A three-phase medium model was proposed for describing wave propagation across filled rock joints in the paper. Parameters in the three-phase medium model were identified by a series of modified split Hopkinson pressure bar (SHPB) tests, where a sand or clay layer was used to represent an artificial filled rock joint. Two granitic pressure bars with the sandwiched sand or clay layer were used to represent the filled joint to simulate longitudinal stress wave propagation across such geological discontinuities. With the parameters fitted from a number of SHPB tests, the closure-pressure relation based on the three-phase medium model were compared with other test results and very good agreement was observed. Then, the three-phase filled joint model is adopted to carry out analysis of the longitudinal wave propagation through a single filled rock joint. The wave transmission coefficients were derived and compared with the test results. Finally, parametric studies with respect to the properties of filled joints and the incident wave on wave propagation through a single filled joint were carried out.
The mechanical behavior of rock mass is significantly affected by the vastly existing discontinuities, primarily joints. One of the main tasks in the fields of rock mechanics and engineering is to well understand the mechanical properties of the discontinuities and their effects on rock mass behavior, so as to ensure the stability of the rock mass and underground structures under dynamic load, which is of great interest to mining engineers, seismologists and geoscientists. In nature, besides unfilled fractures, there are also some open-mode fractures (joints) with filling materials, such as sand, clay, and other geomaterials. The static or quasi-static physical properties of some filling materials have been experimentally investigated and it has been found that they affect the stiffness and strength of the filled rock joints (Singh and Goel, 1999; Sinha and Singh, 2000). Among different filling materials, sand and clay are the most common geologic filling materials and are considered as sift or loose materials. A commonly accepted joint model in rock mechanics and engineering (Cook, 1992) is the Bandis-Barton (B-B) joint model (Bandis et al., 1983), which was originally developed from quasi-static deformation tests for natural unfilled rock joints. There are very limited studies on the mechanical properties of filled rock joints, especially under a dynamic loading condition. The filled rock joints can be considered as a complex three-phase medium consisting of rock solid particles, water and air. As a mixture, the three phases deform under different laws. At lower strain rates, the water and air are assumed to flow through the skeleton driven by the pore pressure. In contrast, at higher strain rates and pressures, such as under shock and blasting loads, water and air are trapped within the pores and the deformation of the matrix is controlled by the deformation and the volume fraction of each of the three constituent phases. Based on the multiphase mass theory of Henrych (1979), Wang et al.
Degraded rock samples were prepared to investigate the effect of degradation on the mechanical behavior observed under an uniaxial compression test. The samples of Småland granite were obtained from Äspö HRL in Sweden. The samples were degraded by submerging in 10% saline water (10% NaCl) for 90 days, and axial and circumferential deformations were observed. The behaviors of uniaxial deformations were investigated using an expansion damage model based on the damage mechanics theory. The damage parameters were identified from the stress-strain relation obtained from the mechanical test results. The effect of degradation was inferred by investigating the change in the damage parameters of the degraded rock. Moreover, finite element simulations based on an analytical model of the uniaxial compression test were performed using the damage parameters. As the results, it was inferred that the Småland-granite becomes more expansive material. It is, also, inferred that a localized deformation on surface of sample causes the decrease in stress.
To discuss the chemical effect on the mechanical and hydraulic behavior of the rock adjacent to the tunnel wall, Backström et al. (2006) investigated the mechanical properties of chemical degraded sample. The samples were obtained from Äspö HRL in Sweden and preserved in the 10 % salt water, formation water and distilled water for 90 days. Then the samples were subjected to the unconfined compression test.
In this study, a numerical modeling of the chemical degradation of rocks is examined with expansion damage mechanics (Yamamoto et al. 2003). The damage parameters were determined from experimental results. The difference in failure process between sound and degraded rock is investigated by comparing the damage parameters. Moreover, FEM analyses with damage mechanics were carried out using the damage parameters. In this paper, firstly, the results of laboratory tests are briefly reviewed.
2 MATERIAL AND MECHANICAL TEST
20 samples of Ävrö granite were collected from drill cores, from -450 m in the Äspö Hard Rock laboratory, Sweden by SKB. The samples were submerged in their respective fluids, i.e., 5 samples in saline water, 3 samples in distilled water and 2 samples in the formation water were preserved for 90 days. In addition, 2 samples were submerged in distilled water for 40 days and 3 samples were kept in formation water for 40 days.
2.2 Uniaxial compression test
After submerging in the respective fluids, the samples were experimented by uniaxial compression test. The axial and circumferential deformation was monitored. Table 1 shows uniaxial compressive strength (UCS) of the samples submerged in three different fluids for 90 days. It can be seen that the result of formation water is the mostly similar to the one of saline water. The samples submarged distilled water (as sound sample) and saline water (as degraded sample) are subjected to determination of damage parameter with those stress-strain relation.
3 EXPASION DAMAGE MODEL
3.1 Fundamental concept
In damage mechanics (Lemaitre 1992), the change in mechanical behavior due to the growth of damage (cracks) in material is dealt with.
Foroptimaldesignofrock-socketedshaftsusedtosupportaxialloading,theendbearing resistance should be considered. The existing empirical methods for determining the end bearing capacityqmaxofrock-socketedshaftsuseempiricalrelationsbetweenqmaxandtheunconfined compressive strength of intact rock, σc. Since rock-socketed shafts are supported by the rock mass (bothintactrockblocksanddiscontinuitiesseparatingthem)notjustbytheintactrock,one should consider not only the intact rock properties but also the influence of discontinuities when determiningqmax.Inthispaper,a databaseconsistingof25testshaftswith RQD (rockquality designation) value available is developed. Using the developed database, a new empirical relation betweenqmaxandtheunconfinedcompressivestrengthofrock mass, σcm,isderived. The new empirical relation explicitly considers the effect of discontinuities by using σcm, which is directly relatedto RQD. Finally, an example is presented to show the application ofthe newly derived empirical relation.Theresultsindicatethatthenewempiricalrelationbetweenqmaxandσcmprovides more accurate prediction of qmax than the old empirical relations between qmax and σc.
Drilled shafts socketed into rock are nowadays amongst thewidelyusedvarietyofdeepfoundations.Loads appliedtotheshaftsaresupportedbytherocksocket throughthesideshearresistanceandtheendbearing resistance(Horvathetal.1983). although “There are significant advantagesin designingtoinclude a base[or end bearing] resistance component” (Williams and Pells 1981), the end bearing resistance is often ignored in current design practice(Crapps and Schmertmann 2002; Turner 2004).According to Crapps and Schmertmann (2002), the most common reasons cited by designers for neglecting endbearingresistanceindesigninclude settled slurrysuspension,reluctancetoinspectbottom, concern forunderlyingcavities,andunknownor uncertain endbearingresistance.Obviously, neglecting the endbearingresistanceindesignwillresultin excessive rocksocketlengths.Due to the high cost of shaft construction in rock, an over-designof sock length will leadtoagreatwasteofmoney.Crapps and Schmertmann (2002) suggested that accounting for end bearing resistanceindesignandusingappropriate construction andinspectiontechniquestoensurequality base conditionsisa better approachthanneglecting end bearing resistance.
To include the end bearing resistance in design, it is necessary todeterminetheendbearingcapacityfirst. Although some methods are available for predict
Many theoretical and empirical failure criteria for rock found in the literature are stress-based. Moreover, current failure criteria are often not adapted to predicting fallout in an underground excavation as opposed to simply predicting failure, i.e., overstressing of the rock. A connection between observable and predictable behavior is often lacking. This could be addressed through deformation monitoring, which is often conducted in underground excavations, but this would also require a failure criterion based on deformation parameters. Based on uniaxial laboratory test data, this paper evaluates the stages of deformation, i.e., the stress-strain relation, and the critical states of deformation of tested hard rock specimens. This study identifies deformation parameters governing failure of hard rocks. Available failure criteria based on deformation parameters are also presented in this paper. Finally, critical deformation parameters for establishing a deformation-based failure criterion are proposed.
The deformation and failure process of brittle rock has been studied by many researchers, e.g., Bieniawski (1967), Martin & Chandler (1994), and Eberhardt et al. (1998, 1999). In the studies at the Underground Research Laboratory (URL) the crack initiation and crack damage stress were used to better quantify rock damage (Eberhardt et al. 1998). Knowledge of the failure process of rock facilitates the evaluation of the stability of underground excavations. Since the behavior of a rock construction is normally assessed by deformation monitoring and damage mapping, a failure criteria based on deformation parameters could be considered to evaluate the stability of an excavation (i.e., predict fallout). Thus, a connection between in situ behavior and predictable behavior could be established through deformation monitoring. However, a review and evaluation of literature carried out by Edelbro (2003) and Perez (2008), regarding existing rock failure criteria and their respective parameters showed that only a few failure criteria had been formulated in terms of deformation quantities. This paper is a study which aims at identifying deformation parameters and the relation between strains at failure for tested hard rock specimens typical of Fennoscandia. The study was based on uniaxial laboratory test data and evaluated the stages and critical states of deformation for the rocks tested.
2 DEFORMATION STAGES OF BRITTLEFRACTURE OF ROCK
Multiaxial compression experiments were carried out by Bieniawski (1967) in order to study the mechanisms of brittle fracture of rock. Martin & Chandler (1994), and Eberhardt et al. (1998, 1999), amongst others, have also studied the fracture process of brittle rock. The different stages of brittle fracture which were identified and described by these researchers are presented in Table 1. The stages of deformation for one specimen of granite from Kuru in Finland are diagrammatically presented in Figure 1. The test was carried out at Luleå University of Technology. Four curves were plotted in Figure 1: (i) axial strain vs. axial stress, (ii) lateral strain vs. axial stress, (iii) axial strain vs. volumetric strain, and (iv) axial strain vs. crack volumetric strain.
(Table in full paper)
Stage I: This stage occurs during the initial phase of loading.