Seepage Evolution Model of the Fractured Rock Mass under High Seepage Pressure in Dam Foundation

The seepage of the fractured rock mass in dam foundations involves complex ﬂuid-structure coupling behavior, due to practical hydrogeological conditions. In this work, the seepage characteristics of the fractured rock mass and their correlations with the structural permeable mediums are experimentally explored to reveal the cracking eﬀect on the hydromechanical properties ﬁrstly. Subsequently, the tangential and the compression creep damage constitutive models are, respectively, established by introducing a nonlinear viscoplastic body to improve the Nishihara model. Afterwards, an innovative evolution equation of the permeability coeﬃcient considering the creep damage is proposed. It can indicate the time eﬀect of the porosity, the permeability, and damage variables of the fractured rock mass under the long-term inﬁltration action of the hydraulic pressures. Ultimately, the proposed methods are applied to the seepage simulation on the dam foundation of the Longyangxia hydropower station and the signiﬁcantly increased leakage is in good agreement with the measured values during the storage period. It was further conﬁrmed that the crack expansion and penetration in the rock masses can be constantly intensiﬁed by the seepage pressures. The research results can provide a reference for engineering repair and supervision through controlling the permeability performance for long-term operations.


Introduction
Dam foundations are often located in high geostress and high hydraulic pressure environment with extremely complex hydrogeological conditions [1][2][3]. A large part of the deformation of the rock mass is primarily caused by various weak intercalations and geological faults. e mechanical evolution of the faults can obviously affect the leakage quantity, and the variation of the seepage field will change the internal fluid pressures [4][5][6]. Under the long-term seepage actions, the cracks in the fractured rock mass expand continuously and the seepage resistance decreases correspondingly to formulate low-resistance seepage channels. ey can cause the stress redistribution, weaken the mechanical strength, and damage the stability. For example, the primary cause of the Malpasset dam failure was the stress concentration in local zones in the foundation during water storage [7]. Moreover, in the Meishan reservoir, the lateral seepage pressure on the weak intercalations increased gradually during high-water level operation and caused the arch stacks to move sideways abnormally in 1962 [8].
In practical engineering projects, the seepage in the fractured rock mass involves complex fluid-structure coupling behavior [9,10] and can usually be generalized to the seepage in fractured networks [11][12][13].
e coupling behavior between the seepage field and the stress field was simulated by Zhang et al. [14] using extended finite element method. Shi and Yang [15] established a coupled flow model to simulate the seepage property and the structural evolution of the fractured rock mass. e hydromechanical effect was studied by Figueiredo et al. [16] to characterize the permeability change at 1000 m deep rock mass. Gan and Elsworth [17] presented a continuum coupled model on the stress and the fluid flow in the fractured rock mass. Liu et al. [18] developed a numerical approach to estimate the shear effects on the fluid flow in the fractured networks. Pappalardo [19] acknowledged that the cooling behavior could affect the hydraulic conductivity by the infrared thermography. Furthermore, various numerical modelling methods of the seepage flow have been proposed and implemented to reveal the complex mechanism. Ren et al. [20] proposed an equivalent permeability method for modelling the fluid flow numerically. Sundararajan and Sankaran [21] developed a groundwater flow and transport model to estimate the seepage loss of Musi basin through simulation. Zhang et al. [22] produced physical models to simulate the seepage flow behavior in rough fractures with different fractal dimensions. e aforementioned studies have promoted further development of the seepage models on the fractured rock mass.
Owing to various disturbances in dam foundations, the propagation of microcracks and joint fissures in the fractured rock mass produce strong heterogeneity and nonlinearity of flow characteristics [23][24][25][26]. Relevant experimental studies are generally subject to technical means of obtaining effective and implicit test information [27,28], including structural properties, seepage deformations, and seepage patterns. Considering the correlation verification of multidimension test methods, it is urgent to study the seepage evolution characteristics of the fractured water and the structural control effect. In addition, the seepage of the fractured rock mass owns obvious characteristics of dynamic evolution due to the transformation of the seepage pressures [29,30]. Few achievements have been made on the seepage damage effect of the foundation rock mass in controlling its permeability performance.
In this study, the seepage characteristics of the fractured rock mass and their correlations with the structural permeable mediums are firstly extracted by combining with seepage tests in Section 2. Secondly, a nonlinear viscoplastic body is newly introduced to improve the Nishihara model to establish novel creep damage constitutive models in Section 3. irdly, an innovative seepage evolution model considering the creep damage is proposed in Section 4. e proposed methods are finally validated and applied to simulate the seepage evolution of the practical dam foundation in Section 5.

Seepage Characteristics of the Fractured Rock Mass
According to triaxial compression tests of the fractured rock, the progressive failure is often accompanied by the compression, crack, expansion, and mutual intersection of internal fractures [31,32]. e permeability changes obviously with the formation of the fractured networks, owing to the expansion and the penetration of primary cracks. ey can formulate seepage channels in the conglomerate and decrease the seepage resistance, resulting in the enhancement of the permeability.

Permeability of the Soft and Hard
Rocks. Under certain constraint pressures and pore pressures, the permeability change can be obtained by rock electrohydraulic servocontrolled permeability tests (Figure 1(a)) through applying axial pressures gradually [33]. e permeability evolutions of the hard and soft rocks in the whole stress-strain process are shown in Figure 1 [34,35]. Figure 1 reflects the close relationship between the permeability and the displacement, indicating the permeability change in different stages. In the elastic stage (primary microcrack closure stage), the permeability coefficient decreases slightly with the increase of the axial stress. After entering the nonlinear strain hardening stage, the permeability coefficient gradually increases and its maximum lags behind the peak strength, due to the propagation of microcracks and the new formation of macrocracks. Subsequently, with the increase of the axial strain, the permeability coefficient may continue to increase and decrease gradually or sharply, depending on rock types, fabric, and void development. e soft rock shows strong plastic rheology after failure and the permeability attenuation range is generally large, while the permeability of the hard rock is relatively stable after failure, with a small change range. ey are both caused by the internal correlations between the rock permeability and the crack propagation.

Permeability of the Fractured Rock
Mass. e permeability measurement of the fractured rock mass can be obtained by laboratory permeability tests or in situ water pumping tests. e seepage pressure and the fractured permeability channel shape are two critical factors affecting the seepage evolution of the fractured rock mass.
(1) According to the laboratory test results (Figure 2) [34], the seepage-guiding state of the penetrated fracture channel is generally characterized by the high seepage resistance, and the seepage of the fractured network is turbulent. Under certain seepage pressures, the seepage velocity decreases with the increase of the seepage channel width, while the seepage pressure along the fractured network gradually decreases with the increase of the seepage distance. ey indicate that the decrease of the seepage pressure and the increase of the seepage resistance are correlated and can be transformed.
(2) In in situ water pumping tests [34,35], the selected sections include the normal fault zone, the reverse fault zone, and the unloading disturbance zone. e dual-porosity seepage method is taken to test the correlations of the exerted water pressures and the flow duration change under high seepage pressures. e whole process of the rock mass reaching the conduction seepage state is shown in Figure 3. e permeability primarily depends on structural planes, that is, the permeability and mechanical characteristics of the fractures change synchronously. Meanwhile, the mechanical, physical, and chemical effects of the internal water in the fractures, microcracks, and rock pores can decrease the structural strength. Moreover, the additional seepage volume force will also change the rock mass displacement and adjust the internal stress states. e in situ test results can indicate the permeability of the rock masses in practical geological conditions. As shown in Figure 3, the seepage evolution and the structural control effect can be regarded as the essential basis for evaluating the permeability and antiseepage failure strength of the fractured rock masses.

Creep Damage Model of the Fractured Rock Mass
In the dam foundations, the joints, fissures, and gaps are not only the migration channels of the groundwater but also the primary mediums of the foundation deformation. e displacement increases with time under continuous loads [36]. Hence, the interior fluid flow is mainly controlled by the structural properties and the connectivity of the fractured networks. e test results of the granite foundation of the Huangdeng Dam are shown in Figure 4 [37], including the initial strain, as well as the steady and accelerated creep strain under different confining pressures. In Figure 4(a), the irreversible plastic deformation became clearer with the increase of the stress levels and the accumulation creep effect, indicating that the internal structure adjustment is more severe under the high axial stress levels. When the stress levels reached 100 MPa and 120 MPa, respectively, the creep failure occurred due to the damage accumulation. In Figure 4(b), under the confining stresses of 2 MPa and 6 MPa, the seepage flow rates decreased remarkably, due to the variations of the fractures and pores under the initial loading, and they became stable gradually after 0.21 h and 0.44 h, respectively.
Under the long-term infiltration action of high hydraulic pressures, the foundation creep leads to certain changes in microcracks of the rock mass and geometric shapes of the  Advances in Civil Engineering 3 structural planes in the faults. ey can affect the hydraulic conductivity and change the seepage laws. e creep effect can be simulated numerically combining with the bionic algorithms [38]. On the contrary, the change of the seepage field can cause the variation of the stress field and the creep of the dam foundation accordingly. As shown in Figure 4, the creep displacement finally tends to be stable when the shear load is small. It can be assumed that the fractured rock mass will not be damaged in the elastic stage and the damage only occurs after entering the viscoplastic stage. Karalar and Çavuşli [39,40] simulated the creep settlements of the Ilısu concrete faced rockfill dam and the nonlinear seismic behaviors of the Boyabat concrete gravity dam with special viscoplastic models using the FLAC 3D software based on the finite difference method. erefore, the creep damage model should contain the stress-strain constitutive equation and the damage evolution equation [41,42]. Because the creep damage of the fractured rock mass can lead to stiffness deteriorating and strength weakening, the establishment of the damage function and the yield function should consider the damage evolution.

Creep Damage Function.
e increase of the viscoplastic creep displacement is accompanied by the damage accumulation in Figure 4  Advances in Civil Engineering 5 variables should be firstly established to indicate the creep damage. According to the second law of thermodynamics, it is a function of the damage dissipation potential, defined as follows: where I is the unit matrix, B and n are material parameters, Y 0 is the initial dissipated energy, and Y is the total dissipated energy after the creep damage. Due to the functional relationship between the damage dissipation energy and the tangential plastic displacement, the elastic-plastic tangential damage D τ and the normal damage D v are where κ, R, κ s , and R s are material parameters and ζ D is the plastic shear displacement.
Assuming that the shear stress in the complete damage is τ c and the normal displacement is v c , the following equation can be obtained: where τ a and v a are the actual shear stress and the normal displacement, respectively; τ i is the shear stress without considering the damage. Equation (3) is consistent with the elastic-plastic damage function. Because there is a functional relationship between the damage dissipation energy and its plastic work accumulation, the functional relationship between the creep damage dissipation energy and the viscoplastic displacement can be constructed, regardless of the normal displacement. Namely, where ω vp � (du ′ vp du ′ vp + dv vp dv ′ vp ) 1/2 ; du ′ vp and dv ′ vp are the viscoplastic displacement increments in the local axes of x ′ and y ′ , respectively; a ′ and b ′ are the material parameters.
Assuming that the tangential damage is isotropic, without original damage, the evolution function of the tangential creep damage and the normal creep damage in the foundation faults can be defined as follows: where a, b, c, and d are material parameters. According to equation (5), the tangential and normal damage degrees are both equal to 0 when the viscoplastic displacement is 0, while they are nearly 1.0 when the fractured rock mass is completely damaged. e friction coefficient of the fractured rock mass changes slightly after the shear damage and is 0.95-1-fold of the original. When the cohesion almost disappears completely, only 0.1-0.2-fold of the original is preserved. e shear creep damage yield function is where μ is the friction coefficient; σ n is the normal stress (the positive value represents the tensile stress and the compressive stress otherwise); c is the cohesion; α is the damage function: α � 1 − D τ . For the undamaged rock mass, D τ � 0 and α � 1; consequently, f � τ + μσ n − c, the traditional Mohr-Coulomb yield criterion; with the increase of the creep displacement, D τ increases, whereas α decreases until the rock mass is completely damaged; that is, α � 0 and f � τ + μσ n .

Creep
where D 0 ijkl is the stiffness tensor, _ σ ij is the stress tensor rate, _ ε kl is the total strain rate, and _ ε vp kl is the viscous strain rate. According to the equivalent strain hypothesis, the viscoelastic-plastic damage constitutive equation can be deduced from equation (7), replacing the apparent stress by the effective stress.
Assuming that the tangential elastic stiffness coefficient is k i x′ � k i y′ � k i s under the positive stress σ n (x ′ and y ′ are mutually perpendicular axes parallel to the structural planes) and that k c s remains in the complete damage condition, the tangential elastic stiffness coefficient in the evolution is defined as follows: According to equation (8), the elastic strain rate can be deduced.
where C 0 ijkl is the flexibility tensor. When C 0 ijkl is replaced by the flexibility tensor C 0− d ijkl of the damaged medium and the effective stress is replaced by the apparent stress σ kl , the following equation can be obtained: e elastic strain rate for the shear creep damage is where j can be x′ or y′.

Advances in Civil Engineering
When the shear stress is small in the fractured rock mass, the shear creep deformation tends to be stable, but the shear deformation after unloading is plastic and does not decrease with time, due to the relative slip and dislocation during the creep development. e tangential creep damage equation can be deduced by the model shown in Figure 5, through improving the Nishihara model with a nonlinear viscoplastic body. e elastic body simulates the instantaneous elastic deformation, the Kelvin body simulates the decaying creep deformation, the plastic body simulates the plastic yield, and the viscous body simulates the irreversible creep. e viscoelastic strain rate can be got according to the equivalent strain assumption.
where τ j is the effective shear stress: e viscoelastic strain can be got as follows: When the yielding phenomenon occurs, the plastic potential function Q should be introduced: where c is the flow coefficient; For the creep model shown in Figure 5, c � 1/η s , where η s is the viscosity coefficient after the creep yield. e associated flow rule is adopted.
When τ x′ and τ y′ are constants and f � (τ 2 x ′ + τ 2 y ′ ) 1/2 +μσ z′ − (1 − D τ )c > 0, σ z′ is constant and z ′ is the axis perpendicular to the structural plane. With the accumulation of the creep damage, f and _ c vp will increase, indicating the creep acceleration.
On this basis, the tangential creep damage constitutive equation can be deduced.
Influenced by the pores in the fractured rock mass, the significant compaction can be produced under the normal force, that is, the instantaneous elastic deformation occurs first, and then the creep rate decreases, and finally the creep deformation tends to be stable. Most of the normal compression deformation cannot be recovered after unloading. e attenuation creep characteristics along the normal direction can be simulated by the model shown in Figure 6. e elastic body reflects the instantaneous deformation, the Kelvin body reflects the decay creep and the hysteresis recovery deformation after unloading, and the unrecoverable creep can be indicated by the viscous body. e normal displacement can be defined as where the viscous displacement is In Figure 6, in addition to the instantaneous recovery during unloading, the hysteresis recovery time is actually determined by the two viscous bodies. e normal compression creep damage constitutive equation is

Seepage Evolution Model considering the Creep Damage
Generally speaking, the seepage in the fractured rock mass conforms to Darcy's law, and the permeability coefficient is a critical index. e relationship between the porosity, the permeability, and damage variables is shown in Figure 7 [43], where β is related to the moisture content and the temperature. e permeability gradually increases with the Advances in Civil Engineering damage accumulation and tends to be stable when the dominant penetrating pores are formed. Most previous porous media models assume that the porosity and the permeability coefficients are material constants independent of time. However, the gradual damage of the foundation rock mass (including the grouting curtain rock mass) will greatly affect the seepage evolution. Here, the influence of the creep damage on the permeability is used to characterize the increase of the hydraulic conductivity, which is primarily caused by the spatial change of the water flow inside the filling. e damage of the grouting curtain rock mass is used to characterize the degradation of its antiseepage function. Figure 8, the lengths of three sides of a damaged unit are dx 1 , dx 2 , and dx 3 , and the anisotropic damage characteristics can be indicated by the damage principal value. Damage variables are defined as

Evolution Equation of the Permeability Coefficient. As shown in
where D i (i � 1, 2, 3) is the primary damage variable; ds * i is the reduction area of the section surface dx i dx k , caused by the porosity variation. e relationship between the porosity n and the damage variable D is For isotropic materials, D 1 � D 2 � D 3 � D and n � D 3/2 , the relationship between the change rate of the porosity and the damage developing rate is According to equation (23), the porosity evolution can be described in view of the continuum damage mechanics due to the quantitative relationship between n and D. Assuming that the permeability coefficient depends on the infilling properties, regarded as the porous rock, the isotropous permeability coefficient can be defined as where μ is the viscosity coefficient, d is the average size of solid particles, and n is the porosity of the infillings.
Due to the variation of the porosity n along the depth z, where n � n(z), the permeability coefficient can be erefore, the relation equations of the permeability coefficient, the damage variable, and their change rates are In view of the permeability evolution of the fractured rock mass, with respect to the time t, the above variables can be transformed as Equations (30) and (31) are evolution equations of the permeability coefficient represented by D and _ D. When D � 0 and k(z, t) � 0, the rock mass is impervious and the porosity is n(t, z) � 0. e initial damage is unavoidable in practical bedrocks with certain permeability. e grouting curtain will lose the impervious effectiveness when its permeability coefficient increases to that of the bedrocks, D < 1 for this condition.

Numerical Simulation of the Seepage Evolution.
e anisotropy equivalent permeability coefficient tensor should be known in advance in the numerical simulation. For infinitely extended and regularly arranged structural planes of the foundation faults, the equivalent permeability tensor is where m is the grouping number of cracks; b l is the equivalent hydraulic gap width of the lth group of fractures; S l is the spacing of cracks; δ ij is the Kronecker symbol; n l i (i � 1, 2, 3) is the cosine along the normal direction; μ is the kinematic viscosity coefficient.
If the viscous displacement is equivalent to an instantaneous stress increment, the equivalent stress increment of the viscous strain ε v kl will be Let K x′ , K y′ , and K z′ be principal permeability coefficients of the permeability coefficient tensor. e effective principal stresses σ s x ′ , σ s y ′ , and σ s z ′ along the penetration principal axes can be obtained from the total stress σ ij + Δσ v ij . According to the relationship between the permeability coefficient tensor and the stress K � K 0 e λσ , the permeability coefficient under continuous loading is where λ is an influence coefficient, determined by test results. e rotation matrix between the infiltration principal axes and the global coordinates is recorded as [T]. e permeability coefficient tensor is Advances in Civil Engineering e seepage motion equation for the fractured rock mass is where K ij,t is the permeability tensor after the creep damage, deduced by equations (34) and (35); h c is the water head in continuous rock mass. For 8-node isoparametric element, the governing equation is where the component of e seepage influence of the fractured rock mass on its stress is considered as where c w is the bulk density of water; F → s is the hydrostatic pressure, and its effect can be equivalent by an effective stress; F → d is the hydrodynamic pressure, considered as an external load in the calculation. e equilibrium equation of the microelement considering the seepage is where c r is the saturated bulk density of rock; h is the total water head.
Combining the stress-strain constitutive equation and the geometric equation, the equilibrium equations expressed by the displacement component and the water head are where G � E/2(1 + υ) is the shear modulus; ∇ 2 � (z 2 /zx 2 ) + (z 2 /zy 2 ) + (z 2 /zz 2 ) is the Laplace operator; ε v � ε x + ε y + ε z � (zδ x /zx) + (zδ y /zy) + (zδ z /zz) is the volumetric strain; X 0 , Y 0 , and Z 0 are equivalent volume forces caused by the initial strain ε 0 . e equilibrium equation of the whole unit matrix derived from equation (41) is where F 1 e is the joint force caused by external loads; F 0 e is the joint force caused by the initial strain; [K ′ ] e is the coupling matrix of the seepage and stress.

Validation and Application
e Longyangxia hydropower station is the first large-scale reservoir in the upper reaches of the Yellow River, with area of 383 km 2 and storage capacity of 24.7 billion m 3 . It is composed of main dam, auxiliary dam, and discharge structures (shown in Figure 9). Dam concrete began to be poured in June 1982, and the diversion tunnel was put down to store water on October 15, 1986. e foundation elevation is 2432 m, the dam crest elevation is 2610 m, the maximum dam height is 178 m, the dam length is 1227 m (including the main dam length of 396 m), the dam crest width is 23.5 m, and the maximum bottom width is 80 m. e dam foundation is granodiorite with hard lithology. e dam abutment faults develop well through complex geotectonic movement and the main faults are shown in Figure 10. Most of the NE-trending faults are filled with wide quartzite veins and form altered rock belts, among which the larger ones are the F 120 fault and the A 2 quartzite, located at the right bank. e F 120 fault locates in the deep part near the dam abutment, with width of 2 m∼6 m and poor behavior, and its strike is nearly orthogonal to the thrust direction of the dam. e filled mylonite and breccia are not very continuous, but there is a fully and strongly weathered altered rock zone with an average thickness of 1.2 cm. e A 2 quartzite has a pulse width of 5 m∼10 m. Its NE-trending vertical fractures and nearly horizontal fractures develop well, with strong water permeability. e F 120 + A 2 affected zone has several to tens of centimeters of intercalated mud containing breccia and detritus, which are dense and impervious to the leakage water. However, the fractured rock mass in the F 120 + A 2 zone constitutes a network-like seepage channel with strong permeability, and the seepage damage has always been in progress under the high hydraulic pressures. e reservoir water level change is shown in Figure 11. Since 1986, the water level had never reached the design water level of 2600 m during 27 years of operation, but it rose continuously in the flood season of 2005 from 2558.70 m on April 26th to 2597.62 m on November 19th. As shown in Figure 11, the leakage at the F 120 + A 2 fault increased obviously and the monitoring leakage at 2463 m elevation increased by 252.7 mL/s during the water rising period.

Validation by the 2D Model
Simulation. An impervious curtain was formed in the fractured rock mass of the dam foundation after grouting, which could prolong the seepage path and reduce the seepage pressure. However, the curtain rock mass was gradually damaged under the long-term action of the stress field, the temperature field, and the North H u a n g r iv e r  . e model range is as follows: the length near the upstream gravity pier is 10 times of the curtain depth, the length near the downstream gravity pier is 3 times, and it is 10 times along the depth. Displacement-pore pressure quadrilateral coupling element is used for modelling. Convergence tests have been implemented to determine the number of elements and nodes: 57131 coupling elements and 57624 nodes in total.
rough geological prospecting, the permeability coefficient of the layered fault decreases along the depth. According to the GB 50487-2008 (code for engineering geological investigation of water resources and hydropower), the permeability coefficient range is 10 − 4 ≤ k < 10 − 2 m/s. In this study, the F 120 + A 2 fault is divided into ten layers of rock 1-rock 10 (shown in Figure 12(b)) and the main parameters are listed in Table 1. e permeability coefficients are distributed as an exponential function with depth, as shown in Figure 13. e proposed methods are used to study the variation laws of the seepage field of the dam foundation. When the damage variables of the F 120 + A 2 fault at different depths are 0.10-0.55, the corresponding increment distributions of the permeability coefficient and the rock porosity are shown in Figure 14.
ey all increase gradually when the damage continues to develop, and they decrease along the rock depth, due to the rock mass confining pressures.
Take 16 groups of calculating conditions for illustration, where the impervious curtain rock mass damage is 0.1-0.84, respectively, with the upstream normal water level of 2600 m and the downstream water level of 2450 m. According to equations (28) and (30), when different damage variables are taken for the curtain rock mass, corresponding curtain porosities and relative coefficients (the ratio of the curtain rock mass permeability coefficient to the first rock stratum permeability coefficient) are shown in Figure 15. e piezometer head values H 2 at a typical point behind the curtain and corresponding osmotic pressure coefficient α 2 both increase gradually. When the damage degree reaches 0.84, the seepage control of the curtain rock mass can be considered completely lost, since the relative coefficient equals 1.
e variations of the pore water pressure in the exposed local area of the downstream slope under different damage degrees are shown in Figure 16. With the increase of the damage degree, the saturation line of the exposed local area gradually rises, indicating that the impervious curtain gradually weakens and also verifies the effectiveness of the proposed methods.

Application on the 3D Model Simulation.
According to the distribution of the main faults in Figure 10, the 3D finite element model is established, as shown in Figure 17, including the main boundary range that affects the seepage behavior. e model range is 1 time the dam height on the left and right banks, 761 m in total, and the upstream and downstream length is 613 m. e model simulates the arch dam, the foundation rock mass, main faults, and antiseepage curtain, especially the F 120 + A 2 fault and the sandwiched mud. After convergence tests, there are 27,291 nodes and 24,631 elements. e simulation of the seepage field primarily considers the following boundary conditions. (1) Interception boundary of the regional basement: the foundation depth of the 3D model is 314.8 m, which is 2 times the curtain depth and it is treated as an impervious boundary condition. (2) e upstream and downstream interception boundary of the dam located area is treated as an impervious boundary.  boundary of the two banks: the distribution of the groundwater is simulated with the measured data of groundwater level holes ( Figure 10) to obtain the calculation boundary. e water head on November 19, 2005, is selected for the simulation. e permeability coefficient values of each region are listed in Table 2.
In order to obtain the leakage through the F 120 + A 2   e results and corresponding measured data are listed in Table 3.
e calculated results at typical elevations significantly increase during the rise of the reservoir water level and are in good agreement with the measured values. With the increase of the permeability coefficient, the F 120 + A 2 fault becomes the main leakage channel, and the grouted curtain has  Advances in Civil Engineering 13 significant effect to reduce the seepage water head. e results also indicate that the water inflow rate is primarily affected by both the hydraulic conductivity and induced microcracks of the damage fault during the storage period. Once the curtain fails, the water level at each measured pore will become higher and the corresponding leakage amount will also increase obviously.
According to the simulated and measured results, the seepage of the dam foundation on the right bank has a remarkable correlation with the change of the reservoir, but there has not been a persistent increase phenomenon. Namely, the seepage behavior has not deteriorated, and it is not necessary to repair the curtain temporarily. Because the high seepage pressures will gradually increase the damage of fractured rock mass, it is also suggested that the monitoring of the fault leakage should be paid special attention during the future operation, especially the high reservoir water period. If necessary, the drainage facilities of the dam foundation should be newly added to reduce the seepage pressure and ensure the safe operation of the dam.

Conclusions
e mechanical characteristics of the fractured rock mass in seepage fields and the interaction mechanism of water-rock are critical for evaluation of the instability of dam foundations and even large-scale geological disasters. In this work, the creep damage and its effect on the permeability evolution are investigated combining with multiple test evidences. e permeability of the fractured rock mass can significantly increase with the growth and coalescence of microcracks under certain seepage pressures. Hence, the creep damage constitutive models are established to indicate the strength weakening under continuous loads. e evolution equation of the permeability coefficient is furtherly constructed with the crack tensor to characterize the mechanical behavior under the seepage-compression and shear action. e proposed approaches are applied to the Longyangxia dam and the simulated results agree well with the measured values, indicating that the presented model can describe the permeability variation of the F 120 + A 2 fault. It was further confirmed that the seepage pressures can intensify the crack expansion and penetration in the rock masses and may lead to the gradual failure of the foundation. As the leakage behavior of dam foundations is constantly changing due to the transformation of the seepage pressures, compared to preexisting models, the presented microcrack-based creep damage and seepage coupled method is capable of appraising the fracturing evolution and the leakage variation in the fractured rock mass of practical dam foundations. e research results can also provide a reference for engineering repair and supervision through controlling the permeability performance. For the future work, the criteria for judging the change of the seepage behavior of dam foundations and the early warning indicators need to be further studied for detecting the potential dangers in time.

Data Availability
All data used in this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that there are no known conflicts of interest.