SCIENCE CHINA Physics, Mechanics & Astronomy Research Paper August 2011 Vol.54 No.8: 1532 1540 doi: 10.1007/s11433-011-4351-8 Application of flow driven pore-network crack model to Zipingpu reservoir and Longmenshan slip ZHU BoJing 1, LIU Chang 1,2, SHI YaoLin 1*, SUN DongSheng 3 & ZHANG Kai 4 1 Key Laboratory of Computational Geodynamics of Chinese Academy of Sciences, College of Earth Science, Graduate University of Chinese Academy of Sciences, Beijing 100049, China; 2 Laboratoire De Geologie, Ecole Normale Supérieure, 24 Rue Lhomond, 75231 Paris CEDEX 5, France; 3 Institute of Geomechanics, Chinese Academy of Geological Sciences, Beijing 100081, China; 4 Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China Received August 27, 2010; accepted February 14, 2011; published online June 14, 2011 The study has analyzed the relationship between the water-drainage sluice process of reservoir, stress triggers and shadows of earthquake and porosity variability of fault slip zone. First, the pore pressure, pressure gradient, viscous stress and Reynolds stress to reservoir-earthquake fault slip problem are analyzed, and these are un-negligible factors of the extended coulomb failure stress under ultra-high temperature and pressure condition. Second, the porosity tensor and permeability tensor are studied, the relationship between Zipingpu reservoir and Longmenshan slip has been analyzed, and the extended viscous stress and Reynolds stress as function of time and infiltration process are obtained. Last, some primary conclusions about the flow-solid coupled facture mechanism to the Zipingpu reservoir and Longmenshan slip problem are presented, which can help understand the flow-solid coupled facture mechanism of reservoir-coseismic fault slip problem. Zipingpu reservoir, 2008 Wenchuan earthquake, coulomb failure stress diffusion, pore stress diffusion, fluid flow driven pore-network crack model PACS: 91.30.Px, 91.10.Kg, 92.40.qf, 91.60.Ba 1 Introduction *Corresponding author (email: shiyl@gucas.ac.cn) A number of factors may contribute to the generation or absence of post-impounding seismicity. Increased vertical stress due to the load of the reservoir and decreased effective stress due to increased pore pressure can modify the stress regime in the reservoir region. The combined effect of increased vertical load and increased pore pressure will have the greatest tendency to increase activity in regions where the maximum compressive stress is vertical [1]. Gupta et al. [2] studied the behavior of earthquakes associated with over a dozen artificial lakes and found that the tremors were initiated or their frequency increased considerably following the lake filling and that their epicenters were mostly located within a distance of 25 km from the lakes. Based on the theory of poroelasticity established by Terzaghi [3] and Biot [4 6], Miller [7] discussed the hydrogeology of karst controls rain-triggered seismicity by channeling the watershed after intense rain fell directly into the karst network. His research shows that the instantaneous fluid pressure increases at a depth is a substantial fraction of the pressure step applied at the boundary, followed by time-dependent pore pressure increases associated with the typical linear diffusion problem. Coulomb failure [8] is used to evaluate the earthquake trigger, and the pore pressure [9 12] parts reflect the effect of reservoir closed to the earthquake fault slip. The fluid flow driven pore-network crack model [13] is a manner to explore the relationship between fluid viscous stress and rock texture and structure Science China Press and Springer-Verlag Berlin Heidelberg 2011 phys.scichina.com www.springerlink.com
Zhu B J, et al. Sci China Phys Mech Astron August (2011) Vol. 54 No. 8 1533 of earthquake fault slip under multi temporal-spatial scale at high temperature and pressure conditions. The Zipingpu key water control project is one of the most complex engineering projects in the world for it is located on the most complex earthquake fault slips zone in the world (Maximum acceleration value of seismic oscillation is equal to 0.20 g [14]). Zipingpu reservoir is located on the Longmenshan earthquake fault slip (below 2 km) and the distance between the reservoir and the 2008 Wenchuan M s 8.0 earthquake initial source is within 17 km (Figure 1). After Wenchuan earthquake, scientists focus on these fields and several mechanics are obtained [7,15 17]. Chen [17,18] analyzed the relationship between large reservoirs and seismicity and the findings by his research groups have been reported by Richard [19]. The Longmenshan fault slip of 2008 Wenchuan M s 8.0 earthquake is obtained by the GPS & InSAR inversion technique [15] (Figure 2), which is composed of two slips and the cross-wised Zipingpu reservoir zone. The relation- Figure 1 Relative position between Zipingpu reservoir and the earthquake source of Wenchuan M s 8.0 earthquake. Zipingpu reservoir [E1033018 E1033448; N310036 N310300]; Yingxiu [N305958.56; E1032921.12]. ship between the pore stress accumulation of Zipingpu reservoir and the trigging and propagation of the Longmenshan coseismic fault slip becomes very important, for its direction affects the dynamic real-time security evaluation and the monitoring of the Zipingpu key water control project. Some research studies focus on the 2D coulomb stress caused by the reservoir and its effect on the Longmenshan fault [16]. The background tectonic stress, extended pore stress, hydrostatic pressure of Zipingpu reservoir and Longmenshan slip are analyzed by using the theoretical green function solution [20]. But the natural problem is more complex (with the depth increased, the relationship between pore parts and core parts of porous media become more complicated. Micro extended viscous stress and Reynolds stress should be considered under different scale levels, and the micro fluid flow effect on the sketch of the solid can not be neglected and simplified by the classed Biot poroelasticity model [3,4]) than the one scale 2D model, and little research about the 3D coulomb stress analysis under different scales has been done because of the practical and theoretical limitations (computing time) and (3D flow driven pore-crack network theory [13], multiple scale fracture mechanics/physics theory [21 26]). In this paper, based on the previous work [13,20], the relationship between the pore stress accumulation on Zipingpu reservoir and the trigging and propagation mechanism of the Longmenshan coseismic fault slip on scales I and II [Scale I: 30.976E 31.105E, 103.45N 103.577N; Scale II: 30.7E 31.3E, 103.05N 103.76N; Scale III: 29E 33E, 101N 105N; Scale IV: IN plate and EU plate] have been studied (Figure 3), and the correlation between Zipingpu reservoir and 2008 Wenchuan M s 8.0 earthquake by the fluid flow driven pore-network crack model had been studied. 2 Basic equation In the present paper, summations from 1 to 3 over repeated lowercase, and of 1 to 7 in uppercase, basic strain equation for strain porous elastic media can be defined as 1 v 3( vu v) kk p, 2G 1 v B(1 v)(1 vu ) m 3 ( v v) 3 p, GB v v B 0 u m0 kk 2 (1 )(1 u ) (1) (2) q l p 0, (3) x l Figure 2 Relative position between Zipingpu reservoir and Longmenshan fault slip. Longmenshan fault slip zone [E103.45 E103.5767; N30.975 N31.105]. where, p, and m are represented as the total stress, pore pressure, total strain and fluid mass per unit volume of the medium. The parameters G, v, v u, m 0, 0, q l,, B are
1534 Zhu B J, et al. Sci China Phys Mech Astron August (2011) Vol. 54 No. 8 Figure 3 Multiple scale virtual model of Zipingpu reservoir/longmenshan coseismic fault slip. (a) Scale I; (b) scale II; (c) scale III; (d) relative position reservoir/slip. represented as the elastic shear modulus (same for drained (p=constant) and undrained (m=constant) conditions), the drained condition Poisson s ratio, the undrained condition Poisson s ratio, the fluid mass content in the unstressed state, mass density of the pore fluid, the mass flux rate per unit area, the permeability and constant related to drained and undrained status, respectively. The equations of motion for a homogeneous, linear elastic and isotropic medium can be defined as: f 2 2 2 j ( cp cs) ui, ij csuj, ii u j 0, (4) Gij ( PQt,,) Pij ( PQt,,) Sij ( PQt,,) PPij ( PQt,,) SS ( P, Q,) t PS ( P, Q,) t SP ( P, Q,), t (5) ij ij ij where Gij ( P, Q, t ) denote the i component of the displacement at point P due to unite impulsive force at position Q acting j direction at time t. The extended coulomb stress can be defined as: where CFS, CFS ( p ), (6) P P p, (7) p 1 3 ' 2 eij ell ij ell ij uu i j, e ij 1 u u i j, 2 xj x i u u i j 2 u m uu i j t Et, xj x i 3 x m,,, p, P,, p,,,, u i, (8) (9) (10) t, u, E are represented as extended coulomb stress, shear stress increments, internal frictional angle, background tectonic stress, extended pore stress, hydrostatic pressure, extended viscous shear force, internal hydrostatic pressure, extended
Zhu B J, et al. Sci China Phys Mech Astron August (2011) Vol. 54 No. 8 1535 viscous force, viscosity, isochoric viscosity, turbulent mean-velocity, turbulent fluctuation velocity and bulk modulus, respectively. 3 Physical model As shown in Figure 4, the Zipingpu key water control project is located on the upstream of Minjiang river, the maximum reservoir storage capacity is 1110 9 m 3, the adjustable reservoir storage capacity is 810 9 m 3, the normal impounded level is 877 m, the dam top altitude is 894 m and the dam bottom altitude is 728 m. The key water control project began on March 3, 2001, the stop flow time was on November 1, 2002, the storage time was on December 1, 2004 and completed on December 1, 2006. The total pore stress accumulation time before Wenchuan Ms 8.0 earthquake (May 12, 2008) is 3 4 years. In our physical model, we use the 15000 time steps (10 ts/d) to describe the effect of pore stress of reservoir on the Longmenshan fault slip. By using the GPS&InSAR inversion technology, the Longmenshan earthquake fault slip is divided into 673 parts. 4 Numerical process and discussion Using the Beijing Synchrotron Radiation Facility (4W1A light, Magnetic density =1.8 T), we can obtain the 2.0 micron resolution structure of the rock sample, and then based on the HHIE-LBM method [13], the anisotropic porosity tensor can be obtained (Figure 5), and if the temperature condition is 300 C and the pressure condition is 1000 MPa, the permeability can be calculated (Figure 6). From Figures 5 and 6, we can find that at ultra high temperature and pressure condition (depth around 7 km), the extended viscous stress and Reynolds stress should be considered. Figure 7 shows the relationship between the extended pore strain and the stress on Zipingpu reservoir and Longmenshan coseismic fault slip on Scale I under 20000 ts. The pore stress accumulation value level is 0.3 MPa. Figure 4 Physical model of Zipingpu reservoir and Longmenshan coseismic fault slip. (a) Mesh grid of Zipingpu reservoir; (b) physical model of Zipingpu reservoir; (c) physical model of Longmenshan fault slip; (d) detailed description of Longmenshan fault slip (composed of 673 parts).
1536 Zhu B J, et al. Sci China Phys Mech Astron August (2011) Vol. 54 No. 8 Figure 5 Anisotropic porosity of the rock sample. (a) Virtual physics for the rock sample; (b) skeleton and pores structure of virtual physics; (c) porosity value as function in the x direction; (d) porosity value as function in the y direction; (e) porosity value as function in the z direction. The relationship between the extended pore stress on Zipingpu reservoir and Longmenshan coseismic fault slip on Scale II under 20000 ts [we let storage time (Dec.1, 2004) as the first time step and one time step equals one hour] is shown in Figure 8. With the increase of water storage time, the extended stress on the Zipingpu reservoir increases, the growth gradient of the extended stress decreases with time increasing, and the extended stress converges to a fixed value (0.022 MPa) at 20000 ts point (around 2.2 years). This means that before Wenchuan earthquake the extended stress mainly caused by the extended viscous stress and Reynolds stress had reached a relatively stable state, but can not be neglected. In these scales, we find that in the penetration process, if
Zhu B J, et al. Sci China Phys Mech Astron August (2011) Vol. 54 No. 8 1537 Figure 6 Anisotropic permeability of the rock sample under ultra high temperature and pressure condition. (a) Skeleton and pore structure of the rock sample; (b) permeability of the rock sample as function of time; (c) the usage of GPU machine for the 200 pix 200 pix 200 pix model; (d) the turbulence flow of the rock sample. we define the fault slip as a fluid-saturated elastic porous media, then the vadose energy (caused by pore pressure and can flow to the fault slip tip) is variable with the undrained or drained zone, and more energy is released under drained zone than undrained zone. If the fault slip is a stable creep rupturing process, the criteria energy (strain energy function factors) must increase with the speed of faults spreading. When penetration reaches a stable stage, the fluid flow pore-network crack function becomes domain. With the time scale increasing, the micro solid-fluid interface will become weak and blurred, while the macro phenomenon, the porosity, becomes larger. The strain energy can be released to the faults process decreased with the drained spreading increasing. The reservoir loading and earthquake trigger relationship depend on fault slip geometry and character, porosity variability of surrounding geological structure and time and size scale. In the case of Zipingpu reservoir and 2008 Wenchuan earthquake, porosity and time scale are the key factors. 5 Conclusion The correlation between Zipingpu reservoir and Longmenshan fault slip is analyzed by using the time-domain hypersingular integral equation and the Lattice Boltzmann method, the permeability and porosity of rock have been calculated, and the extended coulomb stress which included pore pressure, pressure gradient, viscous stress and Reynolds stress is obtained. The results show that to Zipingpu reservoir and Longmenshan fault slip problem, the extended viscous stress and Reynolds stress cannot be neglected, for their magnitude is the same with the summary of background tectonic stress, extended pore stress and hydrostatic pressure.
1538 Zhu B J, et al. Sci China Phys Mech Astron August (2011) Vol. 54 No. 8 Figure 7 Extended pore strain and stress on Zipingpu reservoir and Longmenshan coseismic fault slip on Scale I. (a) Reservoir pore strain in the x direction; (b) reservoir pore strain in the y direction; (c) reservoir pore strain in the z direction; (d) fault slip pore strain in the x direction; (e) fault slip pore strain in the y direction; (f) fault slip pore strain in the z direction; (g) fault slip pore stress; (h) fault slip flow stream trace; (i) fault slips flow marks.
Zhu B J, et al. Sci China Phys Mech Astron August (2011) Vol. 54 No. 8 1539 Figure 8 Extended pore strain and stress on Zipingpu reservoir and Longmenshan coseismic fault slip on scale II. (a) Time steps=8000; (b) time steps=16000; (c) time steps=24000. We thank Professor YUEN DAVID. A., WU Z Y, LIN W R and LIU L B for helpful discussions and comments on the paper. The authors would like to thank the editors for their help and thank the anonymous reviewer s constructive comments. This work was supported by Project SinoProbe-07 of China, the National Natural Science Foundation of China (Grant No. D0408/4097409), the Knowledge Innovation Program of the Chinese Academy of Sciences (Grant No. KJCX2-YW-N42) and the Key Important Project of the National Natural Science Foundation of China (Grant No. 10734070). 1 Simpson D W. Seismicity changes associated with reservoir loading. Eng Geolog, 1976, 10: 123 150 2 Gupta H K, Rastogi B K, Narain H. Common features of reservoir-associated seismic activities. Bull Seismol Soc Am, 1972, 62: 481 492 3 Terzaghi K. Erdbaumechanik auf Bodenphysikalischer Grundlage. Vienna: Deuticke, 1925 4 Biot M A. General theory of three-dimensional consolidation. J Appl Phys, 1941, 12: 155 164 5 Biot M A. Theory of propagation of elastic waves in a fluid-saturated porous solid, part I: Low frequency range. J Acoust Soc Am, 1956, 28: 168 178 6 Biot M A. Theory of propagation of elastic waves in a fluid-saturated porous solid, part II: higher frequency range. J Acoust Soc Am, 1956, 28: 179 191 7 Miller S A. Note on rain-triggered earthquakes and their dependence on Karst geology. Geophys J Int, 2008, 173: 334 338 8 Jaeger J C, Cook N G, Zimmerman R. Fundamentals of Rock Mechanics. Malden: Blackwell Publishing, 2007. 513 9 Biot M A. General theory of three-dimensional consolidation. J Appl Phys, 1941, 12: 155 164 10 Biot M A. Theory of elasticity and consolidation for a porous anisotropic solid. J Appl Phys, 1955, 26: 182 185 11 Biot M A. General solutions of the equations of elasticity and consolidation for a porous material. J Appl Mech, 1956, 23: 91 96 12 Biot M A. Nonlinear and semilinear rheology of porous solids. J Geophys Res, 78: 4924 4937 13 Zhu B J, Shi Y L. Three-dimensional flow driven pore-crack networks in porous composites: Boltzmann Lattice method and hybrid hypersingular integrals. Theor Appl Fract Mech, 2010, 53: 9 41 14 Seismic Safety Evaluation of Composite Report of Zipingpu Key Water Control Project on Minjiang River in Sichuan Provience. Earthquake Prediction Research Institute of the China Seismological Bureau Earthquake Disaster Prevention Center of P.R.China, 2009 15 Shen Z K, Sun J B, Zhang P, et al. Slip maxima at fault junctions and rupturing of barriers during the 2008 Wenchuan earthquake. Nat Geosci, 2009, 2: 718 724 16 Ge S, Liu M, Lu N, et al. Did the Zipingpu Reservoir trigger the 2008 Wenchuan earthquake? Geophys Res Lett, 2008, 36: L20315 17 Chen H Q, Xu Z P, Li M. The relationship between large reservoirs and seismicity. I. Water Power Dam Const, 2010, 1: 29 33 18 Chen H Q, Xu Z P, Li M. Wenchuan earthquake and seismic safety of large Dam. J Hydrau Eng, 2008, 39: 1158 1165
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