A Simplified Analysis Method for the Deformation Response of an Existing Tunnel to Ground Surcharge Based on the Pasternak Model

Surface surcharge changes the existing equilibrium stress field of the stratum and adversely affects the existing tunnel. This paper presents a simplified analytical solution for calculating the longitudinal displacement of existing tunnels that are subjected to adjacent surcharge loading. Based on the Boussinesq solution, the distribution of the additional load matrix caused by the surface surcharge on the existing tunnel was obtained. A Euler–Bernoulli beam with a Pasternak foundation was used as a simplified model for tunnel stress analysis. Using the corrected reaction coefficient of the foundation bed, the differential equation of tunnel deformation was established, and the solution matrix of the longitudinal displacement of the tunnel was obtained by using the finite difference method. The reliability and applicability of the proposed method were verified by comparing the results with finite element simulation results, field test data, and the calculation results of three simplified elastic analysis methods with different foundation bed coefficients. On this basis, the parameters of the load–tunnel model were analyzed, and the effects of the buried depth, the size of the load, the relative positions of the load and the tunnel, and the relative stiffness of the tunnel soil on the maximum displacement of the existing tunnel were calculated. An empirical formula is proposed for calculating the maximum longitudinal displacement of the existing tunnel subjected to surface surcharge. The findings of this research can provide a basis for the theoretical verification of the deformation response of an existing tunnel subjected to adjacent surface surcharge.

To Solution of Contact Problem for Rectangular Plate on Elastic Half-Space

Until the present time there is no exact solution to the contact problem for a rectangular plate on an elastic base with distribution properties. Practical analogues of this design are slab foundations widely used in construction. A lot of scientists have solved this problem in various ways. The methods of finite differences, B. N. Zhemochkin and power series do not distinguish a specific feature in contact stresses at the edges of the plate. The author of the paper has obtained an expansion of the Boussinesq solution for determining displacements of the elastic half-space surface in the form of a double series according to the Chebyshev polynomials of the first kind in a rectangular region. For the first time, such a representation for the symmetric part of the Boussinesq solution was obtained by V. I. Seimov and it has been applied to study symmetric vibrations of a rectangular stamp, taking into account inertial properties of the half-space. Using this expansion, the author gives a solution to the problem for a rectangular plate lying on an elastic half-space under the action of an arbitrarily applied concentrated force. In this case, the required displacements are specified in the form of a double row in the Chebyshev polynomials of the first kind. Contact stresses are also specified in the form of a double row according to the Chebyshev polynomials of the first kind with weight. In the integral equation of the contact problem integration over a rectangular region is performed while taking into account the orthogonality of the Chebyshev polynomials. In the resulting expression the coefficients are equal for the same products of the Chebyshev polynomials. The result is an infinite system of linear algebraic equations, which is solved by the amplification method. Thus the sought coefficients are found in the expansion for contact stresses.

A boundary-type approach for the computation of vertical stresses in soil due to arbitrarily shaped foundations

Purpose This paper aims to present a simple, yet accurate and efficient, formulation for computing the vertical soil stresses due to arbitrarily distributed surface pressures or loads over an arbitrarily shaped area. Design/methodology/approach By leveraging on the strength of Green’s theorem, the present approach is based on the formulation of the classical Boussinesq solution as a boundary-type problem over an arbitrarily shaped simply- or multiply-connected loaded region. The accuracy of the developed formulation was exemplified through a number of illustrative examples, which included both simply- and multiply-connected loaded areas. Findings The results of the test examples presented in this work indicated a high degree of accuracy and flexibility of the developed approach despite its simplicity. Originality/value The main contribution of the present work is the introduction of an efficient meshless approach and an algorithm that can be implemented in few lines of code on any programing platform, as either a stand-alone program or a computational module in larger engineering software packages.

Stresses in Soils Due to External Loading

Stress analysis is often necessary in the design of foundations of all types of structures, particularly buildings, retaining structures, dams, highway pavements, and embankments. In this chapter, the mathematical definitions of stress and strain and the elasticity of an isotropic material are first treated. This is followed by the classical theory of Boussinesq for the stress in a semi-infinite, elastic, isotropic, and homogeneous continuum loaded normally on its upper plane surface by a concentrated load. The Boussinesq solution is later extended to analyze the stresses produced by a uniformly distributed load over a flexible circular foundation, rectangular loading, strip loading, line loading, triangular loading, and embankment loading. The case of irregular loading using the Newmark's Chart is also considered. The settlement of a foundation under external loadings by the use of both the Boussinesq theory and the semi-empirical strain influence factor method proposed by Schmertmann et al. (1978) are considered.

Mechanical Model of Pile-Soil Work Together

Come up with of pile-soil-(foundation) pile cap interaction grounded upon penetration deformation of pile ends and compression of soil between piles. Hyperbolic model is adopted to simulate the development of tip resistance and side resistance in accordance with deformation to reflect the nonlinearity of pile-soil work, Boussinesq solution is utilized to calculate the stresses generated in soil by foundation (pile cap) plate, Mindlin stress solution is used to calculate the stress produced in the soil between piles by side resistance and end resistance, and the stress of soil is the superposition of the two solutions.

The Load Ratio on the Common Work of Micro-Pile and Soil Foundation in the Building Heightening and Transformation

Analyze the stress mechanism of micro-pile and existing mechanism, and come up with the analytic method of pile-soil-(foundation) pile cap interaction grounded upon penetration deformation of pile ends and compression of soil between piles. Hyperbolic model is adopted to simulate the development of tip resistance and side resistance in accordance with deformation to reflect the nonlinearity of pile-soil work, Boussinesq solution is utilized to calculate the stresses generated in soil by foundation (pile cap) plate, Mindlin stress solution is used to calculate the stress produced in the soil between piles by side resistance and end resistance, and the stress of soil is the superposition of the two solutions. Through iterative calculation analytic program RTLOAD for the sharing ratio of a single pile is compiled through VC++.

Analytical Solutions of Spherical Cavity Expansion Near a Slope due to Pile Installation

Based on the hypothesis that the penetration of a single pile can be simulated by a series of spherical cavity expansions, this paper presents an analytical solution of cavity expansion near the sloping ground. Compared with the cavity expansion in the half-space, the sloping free boundary has been taken into account as well as the horizontal free boundary. The sloping and horizontal free surfaces are considered by the introduction of a virtual image technique, the harmonic function, and the Boussinesq solution. The results show that the sloping free boundary and the variation of the inclination angle have pronounced influences on the distribution of the stress and displacement induced by the spherical cavity expansion. The present solution provides a simplified and realistic theoretical method to predict the soil behaviors around the spherical cavity near the sloping ground. The approach can also be used for the determination of the inclination angle of the slope according to the maximum permissible displacement.

Friction Structure Effect Analysis of Granular Materials in Foundation Soil

To research and analyze the additional stress distribution and change of granular materials, the model tests are used to observe vertical additional stress in different position and depth. And the comparison between observed values and theoretical values is conducted to analyze the transmission and attenuation of additional stress in granular materials. The research results show that calculated values are based on Boussinesq solution which ignores the property of soil layer (materials), the distribution of additional stress for fine sand which belongs to granular materials is largely deviated from theoretical value. For granular materials, inner friction structure effect is evident influence to additional stress transfer. And continue using calculation method which is based on continuum materials will have bigger difference and even wrong.