1、1Relationship between the Classification of Rock Surrounding Underground Chambers and the Initial DamAbstract. On the basis of the relationship between each classification index for underground chambers and the elastic wave velocity of rock mass, a corresponding relationship between the classificati
2、on of rock surrounding underground chambers and the initial damage variable is established by using the wave velocity definition of the initial damage variable of rock masses. Calculation and analysis of relevant data from a hydropower dam located in Southwest China show that the initial damage vari
3、able obtained by means of surrounding rock classification has a close relationship with that calculated by wave velocity, which verifies the rationality of the relationship of the two classification indices. This study establishes a foundation for further damage mechanics and stability analysis on t
4、he basis of surrounding rock classification. Key words: underground chamber, rock mass classification, the initial damage variation, elastic wave velocity 1. Introduction 2The classification of rock masses around underground chambers is the basis and precondition for the design, construction, and st
5、ability evaluation of underground chambers. Damage and fracture mechanics is often used to analyze the progressive deformation and destruction, which results from excavation unloading, of rock mass around underground caverns (Fabre et al. 2006; Gatelier et al. 2002). The initial damage variable of s
6、urrounding rocks must be determined to analyze these issues by means of the damage mechanics method. Rock mass damage models and their applicability to the stability of surrounding rocks have attracted much research interest (Sergei 2006;Ji et al. 2005;Zhao 1998; Budiansky B et al. 1976;Cao et al. 2
7、006). Many domestic and international scholars have investigated the dynamic classification of rock masses around underground caverns (Gong FQ et al. 2008; Zeng J et al.2007). However, limited studies have focused on the quantitative relationship between surrounding rock damage and surrounding rock
8、classification during underground cavern excavation. This study establishes the relationship between all types of classification indices and the elastic wave velocity of rock mass to link damage theory analysis with surrounding rock classification. On this basis, the initial damage variable of 3rock
9、 mass is defined by using the wave velocity and damage mechanics theory. In this way, the relationship between the classification of rock mass around underground caverns and the initial damage variable is established. This study confirms the rationality of this relationship by analyzing the relevant
10、 data from a hydropower dam located in Southwest China. This research on the relationship between surrounding rock classification and initial damage variable has great theoretical significance and engineering value in improving the damage mechanics analysis of rock mass stability on the basis of roc
11、k mass classification. 2. Relationship between the classification of rock surrounding underground chambers and the wave velocity of rock masses After the 1960s, the classification of rock masses around underground caverns eveloped rapidly at home and abroad, beginning with semi-quantitative classifi
12、cation of a single factor and eventually reaching a stage that combines quantitative description with assessment of multiple factors and indices. Currently, the following are the most common methods of classifying surrounding rock: the Q system classification as proposed by N. Barton, the geomechani
13、cs classification as proposed by Bieniawski (RMR classification), 4and the BQ classification as defined by the Standard of Engineering Rock Mass Classification. 2.1 Relationship between the Q system classification and the wave velocity of rock masses Norwegian scholar Barton et al. (1974) studied 21
14、2 tunneling cases in Scandinavia and proposed the Q value, which is also called the rock quality index, to be used in rock mass classification to represent the stability of rocks in tunnels: where RQD is the rock quality index, Jn is the fracture size, Jr is the roughness coefficient of the fracture
15、 surface, Ja is the joints and weathering variation coefficient, Jw is the reduction coefficient of the fissure water, and SRF is the reduction coefficient of stress. Equation (1) considers three factors: rock mass quality index (RQD)/Jn, which represents rock integrity; Jr/Ja, which represents the
16、fissure surface, fill characteristics, and the extent of weathering variation; Jw /SRF, which represents the reduction in rock quality resulting from all types of stress in rock mass. The rock quality index (Q) ranges from 0.001 to 1000. On the basis of the Q value, the rock mass is assigned one of
17、nine classifications, ranging from “excellent” to “terrible.” Barton obtains the relationship between the elastic p-wave 5velocity (Vp) of engineering rock mass and the rock quality index Q by means of statistics and a summary of rock engineering data taken from Norway, Sweden, Chinese mainland, and
18、 Hong Kong Special Administrative Region. This relationship is expressed as follows: Q = 10Vp - 3.5. The correspondence among rock quality index Q, elastic wave velocity, and classification are shown in Table 1. Table1 Corresponding relationship between Q and elastic wave velocity 2.2 Relationship b
19、etween RMR classification and wave velocity of rock mass Z.T. Bieniawski (1973) studied 111 engineering cases and proposed the RMR classification method, which has six basic parameters, namely, rock uniaxial compressive strength, RQD, joint spacing, joint conditions, groundwater conditions, and join
20、t orientation. Depending on the situation, each parameter is graded according to a set of criteria, and the sum of marks of each parameter is the RMR score (total score of 100 points). The rock mass is then assigned one of five classifications on the basis of the RMR value. In this study, the relati
21、onship between RMR and Q systems 6is adapted to study the relationship between RMR and rock elastic wave velocity. Different scholars have assigned empirical formulas for the RMR and Q systems for use in different conditions. To obtain a unified expression of the Q and RMR systems, R. Coling (1995)
22、utilized rock engineering data to divide Q into two types: Q and , . This result means that when the Q value is at SRF = 1, which represents rock mass under intermediate stress, the linear relationship is expressed as follows: The above-mentioned linear relationship can simulate the relationship bet
23、ween Q and RMR in many engineering cases. By substituting Equation (2) into Equations (3) and (4), we can obtain the following relationship between RMR and the elastic P wave velocity: The correspondence relationship between RMR classification and elastic wave velocity can be obtained by using Equat
24、ions (5) and (6), as shown in Tables 2 and 3. Table 2 Corresponding relationship between RMR and elastic wave velocity (SRF = 1) Table 3 Corresponding relationship between RMR and elastic wave velocity ( SRF 1) 2.3 Relationship between BQ classification and wave 7velocity of rock mass The secondary
25、classification method is used in the Standard of Engineering Rock Mass Classification (1995). The rock mass quality index (BQ) is used for preliminary classification. To revise the BQ, other factors such as natural stress, ground water, and structural plane are considered according to the characteri
26、stics of all types of engineering rock masses. A detailed classification is conducted by using the corrected BQ value. BQ can be expressed as follows: The BQ of the rock mass should be revised if the rock surrounding the underground caverns is located in an area with high natural stress and is in th
27、e presence of weak structures and groundwater, which can affect the stability of the rock mass. The modified BQ (BQ) is calculated as follows: where K1 is the correction factor affected by groundwater, K2 is the correction factor affected by weak planes, and K3 is the correction factor affected by t
28、he initial stress state. All of these factors are confirmed by the relevent tables. According to the Standard of Engineering Rock Mass Classification(1995), the Code For Design of Road Tunnel(2004), and the surrounding rock classification method of constructing railway tunnels, the relationship betw
29、een the BQ method and 8elastic wave, as well as the physical and mechanical parameters of the surrounding rock at various levels, is summed as follows: Table 4 Corresponding relationship between BQ and elastic wave velocity 3. Relationship between surrounding rock classification and the initial dama
30、ge variable The initial damage of rock, as researched by Ganigi (1976), shows that the failure strength of rock is decreased by the power function with the initial damage of the rock. As the damage variable increases, the failure strength decreases. Zhao (1998) concluded that the damage evolution of
31、 rock is determined by the initial damage variable. The rock surrounding underground chambers contains many joints and fissures (initial damage), which are the origins of potential damage development. The strength of the joint of a weak plane is less than that of rock tension. If a rock bursts becau
32、se of the underground chamber excavation and the high external ground stress, then weak planes, such as joints and fissures, will undergo the same scenario, resulting in rock depravation in that area. Connel and Budiausky (1976) investigated the relationship between the effective modulus of rock wit
33、h fissures and the 9natural elastic modulus of intact rock by using a self-consistent method and strain energy strength theory for fissures. They established the relationship between modulus and fissure density. However, fissure density is difficult to measure and estimate. Thus, Ji(2005) examined e
34、lastic waves to establish the relation equation for wave velocity and fissure density. In this manner, the damage variable of surrounding rock can be expressed in terms of wave velocity: where Vpm and Vpr are the initial rock damage and the elastic P-wave velocity, respectively. The surrounding rock
35、 damage variable responds to the degree of internal damage. Other studies have shown that the elastic wave velocity changes with the stress on the surrounding rock, which in turn responds to damage variations in the internal microfissures. The damage variable given in this paper can be an integrated
36、 response to the degradation extent of each parameter of the surrounding rock because the elastic wave velocity is closely related to the elastic constant and density of the surrounding rock, and presence of internal micro fissures. When RMR is equal to 100, no macro fissures are observed in the roc
37、k mass with elastic P-wave velocity can be equivalent to that of the intact rock. On the basis of the data 10in Table 5 and Definition (21) concerning initial damage, we can estimate the range of initial damage D0(RMR) of each rock mass by using the RMR classification. Table 5 Range of the initial d
38、amage of rock mass on the basis of the RMR classification (SRF = 1) According to Definition (9) concerning initial damage and Equation (5) concerning RMR and Vp, the relationship between the RMR index and the corresponding initial damage D0(RMR) of each rock mass in the RMR classification can be der
39、ived as follows: where In the Q system, when Q is equal to 100, no macro fissures are observed in the rock mass with elastic P-wave velocity equivalent to that of the intact rock. On the basis of Definition (9) regarding initial damage and the data in Table 2, we can estimate the range of the corres
40、ponding initial damage D0(Q) of each rock mass by using the RMR classification. Table 7 Range of initial damage of rock mass on the basis of the Q system Equations (10) and (2) can be used to derive the relationship between the RMR index and the corresponding initial damage D0 (Q) on each rock mass in the Q system:
