Influence of Soil Heterogeneity on the Contact Problems in Geotechnical Engineering

Hao Gu,Kang Liu

doi:10.3390/app11094240

Abstract

Contact problems are widely encountered in geotechnical engineering, such as the contact between soils and concrete used in earth and rockfill dams, tunnels and coastal levees. Due to the unknown contact region and contact forces, the contact problems have strong boundary nonlinearity. In addition, soils have been recognized as heterogeneous materials in geotechnical engineering. The existence of the soil heterogeneity increases the nonlinearity of the contact problems. Currently, the contact problems are mostly analysed without considering the soil heterogeneity, which may not reflect the contact behavior well. In order to investigate the influence of soil heterogeneity on the contact problems, in this paper, a simple plane-strain contact problem is analysed as an example. In this example, Young’s modulus is taken to be a spatially variable. The local average subdivision (LAS) is used to model the heterogeneity of Young’s modulus. The penalty method is utilised to determine the contact behavior. By the first use of linking the penalty method with the LAS, the proposed approach can be used to analyse the contact problems considering soil heterogeneity. The results show that the influence of soil heterogeneity on the elastic contact problems is significant. The contact forces of the heterogeneous case present apparent variation compared to the results of the homogeneous case. The distribution of the contact force at a specific point is also normal when Young’s modulus is normally distributed, moreover, the coefficient of variation (COV) and the horizontal scale of fluctuation of Young’s modulus affect the extent of variation of the normal contact forces. The standard deviation of the normal contact force increases with the increase of the COV and decreases with the increase of the horizontal scale of fluctuation of Young’s modulus. From the analyses, to better predict the deformation/stress in the contact problems, heterogeneity needs to be considered.

Highlights

Contact problems are commonly seen, such as the contact between soils and concrete used in earth and rockfill dams [1,2], tunnels [3] and coastal levees
The comparison results indicated that the penalty method can reflect the contact stress along the interface between the soil and the concrete slab well, especially when there is a gap which emerges between the soil and the concrete slab
The effect of soil heterogeneity has been investigated in many geotechnical problems, such as bearing capacity [18,19], seepage [20,21,22] and slope stability/displacement [23,24]

Summary

Introduction

Contact problems are commonly seen, such as the contact between soils and concrete used in earth and rockfill dams [1,2], tunnels [3] and coastal levees. The effect of soil heterogeneity has been investigated in many geotechnical problems, such as bearing capacity [18,19], seepage [20,21,22] and slope stability/displacement [23,24]. In order to investigate the effect of soil heterogeneity on the elastic contact problems, a simple contact problem of an elastic body on a rigid foundation is analysed in this paper and the penalty method is taken to solve the contact problem. Sci. 2021, 11, 4240 influence of the statistics of Young’s modulus, i.e., the standard deviation and the scale3ooff 15 fluctuation, on the contact force is investigated. Tact, the contact forces at the slave node and the master nodes will be calculated by the penalty method. The detailed derivation of Kc and Fc is referred to in Chapter 5 in Kim [26]

Radom Field Generation

Illustrative Example