this study show that passive earth pressure coefficients determined with an associated flow rule are comparable to the Sokolovski solution. However, comparison with a non-associated flow rule reveals that passive earth pressure coefficients are significantly over predicted when following an associated flow rule. Moreover, this study reveals that computational costs for determination of passive earth pressure are considerably larger following a non-associated flow rule. Additionally, the study shows that numerical instabilities arise and failure surfaces become non-unique. It is shown that this problem may be overcome by applying the approach suggested by Davis (Soil Mech 341–354, 1968).