Key words fractured rock mass, hydro-mechanical coupling, displacement convergence criterion,discontinuous deformation analysis (discontin

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1 ),2) ( ) ( ) ( ).... TU451 A doi / IMPROVEMENTS OF DISCONTINUOUS DEFORMATION ANALYSIS AND ITS APPLICATION 1) ZHENG Chunmei,2) SUN Guofu WANG Mingbin YU Liyuan LI Yingchao (School of Civil Engineering, Ludong University, Yantai , Shandong, China) (School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan , China) (State Key Laboratory for Geomechanics & Deep Underground Engineering, China University of Mining and Technology, Xuzhou , Jiangsu, China) Abstract The DDARF (discontinuous deformation analysis for rock failure) method is improved by using the displacement convergence criterion and a program is developed for the method. Combining the discontinuous deformation analysis (DDA) and the fracture network seepage (FNS) model a hydro-mechanical coupling model is established. The effects of the deformation of the fractured rock mass on the fracture seepage and the failure characteristics of the rock mass under the hydro-mechanical coupling are studied. It is found that the main fracture plays a role of controlling the distribution of the seepage field. The water head with consideration of the coupling effect is larger than that without considering the coupling effect. Meanwhile, it is shown that the coupling helps the slope deformation and will lead to failure more easily. The program convergence criteria in the DDARF are compared with those of the laboratory tests and the engineering example. The form of the crack propagation does not change before and after the improvement. The results show that the program convergence criteria of the DDARF are effective ) ( , ) (ZR2011EL049, ZR2012EEM010) (J15LG01) (LY ). 2). zhchm2007@foxmail.com,,.., 2016, 38(3): Zheng Chunmei, Sun Guofu, Wang Mingbin, et al. Improvements of discontinuous deformation analysis and its application. Mechanics in Engineering, 2016, 38(3):

2 Key words fractured rock mass, hydro-mechanical coupling, displacement convergence criterion,discontinuous deformation analysis (discontinuous deformation analysis, DDA) Shi [1] [2-10]. [11-12] [13] (discontinuous deformation analysis for rock failure DDARF)... [14] 2. [15-17]. [18] (Louis)... [19] (Lamas). [20] [21] m i n D n i D n i D n i D n i < ε (1) ε D n i D n i D n i = ( u n i )2 + ( v n i )2 (2) D n i = (u n i )2 + (v n i )2 (3) u n i v n i i (x, y) n u n i, vn i mm 200 mm c 30 mm 50 mm α = 45 1 ( ) MPa..

第 3 期郑春梅等非连续变形分析方法的改进及应用 301 值模拟与室内试验中裂纹扩展过程的一致性说明程序计算的收敛判据是有效的. 1.2.2 算例 2 某水电站地下厂房计算模型尺寸 50 m 35 m 主厂房高 15 m 宽 10 m.

表 2 模型力学参数图 1 双裂隙布置图 (单位:mm) 材料表 1 模型力学参数材料块体虚拟节理真实节理重度/ 弹性模 (kn m 3 ) 量/GPa 泊松抗拉强凝聚力/ 内摩擦比度/ MPa MPa 角/( ) 26.5 4.2 0.20 0.6 1.0 25 0.

随着载荷的增大翼裂纹逐步向轴压方向扩展. 原生裂隙间的翼图 4 计算模型裂纹向着另一原生裂隙扩展最后形成一个局部的破坏核导致岩桥失稳. 原生裂隙①上缘翼裂纹迅速加入位移收敛准则前后洞室围岩裂纹扩展对比扩展贯通到试件顶端同时原生裂隙②的下缘翼裂如图 5 所示.

3 第 3 期郑春梅等非连续变形分析方法的改进及应用 301 值模拟与室内试验中裂纹扩展过程的一致性说明程序计算的收敛判据是有效的算例 2 某水电站地下厂房计算模型尺寸 50 m 35 m 主厂房高 15 m 宽 10 m. 模型上边界主要承受岩体自重两侧作用有水平压应力侧压力系数取为 1.0. 现模拟洞室开挖后围岩达到平衡的时间. 计算时极小值取为表 2 为计算参数图 4 为数值计算模型. 表 2 模型力学参数图 1 双裂隙布置图 (单位:mm) 材料表 1 模型力学参数材料块体虚拟节理真实节理重度/ 弹性模 (kn m 3 ) 量/GPa 泊松抗拉强凝聚力/ 内摩擦比度/ MPa MPa 角/( ) 重度/ 弹性模 (kn m 3 ) 量/GPa 泊松抗拉强比度/MPa 凝聚力/ 内摩擦 MPa 角/( ) 块体虚拟节理双裂隙试件破坏过程如图 2 所示加压后原生裂隙的端部首先起裂产生翼裂纹. 随着载荷的增大翼裂纹逐步向轴压方向扩展. 原生裂隙间的翼图 4 计算模型裂纹向着另一原生裂隙扩展最后形成一个局部的破坏核导致岩桥失稳. 原生裂隙①上缘翼裂纹迅速加入位移收敛准则前后洞室围岩裂纹扩展对比扩展贯通到试件顶端同时原生裂隙②的下缘翼裂如图 5 所示. 改进后顶板位移随时间的变化曲线如纹也迅速向下扩展翼裂纹间产生次生裂纹并继续图 6 所示. 增多和扩展试件很快失稳破坏. 朱维申等 [22] 以相似材料制作双裂隙岩体试件对试件进行双轴压缩试验试验得出的裂纹扩展过程如图 3 所示. 非连续变形的岩石断裂分析数改进前 (n = 1 000) 改进后 (n = 1 000) 图 5 洞室围岩裂纹扩展情况对比图 2 数值模拟裂纹扩展过程图 3 试验中裂纹扩展过程图 6 顶板位移随时间变化曲线

4 , j i 1, j i, a ij = i 1, j i, i. [23] N ( ) M i ( 1 ) q j (j = 1, 2,, N ) j i Q i i ( ). () N + Q i = 0 (i = 1, 2,, N) (4) q j j=1 i N N. 7 N Aq + Q = 0 P H = Q (5) q = {q 1, q 2,, q M } T (6) Q = {Q 1, Q 2,, Q N } T (7) P H A = [a ij ] N M a ij K i f = ηi γ w ( b i ) 2 12µC i (i = 1, 2, M) (8) K i f i ηi ( η i = 1 η i = 0) γ w b i µ C i. 2.2,.. i (x, y) (u, v) ( u v ) = T i D i (9) T i D i i. n. K 11 K 12 K 1n K 21 K 22 K 2n K n1 K n2 K nn KD = F (10) D 1 D 2. D n = F 1 F 2. F n (11) D i F i (i = 1, 2,, n) 6 1 i K ii K ij (i, j = 1, 2,, n) 6 6 K ii

5 3 303 i K ij (i j) i j (). i k AB A B h A h B 8 AB l α A B x y f Ax = h A sin α f Ay = h A cos α f Bx = h B sin α f By = h B cos α 8 i Π i = l 0 (f xs u i + f ys v i ) ds = [ ] D T i T T i (x A, y A ) E + D T i T T i (x B, y B ) G (12) (13) (14) l E = 3 sin α l 6 sin α h A l 3 cos α l (15) 6 cos α h B l G = 6 sin α l 3 sin α h A l 6 cos α l (16) 3 cos α h B T i u i v i. (14) A B F i = Π i (0) d ri = T T i (x A, y A ) E + T T i (x B, y B ) G (17) d ri i. (17) (11) (5) (10) -- KD = F, P H = Q (18) (18) F H ( ) P D () (18).. [20]. [ 16r 2 e = e m (1 + r) 4 ] 1 3 (19) e m (e 1 + e 2 )/2 e 1 e 2 r = e 1 /e

6 [24]. 28, 20 cm 0.4 mm. 2.9 m m () () [24] Q = 100 cm 3 /s mm mm, mm [25]

7 (1). (2). (3)... (4).. 1 Shi GH. Discontinuous deformation analysis: a new numerical model for the statics and dynamics of block system. [PhD Thesis]. Berkeley: University of California, Ke TC. Simulated testing of two dimensional heterogeneous and discontinuous rock masses using discontinuous deformation analysis. [PhD Thesis]. Berkeley: University of California, Shyu K. Nodal-based discontinuous deformation analysis. [PhD Thesis]. Berkeley: University of California, ,,.., 2014, 35(8): ,.. E :, 2009, 39(10): ,,. DDA., 2008, 27(4): Lee SC. Linear and nonlinear modeling of viscous geomaterials with DDA. [PhD Thesis]. Boulder: University of Colorado Boulder, []. :, []. :, DDA. [] , 2007, 26(4): DDARF. :, [ ]. :, ,.., 2007, 26(10): Jing LR, Ma Y, Fang ZL. Modeling of fluid flow and solid deformation for fractured rock with discontinuous deformation analysis (DDA) method. International Journal of Rock Mechanics and Mining Sciences, 2001, 38(3): ,.., 2007, 26(7): ,,.., 2013, 32(6): Kim Y-I, Amadei B, Pan E. Modeling the effect of water, excavation sequence and rock reinforcement with discontinuous deformation analysis. International Journal of Rock Mechanics and Mining Sciences, 1999, 36(7): ,. -- DDA., 2003, 22(8): DDA. [ ]. :, , 1993, 12(3): ,,.., 1998, 19(4): Louis C. Rock hydraulics//muller L ed. Rock Mechanics. Vienna Springer-Verlag, Öllös G. Examen hydrauligue de lécoulement dans des roches crevasses sur des modoèles réduits. Bull, Int Ass Sci Hydrel, 1963, 8(2) []. :, 2000 (: )

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f 2 f 2 f q 1 q 1 q 1 q 2 q 1 q n 2 f 2 f 2 f H = q 2 q 1 q 2 q 2 q 2 q n f 2 f 2 f q n q 1 q n q 2 q n q n H R n n n Hessian 2012 10 31 10 Mechanical Science and Technology for Aerosace Engineering October Vol. 31 2012 No. 10 1 2 1 2 1 2 1 2 1 300387 2 300387 Matlab /Simulink Simulink TH112 A 1003-8728 2012 10-1664-06 Dynamics