International Journal of Geomechanics

Obtaining the bearing capacity of shallow foundations in a nonhomogeneous soil profile has been a challenging task in geotechnical engineering. In this paper, a new geometric average for the equivalent soil friction angle ($\varphi$) of various layers beneath shallow strip foundations is used to determine the ultimate bearing capacity. This approach is based on the concept of geometric mean value; however, the method involves applying a power to each variable, which is here the internal friction angle of each soil layer. Numerical methods based on finite elements and also experimental data have been used to verify the presented average method. It will be shown that data obtained from the developed method are well in agreement with those obtained from finite-element analysis and with those obtained from full-scale loading. This agreement is closer when the difference between the shear strength parameters of layers is small, which is the case for sedimentary soil profiles and also for artificially compacted soils. A computer program has been developed to investigate the influence of various parameters and to compute equivalent $\varphi$ for different cases.

A simplified analytical method that determines the axial load and biaxial moment capacities of a rigid spread footing of regular or arbitrary shape resting on soil is presented. Three different types of pressure distribution at the soil-footing interface are considered: uniform, linear, and parabolic. The proposed algorithm can be used to determine (1) the maximum soil-bearing stress under rigid spread footings subjected to vertical load and biaxial bending moments; (2) the vulnerability of exceeding the maximum soil-bearing stress by comparing the biaxial moment-axial load interaction diagrams of the footing with those of the attached wall or column; and (3) the development of nomograms for the analysis and design of spread rigid footings of different shapes. Three comprehensive examples are included that show the first two applications. The third application is shown in a companion paper that deals with development of design aids for the analysis and design of rectangular and trapezoidal spread footings.

Design aids (nomograms) for rectangular and symmetrical trapezoidal rigid spread footings are developed using a method previously developed by the writers in a companion paper. The nomograms can be used by designers to directly determine their maximum axial load and biaxial moment capacities without exceeding the bearing capacity of the supporting soil. Three different types of pressure distribution at the soil-footing interface are considered: uniform, linear, and parabolic. The results obtained can then be compared with the biaxial moment-axial load interaction diagrams of the attached concrete walls or columns. This allows the structural designer to determine the vulnerability and likelihood of exceeding the bearing capacity of the supporting soil. Four examples are presented that show the effectiveness and simplicity of the proposed nomograms in the analysis of isolated rectangular and trapezoidal rigid spread footings resting on soil.

One of the most important phenomena in periodic structures is the existence of the band of frequency gaps (BFGs). Elastic waves with frequencies in BFGs cannot propagate in the medium. Therefore, the BFGs can be used to reduce the dynamic response of structures behind periodic pile barriers. Although many achievements have been reported on piles as barriers, the periodic nature of rows of piles has not been considered thus far. In the present paper, the periodic theory of solid-state physics is introduced. The BFGs of two-dimensional periodic rows of piles are obtained. The effect of physical parameters such as soil density and elastic modulus, as well as the geometrical parameters of pile barriers on the BFGs, was investigated. The results show that vibrations can be greatly reduced within the range of the BFGs. Increasing the filling fraction or choosing different configurations can achieve wider BFGs. Moreover, periodic pile barriers with softer soil and a larger periodic constant can produce the lower bound frequency.

A set of small-scale physical modeling of a single pile under lateral loads was performed in a loose sand environment. Digital images were captured during the lateral loading of the pile from the side and from the top of the model simultaneously. The particle image velocimetry (PIV) method was applied, and the deformations of the soil around the pile and the soil strains were obtained from these tests. The soil displacement pattern near the surface around the piles was studied, and the effect of the pile length on the soil deformation pattern was investigated. The effect of pile stiffness and width on soil deformation patterns was also studied. For the study of soil deformation patterns around rigid piles, three tests with rigid piles were undertaken, and strain distribution in the soil was obtained. Based on PIV analysis, a three-dimensional strain wedge with the shape of a circular cone was formulated. The equation of the strain wedge was derived, and with the stress-strain limit equilibrium analysis, the lateral load response of the pile was obtained. Lateral load capacities of several piles from different studies were estimated based on various pile and soil properties, and these results are compared with the measured capacities. Comparisons show good agreement with the load measurements.

The linearization of the Drucker-Prager yield criterion associated with an axisymmetric problem has been achieved by simulating a sphere with the truncated icosahedron with 32 faces and 60 vertices. On this basis, a numerical formulation has been proposed for solving an axisymmetric stability problem with the usage of the lower-bound limit analysis, finite elements, and linear optimization. To compare the results, the linearization of the Mohr-Coulomb yield criterion, by replacing the three cones with interior polyhedron, as proposed earlier by Pastor and Turgeman for an axisymmetric problem, has also been implemented. The two formulations have been applied for determining the collapse loads for a circular footing resting on a cohesive-friction material with nonzero unit weight. The computational results are found to be quite convincing.

The Poisson’s ratio (PR) of asphalt mixtures is a fundamental material property that is an important input parameter to viscoelastic pavement models. It is typically assumed that PR of asphalt is time independent or, in cases where the time dependency of viscoelastic PR is considered, calculated as the negative ratio of the time-dependent transverse and axial strains measured in a uniaxial creep test. This paper presents analytical and experimental results demonstrating the errors involved in these assumptions. The first part of this study derives an expression for viscoelastic PR. The second part of this study reports the results of various experimental tests to measure axial and transverse strains of asphalt concrete specimens under different loading conditions. The viscoelastic PR increased with time in the tensile relaxation test and ramped tensile test, whereas it slightly increased at the beginning of the compressive relaxation test and was subsequently virtually constant. The error introduced by incorrectly determining the PR as the negative ratio of transverse to axial strains in the time domain was found to be significant.

In Shanghai, a number of new underground passages are being constructed, often requiring deep excavations. When the excavations are in the vicinity of existing tunnels, it is necessary to assess the influence of these excavations on existing tunnels such as displacements of the lining and additional loads on the lining. This paper presents a finite-element parametric study of tunnel behavior caused by nearby deep excavation. This study investigates the effects of several parameters that may affect the tunnel response. These parameters are: Relative position of the tunnel with respect to the excavation, tunnel diameter, excavation dimensions, and tunnel protection measures. The results reveal that the influence of the excavation on the underlying tunnel is significant in a range of ∼5 × excavation width measured along the tunnel axis; unloading further than 10 m away from the axis of the tunnel has little effect on the tunnel structure. Based on the study in this paper a better understanding of the interaction between deep excavations and tunnels will be obtained.

Longwall mining is the only technically proven and well-established mining method used worldwide for extracting coal from deep mines. In this paper, two-dimensional (2D) continuum finite-element models of longwall panels are developed and analyzed to understand the interaction of hydraulic-powered support with surrounding rock strata (i.e., roof, floor, and coal seam). The finite-element models thus developed include the structural components of hydraulic-powered support, the surrounding rock mass, and broken rocks. The study focuses on the evaluation of strata behavior while the coal face is supported by hydraulic-powered supports of different capacities. The results from finite-element models are further analyzed in terms of stress distribution in hydraulic legs, abutment, and roof-to-floor convergence. Statistical relations are developed based on deterministic finite-element results, which provide a good correlation with the field measurements.

Terzaghi’s one-dimensional consolidation theory is extended to constant rate of loading, where a simple expression relating average degree of consolidation and time factor is derived. This expression is used to assess Terzaghi’s approximation that the ramp load can be assumed as an instantaneous load, applied at $t_0\text{/}2$, where $t_0$ is the duration of loading. It is shown that this assumption overestimates the degree of consolidation by approximately 10%. Terzaghi’s approximation can be improved in two simple ways: (1) assume the load acts at $t_0\text{/}2$, estimate the degree of consolidation, and reduce it by 10% or (2) assume the load to act at $2t_0\text{/}5$ rather than $t_0\text{/}2$ in estimating the degree of consolidation, with no further adjustment. Nevertheless, the single $U\text{-}T$ expression developed herein maintains a level of simplicity comparable to Terzaghi’s approximation and is adequate for all practical purposes for computing the degree of consolidation during the loading, as well as beyond completion of loading. A numerical example is also given to illustrate the use of the proposed $U\text{-}T$ values for constant rate of loading.