Research on Evaluation Method of Rockburst Proneness Based on Energy Principles


 The study of rockburst criterion is the key to predict whether rockburst occurs or not. First of all, based on the energy principle and taking the rock strength and overall failure criterion as the benchmark, the rockburst proneness criterion of rock mass unit under compression and tension was established. The criterion took into account the integrity factors, mechanical factors, brittleness factors and energy storage factors in the process of rockburst inoculation, and three rockburst classification thresholds (2, 11 and 110) for four grades of none, weak, moderate and severe rockburst were proposed. Second, Taking the typical rockburst disaster as examples, the rationality of the existing classical rockburst criterions and the rockburst proneness criterion proposed in this paper were tested, and the results showed that this criterion had good engineering applicability. Finally, the numerical simulation analysis of rockburst disaster in 2# diversion tunnel of Jinping II hydropower station was carried out by using this criterion. The results were basically consistent with the actual situation, which verified the accuracy and effectiveness of the rockburst proneness criterion proposed in this paper. The research results can provide reference for the evaluation and prediction of rockburst disaster in deep underground engineering.


construction. 45
At present, rock mechanics workers and engineering technicians at home and abroad have 46 carried out in-depth research on rockburst criterion and rockburst classification from theoretical 47 Where U d is the dissipated energy of the rock, which is used to form the internal damage and plastic 90 deformation of the material, as shown in the blank area surrounded by the curve in Fig. 1; U e is the 91 releasable elastic strain energy of the rock, as shown in the shadow area surrounded by the curve in 92 Fig. 1. 93 under the conditions of lithologically medium-hard to hard, good integrity, dry and high geostress. 111 At present, the rockburst criterion for underground engineering mainly considers the following 112 indicators: maximum principal stress of cavern (σ1), maximum tangential stress of cavern (σθ), radial 113 stress of cavern (σr), uniaxial compressive strength of rock (σc), tensile strength of rock (σt), elastic 114 energy index of rock (Wet), integrity coefficient of rock mass (Kv)and lateral pressure coefficient (λ), 115

etc. 116
Through in-depth analysis of existing rockburst criterions, it is known that (1) Most rockburst 117 criteria are expressed by radial stress and tangential stress (or maximum tangential stress). 118 Coordinate transformation is needed when using numerical simulation software to predict and 119 evaluate rockburst risk in underground engineering excavation process, so the application is quite   e  e  e  13  2  2  2  2  3 1 It can be seen from Eq. (7) that: (1) RPCc analysis model reflects the integrity factor (Kv), 159 mechanical factor ((σ1-σ3)σt), brittleness factor (σc/σt) and energy storage factor (U e /σ 4 c ) of rockburst 160 incubation process; (2) RPCc is the product of main stress in mathematical expression, which is easy 161 to understand, use and operate; (3) RPCc not only considers the stress state (σ1, σ2, σ3) of surrounding 162 rock and the integrity of rock mass, but also reflects the influence of rock mechanical parameters 163 (σc, σt) and deformation parameters (E, v). 164

Tension condition (σ3 < 0) 165
Tensile stress often occurs in the surrounding rock mass during excavation and unloading of 166 underground engineering, which is also a stress state leading to the overall failure of rock mass. 167 When there is at least one tensile stress in the principal stress (σi) of rock element ( Fig. 2(b)) and 168 the overall failure of rock mass occurs, the elastic strain energy is proportional to the energy release 169 rate in the direction of principal stress, and it is distributed according to the principal stress value. 170 Assuming that the energy release rate expression is: 171 By analogy with compression condition, it can be seen from Eq. (8) that the maximum energy 173 release rate occurs in the direction of the maximum tensile stress σ3, i.e 174 The energy release rate can meet the following requirements when rockburst occurs: Where Gt is the critical strain energy release rate of rockburst under tension state, which is the 178 material constant and can be determined by laboratory rock mechanics test (uniaxial tensile test). 179 Let σ3=σt and σ1=σ2=0, bring them into Eq. (10), it can be obtained by combining Eq. (2): 180 Further considering the influence of rock mass integrity coefficient (Kv) on inducing rockburst, 182 combining Eqs. (8)-(11), a rockburst proneness criterion (RPCt) based on the energy principle 183 By analogy with compression condition, it can be seen from Eq. (12) that when rock mass is 186 in tensile state, RPCt also reflects the integrity factor (Kv), mechanical factor (σ3/σc), brittleness 187 factor (σc/σt) and energy storage factor (U e /σ 2 t ) of rockburst incubation process. Considering that the probability of the boundary index of different factors reaching the 196 maximum value at the same time is small, in order to facilitate practical application, the boundary 197 indexes of RPC are set to 2, 11 and 110. Therefore, the rockburst proneness criterion and its intensity 198

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In order to further verify the rationality and superiority of the rockburst proneness criterion 202 proposed in this paper, taking rockburst disaster of typical engineering as examples (Table 3), E. 203 Hoek criterion, Russenes criterion, Erlangshan highway tunnel criterion, Gu-Tao criterion and the 204 rockburst proneness criterion proposed in this paper were tested respectively. The results were 205 compared with the actual rockburst intensity grade, as shown in It can be seen from Table 4 and Fig. 3: (1) the total number of moderate and severe rockbursts 218 determined by E. Hoek criterion, Russenes criterion and Erlangshan highway tunnel criterion is 219 relatively close, and the number of weak rockburst determined by E. Hoek criterion is slightly higher 220 than that determined by Russenes criterion and Erlangshan highway tunnel criterion; (2) the 221 rockburst grade determined by the Gu-Tao criterion is mainly concentrated in the moderate 222 rockburst, and the total number of weak and severe rockbursts is relatively close, which indicates 223 that the determination accuracy of Gu-Tao criterion is slightly lower than that of E. Hoek criterion, 224 Russenes criterion and Erlangshan highway tunnel criterion; (3) the total number of weak and 225 moderate rockbursts determined by the rockburst proneness criterion in this paper is close to the 226 actual situation, but its performance in the determination of severe rockburst grade is weak. By 227 comprehensive comparison, the accuracy of the criterion presented in this paper is obviously higher 228 than that of the other four criterions, and it is basically consistent with the actual occurrence of 229 rockburst on the whole, which has good engineering applicability. 230 In summary, the rockburst proneness criterion established in this study is of clear significance, 231 simple and practical, which can reasonably and quantitatively determine the occurrence and 232 intensity grade of rockburst geological disasters in the process of deep underground engineering 233 construction. It comprehensively considers the integrity factors, mechanical factors, brittle factors 234 and energy storage factors in the process of rockburst inoculation. This criterion is more targeted 235 for rockburst prediction and evaluation, and it has good engineering applicability. 236 Table 3 Initial data of rockburst disaster of typical engineering  Through field investigation, it is not found that there is a control structural plane in this section, and 249 the surrounding rock is fresh and complete, which is mainly T2b marble. The section size of 2 # 250 diversion tunnel is shown in Fig. 5. According to the field monitoring results, the ground stress level 251 of the tunnel section was high, which was shown in Table 5.   Table 5 Ground stress grade of 2 # headrace tunnel points is shown in Fig. 7. In the dynamic calculation, in order to make the dynamic energy of the 259 system absorb quickly and achieve convergence, Rayleigh damping was used, the minimum critical 260 damping ratio was 0.05, and the minimum center frequency was 500 Hz. The upper boundary of the

Action form of blasting load 271
Since rockburst is a complex process generated instantaneously, detonating the pre-buried 272 explosive in the cavern will instantly generate irresistible high temperature and high pressure gas, 273 which expand rapidly in the interior of the cavern. The blast shock wave generated acts on the inner 274 wall of the cavern and rapidly attenuates to stress wave. The whole process is very short and the 275 duration is only a few milliseconds. Because the explosion mechanism and its influencing factors 276 are extremely complex, it is difficult to quantitatively determine the details of the explosion process. 277 In the numerical analysis, the blasting load is often assumed to be a triangular shock wave (Zhou et    Table 6, where cm is the peak value 296 of cohesion, cr is the residual value of cohesion, φ0 is the initial value of friction angle, φm is the 297 peak value of friction angle, and ψ is the dilatancy angle. The rock lithology is assumed in the 298 numerical calculation: the rock is homogeneous, isotropic continuum, which conforms to Mohr

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The middle position of the rockburst area (near K11+037) was selected for analysis. In the 303 numerical simulation, the FISH programming language embedded in 3DEC software was used to 304 write calculation functions for Eq. (2), Eq. (7) and Eq. (12), and the change process of all 305 calculation block units was monitored. In this section, the rockburst proneness would be evaluated 306 according to the numerical simulation results and the prediction evaluation indexes. 307

Analysis of energy release evolution process 308
According to the numerical simulation results, the distribution state of elastic strain energy 309 density was shown in Fig. 8, the contour nephogram of principal stress difference was shown in Fig.  310 9, and the space-time distribution of elastic strain energy density was shown in Fig. 10. From the 311 above figure, it could be seen that the maximum principal stress difference was mostly concentrated 312 in the right spandrel, side wall and arch bottom of the cavern after excavation. According to the rock 313 mechanics theory, the energy storage limit of rock mass at the maximum principal stress difference 314 will increase significantly. Combined with the cloud map of the elastic strain energy density 315 distribution, it was found that the surrounding rock masses close to the empty surface of the cavern 316 under the disturbance of dynamic excavation had different degrees of elastic strain energy release 317 phenomenon, and the amount of elastic strain energy release gradually decreased with the increase 318 of the distance to the center of the tunnel. The elastic strain energy release of surrounding rock at 319 the right spandrel, side wall and arch bottom of the cavern was the largest, which further indicated 320 that the gentle acceleration process of rock fracture evolution around the cavern is also the process 321 of energy accumulation and dissipation in the surrounding rock. The stress of surrounding rock was highly concentrated, which increased the energy accumulation. When the storage energy of 323 surrounding rock exceeded the energy storage limit of rock mass, the excess energy was released 324 rapidly in the form of kinetic energy, resulting in rockburst or large deformation failure of rock mass. 325 The rockburst simulation was shown in Fig. 11. It could be seen from Fig. 11 that the largest 326 rockburst pit of the tunnel was located at the right side wall and spandrel of the tunnel face, which 327 was close to the field situation, and the depth of the largest rockburst pit was about 2 m, as shown 328 in Fig. 12. According to the failure shape of the tunnel, the numerical simulation results were 329 basically consistent with the shape of the actual rockburst pit (Fig. 13), which verified the rationality 330 of the prediction and evaluation of the rockburst criterion in this paper, and could meet the 331 requirements of dynamic tracking of the rockburst process.

Distribution characteristics of rock burst energy index 339
The nephogram of the boundary value distribution of rockburst proneness criterion was shown 340 in Fig. 14. From Fig. 14 Figure 1 Stress-strain relation curve of rock Rockburst location of 2# headrace tunnel    RPC thresholds of the cavern cross section (0°-360°) of the section K11+037