Weak sandstones possess deformational behaviors different from hard rocks; these phenomena, including shear dilation and degradation of deformational moduli, are much more significant. Therefore, a model capable of simulating major deformational characteristics of weak sandstones is essentially needed for engineering purposes. An innovative constitutive model is accordingly proposed. The proposed model was formulated based on the linear elastic model, and it accounts for the variations of moduli K and G through different loading conditions. In addition, an anisotropic factor β is introduced to reflect the stress-induced anisotropy. It was found that the proposed model is able to closely simulate the actual deformational characteristics of weak sandstones.

The proposed model was then incorporated into a finite element program and was used to analyze a squeezing tunnel case. Overall, this model can describe the deformation behavior for weak sandstones, especially on the significant shear dilation prior to the failure state. As a result, the proposed model shows the versatility in its applicability.

1 Introduction

The western region of Taiwan is most populous and accompanied with active constructions of the transportation infrastructure. Many tunnel constructions currently in progress or in planning are, or to be, constructed in sedimentary strata of Tertiary Period. Due to this relatively young rock-geneses period, weathering and other factors, these sedimentary strata are mostly weak rocks. In the past, these weak rocks have caused several engineering difficulties such as squeezing of the tunnel under construction due to shear-induced deformations [1]. It was found that some typical weak rocks exhibit problematic characteristics such as substantial wet weakening, shear-dilation as well as creep deformation. Such behavior is often much less significant in hard rocks. In order to realize the deformation characteristics of weak sandstone, a series of laboratory tests including pure-shear triaxial tests and creep tests were performed by Jeng et al. [1], Weng et al. [2] and Tsai et al. [3]. According to the results of these researches, weak rocks typically exhibit the following behaviors:

  1. In the hydrostatic loading stage, the total strain possesses nonlinear behavior, which indicates that bulk modulus would increase as hydrostatic stress increases.

  2. In the shear loading stage, the initial shear modulus increases with increasing hydrostatic pressure applied.

  3. The volumetric strain induced by shear is initially contractive, and then gradually transits to be dilative upon increases of shear stresses.

Since squeezing phenomenon in tunnel constructions is inherently related to the aforementioned shear-induced deformation, proper assessments for the rock mass prone to such behavior is of interest in engineering practice. Therefore, it is needed to develop a constitutive model that can properly describe these deformational characteristics.

2 Model formulation
2.1 Model concept

Incorporating the characteristics of deformation behavior of sandstone, especially for shear contraction/dilation, the compliance matrix in the principal stress coordinate is proposed accordingly based on Weng et al. [4] and Graham and Houlsby [5] as:

  • (Equation in full paper)

where K and G are tangent bulk modulus and shear modulus; β is the anisotropic factor;δσ1, δσ2, and δσ3 are the major.

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