Ming Cai

In-situ Rock Spalling Strength near Excavation Boundaries

It is widely accepted that the in-situ strength of massive rocks is approximately 0.4xa0±xa00.1 UCS, where UCS is the uniaxial compressive strength obtained from unconfined tests using diamond drilling core samples with a diameter around 50xa0mm. In addition, it has been suggested that the in-situ rock spalling strength, i.e., the strength of the wall of an excavation when spalling initiates, can be set to the crack initiation stress determined from laboratory tests or field microseismic monitoring. These findings were supported by back-analysis of case histories where failure had been carefully documented, using either Kirsch’s solution (with approximated circular tunnel geometry and hence σmaxxa0=xa03σ1−σ3) or simplified numerical stress modeling (with a smooth tunnel wall boundary) to approximate the maximum tangential stress σmax at the excavation boundary. The ratio of σmax/UCS is related to the observed depth of failure and failure initiation occurs when σmax is roughly equal to 0.4xa0±xa00.1 UCS. In this article, it is suggested that these approaches ignore one of the most important factors, the irregularity of the excavation boundary, when interpreting the in-situ rock strength. It is demonstrated that the “actual” in-situ spalling strength of massive rocks is not equal to 0.4xa0±xa00.1 UCS, but can be as high as 0.8xa0±xa00.05 UCS when surface irregularities are considered. It is demonstrated using the Mine-by tunnel notch breakout example that when the realistic “as-built” excavation boundary condition is honored, the “actual” in-situ rock strength, given by 0.8 UCS, can be applied to simulate progressive brittle rock failure process satisfactorily. The interpreted, reduced in-situ rock strength of 0.4xa0±xa00.1 UCS without considering geometry irregularity is therefore only an “apparent” rock strength.

Fracture Initiation and Propagation in a Brazilian Disc with a Plane Interface: a Numerical Study

In the present study, fracture initiation and propagation from a pre-existing plane interface in a Brazilian disc is investigated using a finite-discrete element combined method. Different fracture patterns, depending on the frictional resistance of the pre-existing crack or interface, are observed from the numerical simulation. It is found that when there is no or very little frictional resistance on the surfaces of the pre-existing crack, the primary fractures (wing cracks), which are tensile in nature and are at roughly right angles to the pre-existing crack, start from the tips of the pre-existing crack. As the friction coefficient increases, the wing cracks’ initiation locations deviate from the crack tips and move toward the disc center. Secondary fractures, which are also tensile in nature, initiate from the disc boundary and occur only when the length of the pre-existing crack is sufficiently long. The secondary fractures are roughly sub-parallel to the pre-existing crack. The failure load is found to be influenced by the friction coefficient of the pre-existing crack. A 38xa0% failure load increase can result when the friction coefficient changes from 0 to 1. A good understanding of the fracture initiation and propagation in the forms of primary and secondary fractures provides insight into explaining some fracture patterns observed underground.

An Empirical Failure Criterion for Intact Rocks

The parameter mi is an important rock property parameter required for use of the Hoek–Brown failure criterion. The conventional method for determining mi is to fit a series of triaxial compression test data. In the absence of laboratory test data, guideline charts have been provided by Hoek to estimate the mi value. In the conventional Hoek–Brown failure criterion, the mi value is a constant for a given rock. It is observed that using a constant mi may not fit the triaxial compression test data well for some rocks. In this paper, a negative exponent empirical model is proposed to express mi as a function of confinement, and this exercise leads us to a new empirical failure criterion for intact rocks. Triaxial compression test data of various rocks are used to fit parameters of this model. It is seen that the new empirical failure criterion fits the test data better than the conventional Hoek–Brown failure criterion for intact rocks. The conventional Hoek–Brown criterion fits the test data well in the high-confinement region but fails to match data well in the low-confinement and tension regions. In particular, it overestimates the uniaxial compressive strength (UCS) and the uniaxial tensile strength of rocks. On the other hand, curves fitted by the proposed empirical failure criterion match test data very well, and the estimated UCS and tensile strength agree well with test data.

Author’s Reply to Discussion of the Paper “An Empirical Failure Criterion for Intact Rocks” by Peng et al. (2013)

First of all, we welcome the discussion by Bewick and Kaiser (2013) (in which the following will be referred to as ‘‘the Discussion Paper’’) on our paper entitled ‘‘An Empirical Failure Criterion for Intact Rocks’’ (Peng et al. 2013). Healthy discussion is good for advancing science. The Discussion Paper provides a review of the Hoek– Brown failure criterion and analyzes the triaxial test data we utilized to develop our model. The Hoek–Brown failure criterion is an empirical failure criterion developed by fitting triaxial test data of intact rocks, and it is one of the most widely used failure criteria in rock mechanics and rock engineering. One major contribution of the Discussion Paper is that it emphasizes that the Hoek–Brown failure criterion should be used with its applicability condition in mind. We completely agree with this viewpoint. What is the applicability condition of the Hoek–Brown failure criterion? The Discussion Paper emphasizes that the Hoek–Brown failure criterion should be used for data in the confining stress range 0 r3 0.5rc, where rc is the uniaxial compressive strength (UCS). Hoek and Brown (1997) stated that ‘‘the range of the confinement (r3) values over which these tests are carried out is critical to determine reliable mi and rc values’’. According to Hoek and Brown (1997), ‘‘in deriving the original values of rc and mi, Hoek and Brown (1980) used the range 0 r3 0.5rc and, in order to be consistent, it is essential that the same range be used in any laboratory triaxial tests on intact rock specimens’’. Hence, 0 r3 0.5rc can be considered as an applicability condition for using the Hoek–Brown failure criterion. As shown in Fig. 1, laboratory test data of sandstone investigated by Hoek and Brown (1980) show a good fit of all data in a confinement range up to 1.0rc. If that is the case, what is the other applicability condition for the Hoek–Brown failure criterion? The answer has been given by Hoek (1983), who stated that ‘‘A rough rule-of-thumb used by this author is that the confining pressure r3 must always be less than the unconfined compressive strength rc of the material for the behavior to be considered brittle’’. He further commented that ‘‘In the case of materials characterized by very low values of the constant mi, ..., the value of r3 = rc may fall beyond the brittle–ductile transition’’. Although not explicitly stated by Hoek (1983), it is clear that the confinement should be less than the brittle–ductile transition boundary, which is defined by r1/r3 = constant. Hence, rocks should behave in a ‘‘brittle’’ manner is another applicability condition of the Hoek–Brown failure criterion. The constant that defines the brittle–ductile transition boundary is between 3 and 5 (Hoek 1983). In the following discussion, we follow the Discussion Paper and use 3.4 as suggested by Mogi (1966). We will show that ensuring data points be on the left side of the brittle–ductile transition boundary is a looser applicability condition than the condition of 0 r3 0.5rc. In our reply, we will first further explain why we developed our new empirical model, followed by a further discussion on the Hoek–Brown model and our model through some additional examples. We hope that this J. Peng (&) G. Rong C. Zhou X. Wang State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China e-mail: pengiun2010@gmail.com