Chuangbing Zhou

Estimating hydraulic conductivity of fractured rocks from high‐pressure packer tests with an Izbash's law‐based empirical model

High-pressure packer test (HPPT) is an enhanced constant head packer test for characterizing the permeability of fractured rocks under high-pressure groundwater flow conditions. The interpretation of the HPPT data, however, remains difficult due to the transition of flow conditions in the conducting structures and the hydraulic fracturing-induced permeability enhancement in the tested rocks. In this study, a number of HPPTs were performed in the sedimentary and intrusive rocks located at 450 m depth in central Hainan Island. The obtained Q-P curves were divided into a laminar flow phase (I), a non-Darcy flow phase (II), and a hydraulic fracturing phase (III). The critical Reynolds number for the deviation of flow from linearity into phase II was 25−66. The flow of phase III occurred in sparsely to moderately fractured rocks, and was absent at the test intervals of perfect or poor intactness. The threshold fluid pressure between phases II and III was correlated with RQD and the confining stress. An Izbashs law-based analytical model was employed to calculate the hydraulic conductivity of the tested rocks in different flow conditions. It was demonstrated that the estimated hydraulic conductivity values in phases I and II are basically the same, and are weakly dependent on the injection fluid pressure, but it becomes strongly pressure dependent as a result of hydraulic fracturing in phase III. The hydraulic conductivity at different test intervals of a borehole is remarkably enhanced at highly fractured zone or contact zone, but within a rock unit of weak heterogeneity, it decreases with the increase of depth.

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.

Microseism Induced by Transient Release of In Situ Stress During Deep Rock Mass Excavation by Blasting

During deep rock mass excavation with the method of drill and blast, accompanying the secession of rock fragments and the formation of a new free surface, in situ stress on this boundary is suddenly released within several milliseconds, which is termed the transient release of in situ stress. In this process, enormous strain energy around the excavation face is instantly released in the form of kinetic energy and it inevitably induces microseismic events in surrounding rock masses. Thus, blasting excavation-induced microseismic vibrations in high-stress rock masses are attributed to the combined action of explosion and the transient release of in situ stress. The intensity of stress release-induced microseisms, which depends mainly on the magnitude of the in situ stress and the dimension of the excavation face, is comparable to that of explosion-induced vibrations. With the methods of time–energy density analysis, amplitude spectrum analysis, and finite impulse response (FIR) digital filter, microseismic vibrations induced by the transient release of in situ stress were identified and separated from recorded microseismic signals during a blast of deep rock masses in the Pubugou Hydropower Station. The results show that the low-frequency component in the microseismic records results mainly from the transient release of in situ stress, while the high-frequency component originates primarily from explosion. In addition, a numerical simulation was conducted to demonstrate the occurrence of microseismic events by the transient release of in situ stress, and the results seem to have confirmed fairly well the separated vibrations from microseismic records.

The Friction Factor in the Forchheimer Equation for Rock Fractures

The friction factor is an important dimensionless parameter for fluid flow through rock fractures that relates pressure head loss to average flow velocity; it can be affected by both fracture geometry and flow regime. In this study, a theoretical formula form of the friction factor containing both viscous and inertial terms is formulated by incorporating the Forchheimer equation, and a new friction factor model is proposed based on a recent phenomenological relation for the Forchheimer coefficient. The viscous term in the proposed formula is inversely proportional to Reynolds number and represents the limiting case in Darcy flow regime when the inertial effects diminish, whereas the inertial term is a power function of the relative roughness and represents a limiting case in fully turbulent flow regime when the fracture roughness plays a dominant role. The proposed model is compared with existing friction factor models for fractures through parametric sensitivity analyses and using experimental data on granite fractures, showing that the proposed model has not only clearer physical significance, but also better predictive performance. By accepting proper percentages of nonlinear pressure drop to quantify the onset of Forchheimer flow and fully turbulent flow, a Moody-type diagram with explicitly defined flow regimes is created for rock fractures of varying roughness, indicating that rougher fractures have a large friction factor and are more prone to the Forchheimer flow and fully turbulent flow. These findings may prove useful in better understanding of the flow behaviors in rock fractures and improving the numerical modeling of non-Darcy flow in fractured aquifers.

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