•We determine tunnel stability in soil with a soft upper layer and hard lower layer.•The effects of multiple soil layers and different soft soil parameters on an underground tunnel in China are ...studied.•We present the upper-bound finite element method with a mesh adaptive strategy.•Two main reasons for tunnel instability and large surface settlement are presented.•Two construction proposals are presented to ensure normal working conditions and safety of engineering.
This paper presents a limit analysis of a tunnel in non-homogeneous soil using the upper-bound limit analysis in combination with finite element technology and a mesh adaptive strategy by investigating the critical loads and failure mechanisms of a tunnel cross-section and tunnel face. A case study of an underground tunnel in China is conducted, with a focus on the effects of multiple soil layers and different soft soil parameters. This work demonstrates that the variation in the soil layering plays an important role in the initiation of tunnel collapse, possibly shifting the failure region and even changing the failure mechanism. When the soil changes from a strongly weathered conglomerate to a soft soil, not increasing the low tunnel pressure quickly enough and using the wrong excavation mode are the two main reasons for tunnel instability and large surface settlement.
Piles are one-dimensional (1D) beam–column elements used to support tall buildings, onshore and offshore structures, bridges, wind turbines, etc. In practice, piles are commonly designed using the ...Euler–Bernoulli Theory. However, this theory is only considered appropriate for long, slender piles because it neglects the contribution of the shear deformation on the pile response. The effect of the shear deformation might be of importance in short, rigid and large-diameter piles such as monopiles, and it should be considered in the analysis. In geotechnical engineering, studies addressing this effect and its interaction with the surrounding soil are scarce and very limited. The aim of this work is to conduct a parametric study to investigate the influence of the shear deformation, semi-rigid connections and pile/soil stiffness ratio on the head deflection, head rotation and first-mode of critical load of an embedded pile. For this purpose, the well-known commercial FE software SAP2000 is employed. Four examples are presented to show the effect of the shear deformation on reinforced concrete (RC) and hollow circular piles embedded in either homogeneous or non-homogeneous soil. For lateral deformation analysis, it is found that deflections and rotations at the pile head considerably increase when the shear deformation is taken into account and they are of most significance at low values of pile/soil stiffness ratios. For buckling analysis, Timoshenko’s theory shows that the critical load notably increases as the stiffness of the surrounding soil increases and, regardless of the soil/pile stiffness ratio, it rapidly decreases as the shear stiffness of the pile decreases.
•The effects of shear deformation on the lateral response of piles are investigated.•The effects of shear deformation on the critical load of piles are examined.•The influence of the soil inhomogeneity in conjunction with the effect of shear deformation is examined.•Ranges of pile/soil stiffness ratios where shear deformation are of significance are provided.•Results from Timoshenko’s and Euler–Bernoulli’s beam theories are discussed.
The dynamic response of a three-dimensional multi-layered pavement system subjected to a moving load is calculated by an analytical solution method. In this method, the pavement structure is assumed ...to be a transverse isotropic viscoelastic multi-layered structure with partially bonded interface, and the subgrade is considered to be a transverse isotropic half-space medium with its modulus varying with depth. The load is considered as a three-dimensional elliptical moving load with a constant speed. This study is divided into three key steps. Firstly, the ordinary differential equations of pavement and subgrade structures are obtained via the double Fourier transform, and the general solutions of dynamic response are obtained according to the theory of ordinary differential equations and the Frobenius method. Secondly, combined with the boundary conditions, the method of wave vector matrix, and the inverse Fourier integral transform, the dynamic responses of pavement structure in time domain are calculated. The accuracy of the analytical solution is verified by comparing against the solution from a finite element method. Lastly, the sensitivity analysis is conducted to assess the influence of four parameters on the dynamic response, namely, the horizontal load, the condition of interlayer contact, the transverse isotropy, and the non-uniform distribution of subgrade moduli. The calculation methods and the corresponding results can further develop a theory of the multi-layered system.
•Propose a fast method for calculating the dynamic response of pavement structure.•Consider the non-uniform distribution of subgrade modulus along depth.•Comprehensively investigate the effects of load and interlayer contact conditions.
•Beam-column elements with generalized end-boundary conditions in Pasternak soil.•Differential Transformation Method (DTM) applied to solve the governing equation.•Flexibility to incorporate ...semirigid connections and lateral restraints.•Comparison with other methods to highlight accuracy and implementation.
A simplified analytical approach to analyze soil-structure interaction of beam-column elements (i.e., beams, columns, piles, etc.) with generalized end-boundary conditions on a homogeneous or non-homogeneous Pasternak foundation is developed. The Differential Transformation Method (DTM) is employed to solve the equation that governs the mechanical response of the proposed beam-column element. Using the same set of expressions, the proposed formulation can be used to conduct both static and stability analyses. It also provides the flexibility to incorporate the effects of semirigid connections, lateral restraints, and axial and lateral load at the ends of the element. The effects of any slenderness ratio and element/soil stiffness ratio are captured with the proposed formulation. Five examples are examined to illustrate the simplicity of the method to conduct static and stability analyses. The proposed method is compared with more rigorous, but cumbersome, methods to highlight the accuracy and relative ease of implementation.
A simplified method to study the response of embedded piles in a non-homogeneous Pasternak elastic soil is developed. The governing differential equation (DE) derived from equilibrium is solved using ...the Differential Transformation Method (DTM), providing a compact solution for static and stability analyses that is easy to implement. The solution derived with the DTM overcomes the limitation of conventional approaches used to solve the proposed structural model, where the mathematical derivation and solution become cumbersome and tedious to implement. The proposed formulation is a continuation of the work recently presented by the authors for frictionless beam-column elements, and now incorporates the magnitude and distribution of friction along the element. The applied axial load is carried by both end-bearing resistance and skin friction, so that purely end-bearing, partially frictional, and purely frictional piles can be studied. In practice, the influence of side friction on pile stability is typically neglected, but can have a substantial influence on the buckling capacity of embedded elements---a practical benefit that has received little attention. This work provides an analytical solution for the governing DE with the flexibility to account for different distributions and magnitudes of skin friction, different combinations of geotechnical end- and side-resistance, and generalized end-boundary conditions. The model is applied to elucidate the effects of intermediate end-boundary conditions, as well as the distribution and magnitude of soil-pile interface friction on pile stability.
This paper presents a new, simplified analytical method to study the static and stability response of circular tapered friction piles in homogeneous or non-homogeneous Pasternak soil. The governing ...differential equation (GDE) of the proposed element is derived in a classical manner and solved using the Differential Transformation Method (DTM). This complex analysis is reduced to solve a system of two linear algebraic equations, which solution is readily available and easy to code. The proposed formulation is of practical interest for both onshore and offshore structures, and it can be used to conduct: (a) lateral load–deformation, (b) elastic stability, and (c) second-order analysis of prismatic and tapered friction piles. Tapered friction piles with various distributions of end-bearing resistance and skin friction can be investigated. The proposed formulation includes the effect of (i) any end-boundary condition at the ends of the element (i.e., translational and rotational constraints), (ii) a uniform or linear variation of skin friction, and (iii) a uniform or linear variation of the modulus of subgrade reaction. Five examples are presented to validate the accuracy of the proposed approach.
•A new, simple approach to analyze tapered friction piles is proposed.•The effect of semirigid connections, friction, and soil non-homogeneity are included.•The Differential Transformation Method (DTM) is applied to solve the governing equation.•Lateral load–deformation, elastic stability, and second-order analyses can be conducted.•Purely end-bearing, partially frictional, and purely frictional piles can be analyzed.
Heat transfer through the soil is important in shallow geothermal applications, in plant growth as well as in the surface energy balance. In this work, an analytical solution for a ...conduction–convection equation that models heat transfer is presented for non-homogeneous soil. The main assumption underlying the solution is that the thermal diffusivity of soil is piecewise-constant. A method to determine the depth-dependent thermal diffusivity and the water flux density through the porous medium based on temperature measurements is also developed and applied to field data from a site in Ioannina, Greece. The thermal diffusivity was found to increase in the layer below the surface and decrease for larger depths, while convection through the porous medium was found to be present in wet conditions and to account for about 10% of the heat flux in terms of the annual variability of temperature. Finally, the capability of the novel method in capturing the spatio-temporal variability of soil temperature is compared to three commonly used algorithms: the amplitude, the phase, and the conduction–convection algorithm. The novel method is able to reduce the root-mean-square error for the predicted variability of temperature at all depths by an order of magnitude compared to the other three algorithms.
