Comparative study of four failure criteria for intact bedded rock salt

doi:10.1016/j.ijrmms.2010.08.017

International Journal of Rock Mechanics and Mining Sciences

Volume 48, Issue 2, February 2011, Pages 341-346

https://doi.org/10.1016/j.ijrmms.2010.08.017 Get rights and content

Introduction

Due to the low permeability (10⁻²²–10⁻²⁰ m²), favorable creep, and damage healing properties of rock salt, underground resource storage and radioactive waste disposition in rock salt have become increasingly popular since its first use in 1940s [1]. In contrast to the European and American “pure” salt domes, bedded salt deposits with the existence of vertically different interbeds are widespread in China. To conduct the experimental study, a set of 23 specimens were obtained from Yingcheng salt deposit located at the depth of around 1000 m underground in Hubei Province [2]. Typically, Yingcheng bedded salt specimens (Fig. 1) consist of 17–25% NaCl (halite), 4–20% Na₂SO₄ (sodium sulfate), 25–32% CaSO₄ (anhydrite), with the rest of the insoluble part making up to 36–43%. Among them, five samples were used for Brazilian tests, another five for unconfined compression tests, and seven for conventional triaxial tests (σ₁>σ₂=σ₃) at confining pressures of 5, 10, 15, and 20 MPa, respectively.

Since the input of failure criteria and relevant parameters is of great importance in numerical analysis of the salt cavity stability, as well as in the design and operation evaluation of the cavern filed, the question arises of which failure criterion best fits the previous test data and describes the mechanical behavior of the bedded rock salt. In 1984, Skrotzki [3] established the Mohr–Coulomb strength theory for rock salt based on uniaxial tensile test data. Carter [4] attempted to modify the Hoek–Brown criterion through the inclusion of a third parameter to account for the low tensile strength of the rock salt from the Saskatoon area of Saskatchewan. In addition, Bruno [5] simulated the response of salt at the Permian, Michigan and Appalachian Basins directly with the viscoplastic salt model built into FLAC^3D, which combined the empirical WIPP creep law with the Drucker–Prager criterion, but without the applicability analysis of the failure criterion. However, the situation has been somewhat different for the “mixed” bedded salt with interlayers of either anhydrite or mudstone alternating with halite in the specimens.

There are around 20 rock failure criteria available [6] for predicting the strength of rocks, and each one is particularly suitable for one rock type or some rock types. In this study, we picked up three of the most popular criteria: Mohr–Coulomb (MC) criterion, Hoek–Brown (HB) criterion, and Drucker–Prager (DP) criterion. Moreover, a new modified generalized Hoek-Brown criterion (MGHB), proposed by Bhawani Singh [7], was also investigated.

Section snippets

Mohr–coulomb criterion

The Mohr–Coulomb (MC) criterion is one of the most trusted and widely used linear failure criteria for soils and rocks, which is based on the Mohr hypothesis that failure happens when the shear stress in any plane reaches the failure shear stress τ_m, defined as $τ_{m} = c + σ_{n} \tan φ$ where σ_n is the effective normal stress acting on the failure plane, c the cohesion of the rock, and φ the internal friction angle of the rock. The MC criterion can be also written as $σ_{1} = \frac{1 + \sin φ}{1 - \sin φ} σ_{3} + \frac{2 c \cdot \cos φ}{1 - \sin φ}$

The uniaxial

Experimental data

Compression tests were conducted with a XTR01 mechanical frame at a constant strain rate (5×10⁻⁵ s⁻¹) until the specimen was irrevocably damaged, which was aimed to explore short-term behavior in a case of rapid pressure drawdown in a cavern [2], [10]. These sets of data as well as stress–strain curves are shown in Table 1, Table 2 and Fig. 2, Fig. 3, respectively.

Statistical methods

A good curve fitting performance needs not only a full range of strength data from uniaxial tension to triaxial compression area but also a proper scientific methodology to utilize. A number of mathematical approaches are available in curve fitting for determining material parameters [11]. Among them, the conventional least squares method is a commonly used technique, whereas the least median method could effectively identify the scattered data points especially at higher confining stresses, in

Curve fitting results and analysis for the four failure criteria

All fitting associated with four criteria was accomplished in the σ₁–σ₃ space, except for the DP criterion. To analyze the rock test data for the DP criterion, we derived the relationship between I₁ and J₂ first, using minimum square method, then switched to plot together with three other strength criteria in the σ₁–σ₃ plane for comparison, corresponding indexes were calculated in the meantime.

As can be seen in Fig. 4, the linear MC and DP criteria fit equally poor to the test data with nearly

Further numerical experiments

The numerical analysis of conventional triaxial compressive tests under different confining pressures (10 and 20 MPa) was conducted with explicit three-dimensional finite difference program FLAC^3D. Different constitutive models built in FLAC^3D are characterized by relevant failure criterion, hardening/softening functions, and flow rules. For the Mohr–Coulomb and the Drucker–Prager models, the failure envelopes correspond to their strength criteria, respectively, with tension cutoff (tension

Dependency of the intermediate principal stress

With the development of underground resource storage in rock salt at great depth, the mechanical properties of which in highly stressed state are needed for safety and stability evaluation of rock salt cavities. The experimental and theoretical investigation on the unusual bedded rock salt is far from thorough and complete. How the failure criteria act according to engineering practice when the confining stress much larger than 20 MPa. Besides, because of the difficulty and the expense of

Acknowledgement

This research has been financed and fully supported by the National Basic Research Program of China (973 Program, No. 2009CB724608), which is greatly appreciated.

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Technical NoteComparative study of four failure criteria for intact bedded rock salt

Introduction

Section snippets

Mohr–coulomb criterion

Experimental data

Statistical methods

Curve fitting results and analysis for the four failure criteria

Further numerical experiments

Dependency of the intermediate principal stress

Acknowledgement

First page preview

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Technical Note
Comparative study of four failure criteria for intact bedded rock salt