Article A New Approach to Permeability Inversion of Fractured Rock Masses and Its Application

Lei Gan 1,2,* , Guanyun Chen 2 and Zhenzhong Shen 1,*

1 College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, China 2 Department of Civil and Environmental Engineering, Pennsylvania State University, University Park, PA 16802, USA; [email protected] * Correspondence: [email protected] (L.G.); [email protected] (Z.S.); Tel.: +86-139-1380-1656 (L.G.); +86-138-1399-8232 (Z.S.)  Received: 25 January 2020; Accepted: 5 March 2020; Published: 7 March 2020 

Abstract: This paper presents a new seepage inversion technique to predict the permeability coefficient of the rock mass with developed fracture or fault. With the measured data of flow and water head of boreholes, the permeability coefficient of the rock masses near the boreholes are obtained by inverse calculation on the basis of unsteady seepage tests. Then, a flexible tolerance method is proposed to invert the permeability coefficient of rock masses in different zones of the reservoir area. This comprehensive inversion analysis method is applied in one actual project of the water supply reservoir. The equivalent permeability coefficient of the rock masses in the range of 0 m to 16.0 m below the surface near the dam axis on the left bank of the mountain is 1.12 10 3 cm/s. × − The root mean squared error and coefficient of determination of the measured and calculated values are 1.33 10 4 m3/s and 0.9976 m3/s, respectively. The rock masses in the reservoir site area have × − high permeability. The groundwater level in the junction area and the mountains on both sides of Shangmo reservoir is low, and the hydraulic gradient is small. The maximum error between the calculated value of the groundwater level and the measured values is 0.41 m, and the relative error − is 4.36%. The recommended anti-seepage scheme can effectively solve the problem of large leakage − in the reservoir area. The results show that the innovative approach is appropriate for the seepage analysis of the field with the fractured rock masses and more meaningful from an engineering point of view.

Keywords: seepageinversion; unsteadyseepagetest; borehole; fracturedrockmass; permeabilitycoefficient

1. Introduction Seepage generally indicates the flow of water through the connected pores or fissures under an active pressure gradient. Fractures influence the seepage and stability of rock masses [1]. The deformation and stability of hydraulic engineering, such as dam , dam slope, underground plant, and , are significantly affected by their seepage activities [2–4]. Seepage analysis and control technology are closely related to saturated-unsaturated seepage field and have a strong influence on the safety of the hydraulic structures and rock masses at the dam site [5–7]. Seepage field analysis and flow prediction are the two main contents of anti-seepage effect evaluation of hydraulic engineering. The equivalent continuous medium model is widely used for numerical analysis of engineering [8,9]. The model simulates discontinuous fractured rock mass as continuous permeable medium, and generalizes the distribution characteristics of fractures. The seepage anisotropy of fractured rock mass is reflected by its permeability tensor. However, the determination of the permeability coefficient or tensor is the premise for numerical analysis of seepage problems using an equivalent continuous model [10,11].

Water 2020, 12, 734; doi:10.3390/w12030734 www.mdpi.com/journal/water Water 2020, 12, 734 2 of 17

Currently, the most direct method to determine the permeability coefficient of fractured rock mass is the field measurement method based on statistics and cubic law [10,12]. This method is simple, but it is difficult to obtain representative fracture parameters by outcrop measurement or borehole measurement. The permeability parameters of the are obtained by an analytical or a semi-analytical method on the basis of the water pressure test [13,14]. The cross-hole tests and isotopic tracer methods are developed to determine the permeability tensor of the rock masses [15–18]. This permeability tensor can only represent the seepage characteristics of medium near the test area. In recent decades, the inversion methods, such as the Pulse Spectrum method, the Numerical Optimization method, the Artificial Neural Network method (ANN), and the Genetic Algorithm (GA), are widely used in the seepage parameters inversion of fractured rock masses [19–22]. He et al. (2011) proposed a new approach to determine the equivalent permeability tensor of fractured rock masses by combining the geological method, the packer test method, and ANN [10]. Ren et al. (2016) applied the flexible tolerance inversion method to obtain the seepage parameters of rock masses and faults in the dam foundation of the Maerdang dam [23]. Existing research is usually based on the field water pressure test to calculate the permeability parameters of the rock masses near the test area, but its determination object is usually hard or semi-hard rock mass [24,25]. Scholars have also adopted the stable seepage theory to assess the seepage parameters of the rock masses by an inversion method on the basis of the groundwater level monitoring data. However, for the rock strata with extremely developed fissures, fault fracture zones, or , the stability of field water pressure test is poor [26]. Even if the water pump reaches the maximum water supply capacity of 100 L/min and shortens the length of the test section to 1.5 m, water cannot fill the test section. The pressure value in the hole is always zero. The permeability of this strata is greater 3 than 10− cm/s, which exceeds the range of the Lugeon value measured by the test equipment. In view of this kind of rock strata with high permeability, we attempt to propose a back-analysis method to determine the equivalent permeability parameters of rock masses near the test boreholes. The main objective of this paper is, based on the equivalent continuum model, to propose a comprehensive back analysis approach to determine the seepage parameters of the rock masses with the developed fractures or fault fracture zone. First, based on the measured data of the flow rate and water level in the borehole during the unstable seepage period of the water pressure test, a three-dimensional seepage analysis model of the borehole and surrounding rock masses is established to invert the the equivalent permeability coefficients of the rock masses around the borehole by using the unstable seepage calculation theory. Next, a three-dimensional seepage finite element model of reservoir site area in a natural period is modelling, and the equivalent permeability coefficients of rock masses in each zone of the whole reservoir site area is obtained by the flexible tolerance method. Lastly, the proposed method is applied to evaluate the seepage control effect of the recommended anti-seepage scheme for the Shangmo water supply project.

2. Mathematical Model Assuming that seepage in unsaturated obeys generalized Darcy’s law, and the tensor is introduced to describe the permeability of rock and soil. The basic differential equation for the heterogeneous anisotropic saturation-unsaturated soil seepage is written as follows [23]. ! ∂ s ∂hc ∂hc kijkr(hc) + ki3kr(hc) f = (C(hc) + βSs) , (1) ∂xi ∂xj − ∂t

s where xi and xj are the coordinates (i.e., i = 1, 2, 3), kij is the saturated hydraulic conductivity tensor (m/s), kr is the hydraulic conductivity, 0 < kr < 1, and kr = 1 represent the unsaturated and saturated s zone, respectively, hc is the pressure head (m), ki3 is the saturated hydraulic conductivity (m/s), j = 3, f is the source and sink (m3/s), which indicates whether there is an external injected flow (source) or outflow flow (sink) in the seepage calculation area, β is a constant, where β = 0 in the unsaturated zone, Water 2020, 12, x FOR PEER REVIEW 3 of 17

(m/s), j = 3, f is the source and sink (m3/s), which indicates whether there is an external injected flow (source) or outflow flow (sink) in the seepage calculation area, β is a constant, where β = 0 in the β −1 unsaturated zone, and = 1 in the saturated zone, and Ss is the elastic water storage rate (m ), which represents the amount of water released by saturated soil per unit volume due to the Watercompression2020, 12, 734 (expansion) of soil and expansion (compression) of water when a unit head is lowered3 of 17 (raised). Ss is a constant in the saturated zone and zero in the unsaturated zone. C(hc ) is the specific water capacity, and C = 0 in the saturated zone, in the unsaturated zone,1 C(hc ) , can be solved and β = 1 in the saturated zone, and Ss is the elastic water storage rate (m− ), which represents the amountas follows. of water released by saturated soil per unit volume due to the compression (expansion) of soil ∂θ − 1/ n−2 and expansion (compression)C(h of) = water= whenα(θ − aθ unit )()()()n − head1 αh isn lowered1()1+ αh (raised).n Ss is a constant in the c ∂ r s c c , (2) saturated zone and zero in the unsaturatedhc zone. C(hc) is the specific water capacity, and C = 0 in the saturatedθ zone, in the unsaturated zone, C(hc),θ can be solved as follows. α where s is the saturated , r is the residual water content, and m are = − < < empirical fitting parameters, and∂θ m 1 1/ n and 0 m n1 1 are satisfied.n1/ n 2 C(hc) = = α(θr θs)(n 1)(αhc) − 1 + (αhc) − , (2) The definite solution condition∂hc used− for solving− Equation (1) includes the initial condition and boundary conditions. whereTheθs isinitial the saturated condition water is expressed content, asθ rEquationis the residual (3) shown water below. content, α and m are empirical fitting parameters, and m = 1 1/n and 0 < m < 1 are satisfied. − h ()(x , 0 = h x , t ), i = 1, 2, 3 , The definite solution condition usedc fori solvingc i Equation0 (1) includes the initial condition and(3) boundaryThe boundary conditions. conditions can be expressed as the formulas below. The initial condition is expressed= as Equation (3) shown below. hc (xi ,t) Γ hc1 (xi ,t)  1 h (x , 0) = h (x , t ), i = 1, 2, 3, (3)   c i ∂h c i 0 −  k s k ()h c + k s k ()h n = q   ij r c ∂x i3 r c  i n  j  Γ The boundary conditions can be expressed as the formulas2 below.     ∂  , (4)  h −(x , ts) ()= hhc(x+ , ts) () ≥ =  c ikij k rΓ hc c1 iki3kr hc ni 0 and hc Γ 0   1 ∂  3   x j   s ∂hc s  Γ   k kr(hc) + k kr(hc) ni =3 qn  − ij ∂xj i3    ∂  Γ2  s h s   − s ()∂hc c +s () = < , (4)   k kkij(khr )hc + k ki3(khr )hcn ni 0 andqθ andh h=c Γ0 0  ij r c ∂x ∂ i3 r c i c Γ3 4  − j x j ≥ |    Γ3 Γ4     ks k (h ) ∂hc + ks k (h ) n = q and h < 0 n  ij r c ∂x i3 r c i θ t c Γ4 Γ where i is the boundary− surface normalj direction cosine,Γ4 0 is the| initial time, 1 is the known Γ Γ Γ head boundary, 2 is the known flow boundary, 3 is the saturation overflow boundary, 4 is where ni is the boundary surface normal direction cosine, t0 is the initial time, Γ1 is the known head the unsaturated zone overflow boundary, qn is the normal flow, and qθ is the rainfall boundary, Γ2 is the known flow boundary, Γ3 is the saturation overflow boundary, Γ4 is the unsaturated flow. zone overflow boundary, qn is the normal flow, and qθ is the rainfall infiltration flow. TakeTake an an earth earth dam dam as anas example.an example. The The seepage seepage boundary boundary diagram diagram is shown is shown in Figure in 1Figure. The known 1. The known water head boundaries, BC, CD, HI, and IJ, belong to Γ . Boundary AB, AK, and JK are water head boundaries, BC, CD, HI, and IJ, belong to Γ1. Boundary1 AB, AK, and JK are impermeable Γ boundariesimpermeable and boundaries belong to Γ and2. DG belong and GH to are2 . takenDG and as the GH infiltration are taken boundaryas the infiltration and seepage boundary boundary, and Γ respectively,seepage boundary, both of respectively, which are classified both of which to Γ3. are Boundary classified DE, to EF,3 . and Boundary FG are DE, the EF, unsaturated and FG are zone the Γ overflowunsaturated boundaries zone overflowΓ4. boundaries 4 .

Figure 1. Seepage boundary conditions of a mean earth dam. Figure 1. Seepage boundary conditions of a mean earth dam. 3. Back Analysis Method

3.1. Objective Function of Back Analysis In many practical projects, the permeability coefficient is usually obtained from water pressure test data used for back analysis. The residual of a finite element calculation head and observation head Water 2020, 12, 734 4 of 17 is the weighted sum of squares in the objective function of a parameter inverse optimization problem, which is used to find matching parameters closer to the actual basic parameters. The objective function adopted to optimize the parameter inversion can be expressed by the equation below [23,27].

Xn  2 N f (X) = ω h0 h , X D , (5) i i − i ∈ i=1 where X is the permeability coefficient of the undetermined parameter, n is the total number of observation points, ωi is the weight of the measured values at observation point i, hi0 and hi are the calculated value and measured value of the water head for observation point i, respectively, N is the number of inversion parameters, and DN represents the space domain. The method based on the approximate viable concept using the nonlinear simplex method finds the optimal solution directly, which can solve the optimization problem with various types of constraints and parameter inversion problems and, in general, engineering seepage problems. In this paper, the water head are taken as the the known quantity. The flexible tolerance method is applied to obtain the seepage parameters of the different material zones.

3.2. Procedures of Back Analysis The borehole water pressure test is a kind of in-situ permeability test carried out in the borehole, which is used to determine the permeability of the rock mass and understand the relative permeability and fracture development degree of the rock strata at different depths of the underground. However, when the rock masses with very developed fissures or fault fracture zone are measured, the stability of in-situ borehole water pressure test is poor. Therefore, the permeability of rock mass cannot be calculated directly through the test data. In this paper, a new approach to permeability inversion of fractured rock masses is proposed to address the problem. The specific implementation steps are as follows. (1) Step 1: The permeability parameter of the rock masses near the borehole in the rock mass area to be measured is recorded as xi. The liquid level in the borehole is allowed to drop freely after water is injected into the borehole, and the liquid level elevation hj at different times tj is recorded. i Therefore, the measured leakage Qj amount in the borehole in each time period can be expressed by the following formula. i Q = (hj hj 1) A (6) j − − × where A is the cross-sectional area of the borehole (m2). (2) Step 2: A three-dimensional finite element model of seepage in the borehole area is modelling. After the seepage boundary conditions of the model are determined, the initial values of seepage parameters are given. Based on the unstable seepage analysis method, the seepage field in the drilling i area at different times is calculated. Then, the seepage flow qj of the drilling model at different times is i calculated by using the mid-section method [28]. The calculated seepage flow Qj∗ in the drilling area at each time period can be solved by the following formula.

i i 1 q + q − i j j Q ∗ = (tj tj 1), (7) j 2 × − − (3) Step 3: Adjust the seepage parameters, the error percentage between the calculated seepage flow rate, and the measured seepage amount in the borehole area in each time period η(xi) can be expressed as follows.  i i  i η(x ) = Q Q ∗ /Q 100%. (8) i j − j j· The permeability coefficient is monotonically decreased by using a simple acceleration method [23], and the control error percentage is within 5%. Therefore, the permeability parameters of the rock mass Water 2020, 12, x FOR PEER REVIEW 5 of 17

(3) Step 3: Adjust the seepage parameters, the error percentage between the calculated seepage η flow rate, and the measured seepage amount in the borehole area in each time period (xi ) can be expressed as follows.  i i ∗  i η(x ) = Q − Q  Q ⋅100% . (8) i  j j  j Water 2020, 12, 734 5 of 17 The permeability coefficient is monotonically decreased by using a simple acceleration method [23], and the control error percentage is within 5%. Therefore, the permeability parameters of the rock massin the in drilling the drilling area at area different at different times are times inverted, are andinverted, the inversion and the of inversion the permeability of the permeability coefficients of coefficientsthe rock mass of the at dirockfferent mass depths at different near a depths drilling near hole a is drilling completed. hole is completed. (4)(4) Step Step 4: 4: For For other other similar similar drilling drilling water water pressure pressure tests. tests. Steps Steps (1) (1) to to (3) (3) are are repeated repeated until until the the permeabilitypermeability coefficients coefficients at at different different depths depths near near the the boreholes boreholes are are all all obtained. obtained. (5)(5) Step Step 5: 5: Based Based on on the the existing existing seepage seepage system system of of the the rock rock masses masses in in the the area area near near the the limited limited numbernumber of boreholes,boreholes, aa three-dimensional three-dimensional finite finite element element seepage seepag analysise analysis model model of the wholeof the reservoir whole reservoirdam area dam in the area natural in the periodnatural isperiod established, is establis andhed, the and permeability the permeability coefficients coefficients of the rockof the masses rock massesin different in different zones inzones the global in the rangeglobal of range the reservoir of the reservoir dam area dam are obtainedarea are obtained by inversion by inversion using the usingflexible the tolerance flexible tolerance method. method. Next, a three-dimensionalNext, a three-dimensional seepage seepage model ofmodel the dam of the engineering dam engineering during duringthe operation the operation can be establishedcan be established to further to evaluate further the evaluate rationality the ofrationalit the seepagey of controlthe seepage measures control and measuresschemes ofand the schemes project. of the project.

4.4. Method Method Verification Verification

4.1.4.1. Case Case Introduction Introduction TheThe seepage seepage field field of of rock rock mass mass around around the the boreho boreholele is is calculated calculated based based on on the the unsteady unsteady seepage seepage analysisanalysis method, method, and thethe seepage seepage flow flow rate rate at eachat each time time point point in the in test the process test process is obtained. is obtained. The seepage The seepagecoefficient coefficient of rock massof rock in themass corresponding in the corresponding test section test is section inverted is byinverted comparing by comparing with the field with water the fieldpressure water test pressure results. Thetest schematicresults. The diagram schematic of the di single-holeagram of the water single-hole pressure testwater is shown pressure in Figuretest is2 . shownThe drilling in Figure layout 2. The of the drilling Shangmo layout reservoir of the Shan projectgmo in Gansureservoir Province, project Chinain Gansu is presented Province, in China Figure is3 . presentedThe water in pressure Figure 3. test The hole water is ZK0, pressure which test is about hole 7is mZK0, away which from is the about left end7 m ofaway the dam.from the The left contrast end ofhole the isdam. ZK1, The located contrast at hole the rock is ZK1, mass located with at better the rock lithology mass with on the better downstream lithology on side the of downstream the left bank sidemountain. of the Theleft otherbank sevenmountain. pressurized The other water seven test holespressurized are ZK2 water to ZK8, test respectively. holes are ZK2 to ZK8, respectively.

pressure gauge

test borehole

packer test segment

Rock

FigureFigure 2. 2. SketchSketch of of a asingle-hole single-hole water water pressure pressure test. test.

Water 2020, 12, 734 6 of 17 Water 2020, 12, x FOR PEER REVIEW 6 of 17 Water 2020, 12, x FOR PEER REVIEW 6 of 17

Figure 3. LayoutLayout of of boreholes boreholes in the dam site. Figure 3. Layout of boreholes in the dam site. Pressure water test hole water level measurement process: The water level in the hole at a higher higher Pressure water test hole water level measurement process: The water level in the hole at a higher position. After After a a period of water injection, the pump stops supplying water. A modified modified water level position. After a period of water injection, the pump stops supplying water. A modified water level observation device was used to monitor the variation of the water level in the borehole. The water observation device was used to monitor the variation of the water level in the borehole. The water level in thethe boreholeborehole waswas recorded recorded until until no no water water was wa found.s found. The The water water pressure pressu testsre tests indicate indicate that that the level in the borehole was recorded until no water was found. The water pressure tests indicate that therock rock masses masses are theare fracturedthe fractured rock massrock mass with highwith permeability.high permeability. Figure Figure4 shows 4 oneshows rock one core rock sample core the rock masses are the fractured rock mass with high permeability. Figure 4 shows one rock core sampleof the water of the pressure water pressure tests. tests. sample of the water pressure tests.

Figure 4. Photo of the rock core sample. Figure 4. Photo of the rock core sample. 4.2. Model and Parameters of the Case 4.2. Model and Parameters of the Case Considering the symmetry of a single-hole water pressure test model, a 1/4-cylinder model with Considering thethe symmetrysymmetry ofof aa single-holesingle-hole water water pressure pressure test test model, model, a a 1 /1/4-cylinder4-cylinder model model with with a a radius of 0.12 m are established. The length and width of the model are both 10 m, and the heights radiusa radius of of 0.12 0.12 m m are are established. established. The The length length and and width width of theof the model model are are both both 10 m,10 andm, and the the heights heights are are 32 m, respectively. The depth of the borehole h is 16 m. The top elevation of the model is 1637.10 32are m, 32 respectively.m, respectively. The The depth depth of the of the borehole borehole h is h 16 ism. 16 Them. The top top elevation elevation of theof the model model is 1637.10 is 1637.10 m. m. The 3-D finite element mesh of the calculation model is shown in Figure 5. The total number of Them. The 3-D 3-D finite finite element element mesh mesh of the of calculation the calculation model mo isdel shown is shown in Figure in Figure5. The total5. The number total number of model of model nodes and units are 19,056 and 18,000, respectively. nodesmodel andnodes units and are units 19,056 are and19,056 18,000, and 18,000, respectively. respectively. In the unstable seepage period, the boundary types of seepage analysis mainly include the InIn thethe unstableunstable seepageseepage period,period, thethe boundaryboundary typestypes ofof seepageseepage analysisanalysis mainlymainly includeinclude thethe known head boundary, seepage boundary, and impermeable boundary. (1) The known head known headhead boundary, boundary, seepage seepage boundary, boundary, and impermeableand impermeable boundary. boundary. (1) The known(1) The head known boundary head boundary includes the boundary around the borehole and the intercept boundary of the given includesboundary the includes boundary the aroundboundary the around borehole the and bore thehole intercept and the boundary intercept of theboundary given groundwaterof the given groundwater level, the periphery of the borehole is the upstream boundary, and the outer side of the level,groundwater the periphery level, the of theperiphery borehole of isthe the borehole upstream is the boundary, upstream and boundary, the outer and side the of theouter model side of is thethe model is the downstream boundary. (2) The seepage boundary is the surface below the upstream downstreammodel is the boundary.downstream (2) boundary. The seepage (2) boundary The seepag is thee boundary surface below is the the surface upstream below water the upstream level and water level and above the downstream water level of the model. (3) An impervious boundary water level and above the downstream water level of the model. (3) An impervious boundary includes the symmetry plane of the model (i.e., intercept boundary of x = 0 m and y = 0 m), partial includes the symmetry plane of the model (i.e., intercept boundary of x = 0 m and y = 0 m), partial

Water 2020, 12, x FOR PEER REVIEW 7 of 17 boundary between upstream and downstream water levels except the given groundwater level, and the bottom surface of the model. (4) For the unsteady seepage in this test, the drilling water level changes with time, that is, the upstream boundary water head around the drilling hole changes with time. The flow rate is used as the basis of inversion, the error percentage between the measured seepage value in the borehole, and the calculated seepage flow rate in the borehole area is controlled within 5%, so as to inverse the seepage parameters of the rock mass around the borehole. The variationWater 2020trend, 12 of, x theFOR waterPEER REVIEW level in the comparative hole with time is presented in Figure 6. As seen7 of 17 in Figure 6, the water level in the hole decreases monotonically with time. Each rock stratum is generalizedboundary into between an equivalent upstream andcontinuous downstream permeable water levelsmedium except to therepresent given groundwater the macroscopic level, and permeabilityWaterthe 2020bottom, 12 characteristics, 734 surface of the of themodel. rock (4)stratum, For the including unsteady the seepage permeability in this of test, the thefaults drilling and fissures, water7 oflevel 17 but thechanges seepage with heterogeneity time, that is, theof the upstream faults and boundary fissures water is not head considered around thein thedrilling model. hole The changes initial with proposedtime. permeability coefficient of the rock masses in different depths around the borehole are above the downstream water level of the model. (3) An impervious boundary includes the symmetry supposedThe to be flow 1.0 ×rate 10− 5is cm/s used to as1.0 the× 10 basis−1 cm/s. of inversion, the error percentage between the measured plane of the model (i.e., intercept boundary of x = 0 m and y = 0 m), partial boundary between upstream seepageBased on value the variation in the borehole, curve of and the waterthe calculated level in each seepage borehole, flow rate the unstablein the borehole seepage area calculation is controlled and downstream water levels except the given groundwater level, and the bottom surface of the model. schemewithin is adopted 5%, so asto toinvert inverse the thepermeability seepage parameters coefficient ofof therock rock mass mass with around different the depthsborehole. by The (4) For the unsteady seepage in this test, the drilling water level changes with time, that is, the upstream controllingvariation the trend error of between the water the level calculated in the comparativeseepage flow hole rate withand thetime measured is presented seepage in Figure amount 6. As in seen boundary water head around the drilling hole changes with time. each intime Figure period. 6, the water level in the hole decreases monotonically with time. Each rock stratum is generalized into an equivalent continuous permeable medium to represent the macroscopic permeability characteristics of the rock stratum, including the permeability of the faults and fissures, but the seepage heterogeneity of the faults and fissures is not considered in the model. The initial proposed permeability coefficient of the rock masses in different depths around the borehole are supposed to be 1.0 × 10−5 cm/s to 1.0 × 10−1 cm/s. Based on the variation curve of the water level in each borehole, the unstable seepage calculation scheme is adopted to invert the permeability coefficient of rock mass with different depths by controlling the error between the calculated seepage flow rate and the measured seepage amount in each time period.

Figure 5. Unsteady seepage calculation model (unit: m). Figure 5. Unsteady seepage calculation model (unit: m). The flow rate is used as the basis of inversion, the error percentage between the measured seepage value in the borehole, and the calculated seepage flow rate in the borehole area is controlled within 5%, so as to inverse the seepage1632 parameters of the rock mass around the borehole. The variation trend

of the water level in the comparative hole with timeis h = presented 16 m in Figure6. As seen in Figure6, the water level in the hole1631 decreases monotonically with time. Each rock stratum is generalized into an equivalent continuous permeable medium to represent the macroscopic permeability characteristics of 1630 the rock stratum, including the permeability of the faults and fissures, but the seepage heterogeneity of the faults and fissures is not considered in the model. The initial proposed permeability coefficient of the rock masses in different(m) level water depths1629 around the borehole are supposed to be 1.0 10 5 cm/s to 1.0 10 1 cm/s. Figure 5. Unsteady seepage calculation model (unit:× m).− × −

1628

1632 0 20406080100120140

time (s) h = 16 m 1631 Figure 6. Variation trend of the water level in borehole ZK0 (unit: m).

1630

(m) level water 1629

1628

0 20406080100120140 time (s) FigureFigure 6. 6.Variation Variation trend trend of of the the water water level level in in borehole borehole ZK0 ZK0 (unit: (unit: m). m).

Based on the variation curve of the water level in each borehole, the unstable seepage calculation

scheme is adopted to invert the permeability coefficient of rock mass with different depths by

Water 2020, 12, 734 8 of 17 Water 2020, 12, x FOR PEER REVIEW 8 of 17

4.3.controlling Case Analysis the error between the calculated seepage flow rate and the measured seepage amount in each time period. The time interval of the pressure water test of borehole ZK0 and its measured values of the seepage4.3. Case flow Analysis are shown in Table 1. The water head distribution of the borehole profile at different time periods is shown in Figure 7. The figure indicates that the water level near the borehole location The time interval of the pressure water test of borehole ZK0 and its measured values of the drops significantly more than in other areas, and the distribution of water head is consistent with the seepage flow are shown in Table1. The water head distribution of the borehole profile at di fferent general rule. time periods is shown in Figure7. The figure indicates that the water level near the borehole location drops significantly more than in other areas, and the distribution of water head is consistent with the Table 1. Time interval and measured values of the borehole ZK0. general rule. Time Interval Time Measured Value Table(-) 1. Time interval and(s) measured values of the borehole(m3/s) ZK0. 1 0–18 4.67 × 10−3 Time Interval Time Measured Value 2 (-) 18–34(s) (m 4.503/s) × 10−3 3 3 1 34–52 0–18 4.67 4.0010 × −10−4 × 3 2 18–34 4.50 10− 4 52–72 3.60× × 104 −4 3 34–52 4.00 10− × 4 4 52–72 3.60 10 −4 5 72–102 3.20× × −10 5 72–102 3.20 10 4 × − 6 6 102–144 102–144 2.57 2.5710 × 104 −4 × −

Figure 7. Water head distribution of the borehole profile at different time periods (unit: m): (a) t = 0 s, Figure 7. Water head distribution of the borehole profile at different time periods (unit: m): (a) t = 0 s, (b) t = 72 s, and (c) t = 144 s. (b) t = 72 s, and (c) t = 144 s. To quantitatively evaluate the simulation performance of the models, the root mean squared error (RMSE)To quantitatively and coefficient evaluate of determination the simulation (R2) wereperformance considered of asthe statistical models, performancethe root mean evaluations squared in 2 errorthis (RMSE) study [ 29and]. The coefficient value of RMSEof determination is a nonnegative (R ) value,were andconsidered a low RMSE as statistical indicates goodperformance consistency evaluationsbetween thein this observed study [29]. and simulatedThe value values.of RMSE R 2isranges a nonnegative from 0 to value, 1, and and a larger a low R RMSE2 value indicates indicates a 2 2 goodbetter consistency match of between the simulated the observed and observed and simulated data. values. R ranges from 0 to 1, and a larger R value indicatesFigure8 ashows better thematch comparison of the simulated between and the observed calculated data. seepage flow and the measured seepage flowFigure in the8 shows comparative the comparison hole. From between this the figure, calculated it can beseepage noticed flow that and the the maximum measured error seepage ofthe flowmeasured in the comparative leakage values hole. and From calculated this figure, values itin can each be periodnoticed are that 4.67%, the RMSE,maximum and error R2 of of those the are measured leakage4 3 values and calculated values in each period are 4.67%, RMSE, and R2 of those are 1.33 10− m /s and 0.9976, respectively, which indicates the inversion values can match with the ×−4 3 1.33measured × 10 m /s data. and 0.9976, respectively, which indicates the inversion values can match well with the measuredInversion data. analysis results show that the permeability coefficients of the rock masses at the depths Inversion analysis results show that the permeability coefficients of3 the rock masses at the depths of 0–16 m below the road surface at the position of ZK0 is 1.12 10− cm/s, respectively. According to of 0–16 m below the road surface at the position of ZK0 is 1.12 × 10×−3 cm/s, respectively. According to the geological conditions of the mountain and the distribution law of rock strata, the mountain fissures in the left abutment are developed and the permeability coefficient is relatively large.

Water 2020, 12, 734 9 of 17 the geological conditions of the mountain and the distribution law of rock strata, the mountain fissures inWater the 2020 left, 12 abutment, x FOR PEER are REVIEW developed and the permeability coefficient is relatively large. 9 of 17

0.005 measured values inversion values 0.004 R2 = 0.9976 s) -4 3 3/ RMSE = 1.33ൈ10 m /s

0.003

5 4.67 % 4.28 % 3.89 % 4

3 0.002 2

1

0 123456 -1

seepage discharge (m 0.001 -2 percentage percentage differences (%) -3 -2.19% -2.67 % -3.00 %

0.000 123456 time interval FigureFigure 8.8. Comparison of seepage discharge between measuredmeasured valuesvalues andand inversioninversion values.values.

ForFor thethe rock masses with extremely developed fissuresfissures oror faultfault fracture zones,zones, thisthis new approach isis usedused toto obtain the permeability coecoefficientfficient ofof the rock mass with didifferentfferent thicknessesthicknesses nearnear thethe other boreholesboreholes (ZK2 to ZK8, shown shown in in Figure Figure 33).). The The inve inversionrsion results results of of each each test test boreholes boreholes are are listed listed in inTable Table 2.2 . Table 2. Inversion results of rock permeability of other boreholes. Table 2. Inversion results of rock permeability of other boreholes. Borehole Depth Rock Permeability Code Borehole Depth Rock Permeability Code (m) (cm/s) (m) (cm/s) 1 h = 0–12 2.3 10− ZK2 h = 0–12 × 2.3 × 210−1 h = 12–24 4.7 10− ZK2 × 1 h = 12–24h = 0–14 4.1 4.710 ×− 10−2 ZK3 × 2 h = 14–26 7.4 10− h = 0–14 × 4.1 × 110−1 h = 0–13 3.1 10− ZK3 ZK4 × h = 13–25 5.7 10 2 h = 14–26 × 7.4 ×− 10−2 ZK5 h = 0–10 7.5 10 1 × − h = 0–13h = 0–16 5.8 3.110 × 210−1 ZK6 × − ZK4 h = 16–34 2 7.4 10− −2 h = 13–25 × 5.7 × 110 h = 0–14 4.7 10− ZK7 × 2 ZK5 h = 0–10h = 14–30 6.1 7.510 ×− 10−1 × 1 h = 0–12 3.3 10− ZK8 × −2 h = 0–16h = 12–28 5.7 5.810 × 210 ZK6 × − h = 16–34 7.4 × 10−2

5. Engineering Application h = 0–14 4.7 × 10−1 ZK7 5.1. General Description h = 14–30 6.1 × 10−2 The Shangmo project is a waterh = source0–12 project for the water3.3 supply × 10−1 in Tianshui city, Gansu ZK8 Province, China. It is a reservoir hubh = project 12–28 with full annual regulation.5.7 × 10 The−2 dam is a sandy dam with core wall with a crest width of 6.0 m, a length of 202.8 m, a crest elevation of 1637.10 m, and5. Engineering a maximum Application dam height of 50.0 m. The sandy gravel cover in the riverbed is provided with loam anti-seepage gullies with a bottom width of 8.0 m, a slope of 1:1.5, and gullies 2.5 m deep below the bedrock5.1. General surface. Description Two rows of dam foundation anti-seepage curtains are built under the foundation. The first row of curtains goes deep under the severely weathered layer of 5.0 m, the second row of curtainsThe goes Shangmo deep underproject the is weaka water permeable source project zone at for 5 m, the and water a single supply row in of anti-seepageTianshui city, curtains Gansu Province, China. It is a reservoir hub project with full annual regulation. The dam is a sandy gravel dam with loam core wall with a crest width of 6.0 m, a length of 202.8 m, a crest elevation of 1637.10 m, and a maximum dam height of 50.0 m. The sandy gravel cover in the riverbed is provided with loam anti-seepage gullies with a bottom width of 8.0 m, a slope of 1:1.5, and gullies 2.5 m deep below

Water 2020, 12, x FOR PEER REVIEW 10 of 17

the surface. Two rows of dam foundation anti-seepage curtains are built under the

Waterfoundation.2020, 12, 734 The first row of curtains goes deep under the severely weathered layer of 5.0 10m, of the 17 second row of curtains goes deep under the weak permeable zone at 5 m, and a single row of anti- seepage curtains are set up within the range of 30 m extending from the dam abutment to both banks. areThe set design up within scheme the of range grouting of 30 curtains m extending is to hit from the rock the damfoundation abutment with to a bothpermeability banks. The less designthan or schemeequal to of 5 grouting Lu. curtains is to hit the rock foundation with a permeability less than or equal to 5 Lu. TheThe Shangmo Shangmo reservoir reservoir is ais canyona canyon type type reservoir reservoi withr with most most bank bank slopes slopes above above 35◦, the 35°, right the bankright steeperbank steeper than the than left the bank, left andbank, some and steepsome walls.steep walls. The abutment The abutment rock massrock mass is strongly is strongly weathered weathered and unloaded,and unloaded, and the and highly the highly weathered weathered and unloaded and unloaded zone at zone the topat the of top the bankof the slope bank isslope relatively is relatively thick. Alongthick. theAlong river the bed, river there bed, are there steep are dip steep angles dip alongangles the along river the to river tectonic to tectonic crushed crushed rock zones rock with zones a widthwith a of width tens of of meters, tens of whichmeters, may which cause may reservoir cause re bottomservoir leakage bottom along leakage the alon riverg tothe tectonic river to crushed tectonic rockcrushed zones. rock zones.

5.2.5.2. SeepageSeepage AnalysisAnalysis of of the the Reservoir Reservoir Site Site in in a a Natural Natural Period Period 5.2.1. Model and Parameters 5.2.1. Model and Parameters The three-dimensional seepage finite element calculation model for the natural period of the The three-dimensional seepage finite element calculation model for the natural period of the reservoir site area is modelling. The right control point of the dam is selected as the origin of the reservoir site area is modelling. The right control point of the dam is selected as the origin of the model, the x axis is along the river direction, and the upstream direction is positive to the downstream model, the x axis is along the river direction, and the upstream direction is positive to the downstream direction. The y axis is along the direction of the dam axis, and the right bank pointing to the left direction. The y axis is along the direction of the dam axis, and the right bank pointing to the left bank bank is positive. The z axis is vertical and positively upward. The scope of the model is set as follows: is positive. The z axis is vertical and positively upward. The scope of the model is set as follows: the the left boundary near the dam site is at least 150 m from the left dam end. The right boundary is at left boundary near the dam site is at least 150 m from the left dam end. The right boundary is at least least 150 m from the right dam end, and the right boundary at the downstream of the dam is taken 150 m from the right dam end, and the right boundary at the downstream of the dam is taken to the to the middle line of the gully at the downstream of the right mountain. The reservoir intercepts the middle line of the gully at the downstream of the right mountain. The reservoir intercepts the mountains on both sides of the river according to the trend of the river. The upstream interception mountains on both sides of the river according to the trend of the river. The upstream interception boundary is at least 1500 m from the upstream dam toe. The downstream boundary is at least 250 m boundary is at least 1500 m from the upstream dam toe. The downstream boundary is at least 250 m from the downstream dam toe. The reservoir and dam foundation boundary is taken at least 150 m from the downstream dam toe. The reservoir and dam foundation boundary is taken at least 150 m below the curtain bottom line. below the curtain bottom line. A three-dimensional finite element model including , rock strata, faults, and the like in A three-dimensional finite element model including terrain, rock strata, faults, and the like in the calculation area is shown in Figure9. The boundary conditions of the seepage model mainly the calculation area is shown in Figure 9. The boundary conditions of the seepage model mainly include the known head boundary, seepage boundary, and impermeable boundary. (1) The known include the known head boundary, seepage boundary, and impermeable boundary. (1) The known head boundary includes the riverbed surface below the river level of the natural river course and the head boundary includes the riverbed surface below the river level of the natural river course and the left and right boundary (known groundwater level) of the model. (2) The seepage boundary is the left and right boundary (known groundwater level) of the model. (2) The seepage boundary is the hillside surface on the left and right bank of the reservoir, which is the boundary that is in contact with hillside surface on the left and right bank of the reservoir, which is the boundary that is in contact the atmosphere. (3) The impermeable boundary includes the intercepting boundary on both upstream with the atmosphere. (3) The impermeable boundary includes the intercepting boundary on both and downstream sides of the model and the bottom surface of the model. upstream and downstream sides of the model and the bottom surface of the model.

FigureFigure 9. 9.Model Model of of the the reservoir reservoir site site area area during during the the natural natural period. period.

TheThe seepage seepage parameters parameters are are drawn drawn up accordingup according to the to results the results of field of tests field and tests inversion and inversion analysis ofanalysis unstable of seepageunstable tests. seepage Through tests. inversion Through analysis inversion of aanalysis natural of period a natural model, period the permeability model, the coefficients of dam foundation and reservoir rock masses can be obtained by the flexible tolerance method. The parameters of each layered rock masses are presented in Table3. Water 2020, 12, x FOR PEER REVIEW 11 of 17 permeability coefficients of dam foundation and reservoir rock masses can be obtained by the flexible toleranceWater 2020, method.12, 734 The parameters of each layered rock masses are presented in Table 3. 11 of 17

TableTable 3. 3. ParametersParameters of of each each layered layered rock rock mass. mass. Rock Permeability Rock Classification Rock Permeability Rock Classification (cm/s) (cm/s) strong permeable layer, strong permeable layer, 2.0 × 10−3 q ≥ 100 Lu 2.0 10 3 q 100 Lu × − medium permeable≥ layer, medium permeable layer, 3.0 × 10−4 10 Lu ≤ q < 100 Lu 3.0 10 4 10 Lu q < 100 Lu × − weak permeable≤ layer, weak permeable layer, −5 5.0 5.010 ×5 10 5 Lu 5≤ Luq < 10q Lu< 10 Lu × − ≤ relativelyrelatively impermeable impermeable layer, layer, 2.0 2.010 ×5 10−5 q < 5 qLu< 5 Lu × − fault faultfracture fracture zone, zone, 2 1.5 1.510− × 10−2 q 100 Lu × q ≥ 100≥ Lu

5.2.2.5.2.2. Results Results and and Discussions Discussions FourFour typical typical sections sections are are selected, selected, including including dam dam axis axis section section x x == 00 m, m, upstream upstream channel channel section section xx == −500500 m, m channel, channel longitudinal longitudinal section section y y == −150150 m, m, and and maximum maximum dam dam height height channel channel longitudinal longitudinal − − sectionsection y y = 100100 m (see FigureFigure 10 10)) to to analyze analyze the the groundwater groundwater level level distribution distribution in thein the reservoir reservoir site area.site area. y (m)

200 y = 100 m flow 0 x (m) river channel flow -200 y = -150 m

x = -500 m x = 0 m -400

-1600 -1400 -1200 -1000 -800 -600 -400 -200 0 200 FigureFigure 10. 10. LayoutLayout of of the the main main typical typical sections sections (unit: (unit: m). m).

AccordingAccording to to geological geological prospecting prospecting data data and and in inversionversion analysis, analysis, the the highest highest groundwater groundwater level level inin the the reservoir reservoir site site area area of of this this project project is is 1607. 1607.0000 m, m, and and the the lowest lowest groundwater groundwater level level is is 1597.60 1597.60 m. m. FigureFigure 11 11 shows shows the the groundwater groundwater level level drawn drawn by by a a geological geological survey survey of of the the dam dam axis axis profile profile and and the the groundwatergroundwater levellevel obtained obtained by inversionby inversion analysis. analysis. The inversion The inversion calculation calculation values of thevalues groundwater of the groundwaterlevel of the dam level axis of sectionthe dam are axis basically section consistentare basically with consistent the measured with values.the measured In the localvalues. area In nearthe localthe riverbed area near on the the riverbed right bank, on the the right fitting bank, error th ise fitting large, theerror maximum is large, the error maximum between error the calculated between thevalue calculated of the groundwater value of the levelgroundwater and the measured level and valuethe measured is 0.41 m,value and is the −0.41 relative m, and error the is relative4.36%, − − errorwhich is meets−4.36%, the which engineering meets the precision engineering requirements. precision re Therefore,quirements. the Therefore, inversion resultsthe inversion fit the naturalresults fitgroundwater the natural seepagegroundwater field well,seepage and field the calculation well, and the model calculation and boundary model conditionsand boundary are suitable.conditions are suitable.Figure 12 shows a contour map of the natural groundwater level in the reservoir site area. It can be seen in Figure 10 that the underground water level on the left bank of the reservoir site area is relatively high, and the underground water level on the right bank is relatively low and basically equal to the river bed water level. This is mainly due to the existence of a deep gully near the downstream of the dam axis of the right abutment, which is close to the dam axis and has a large angle with the dam axis, which makes the mountain body of the right abutment thin and the underground water level low. The groundwater level on the left and right banks of the upstream reservoir is also slightly higher than the river level, but the natural groundwater watershed on both sides of the reservoir does not exist, which is consistent with the actual situation. Water 2020, 12, x FOR PEER REVIEW 12 of 17

m easured values calculated values 1599.82 1597.22 calculated values m easured values Water 2020, 12, 734 12 of 17 Water 2020, 12, x FOR PEER REVIEW 12 of 17

1604.60 1602.20 1599.80 1598.60 1603.40 1601.00 1605.80

Figure 11. Measured and calculated values of a natural groundwater level in the dam axis section (unit: m).

m easured values calculated values Figure 12 shows a contour map15 of99.8 2the natural groundwater1597.22 level in the reservoir site area. It can be seen in Figure 10 that the undergroundcalculated values water level on the leftm eas ubankred value sof the reservoir site area is relatively high, and the underground water level on the right bank is relatively low and basically

equal to the river bed1604.60 water1602.20 level.1599.8 0 This is mainly due to the existence of a deep gully near the 1598.60 downstream of the dam160 3axis.40 of the right abutment, which is close to the dam axis and has a large 1601.00 angle with the dam1605.80 axis, which makes the mountain body of the right abutment thin and the underground water level low. The groundwater level on the left and right banks of the upstream reservoir is also slightly higher than the river level, but the natural groundwater watershed on both sidesFigure of 11.theFigure Measuredreservoir 11. Measured doesand and notcalculated calculated exist, which values ofis of aconsistent natural a natural groundwater with groundwater the level actual in the level damsituation. axis in sectionthe dam (unit: axis m). section (unit: m). y (m) Figure 12 shows a contour map of the natural groundwater level in the reservoir site area. It can be seen in Figure 10 that the underground water level on the left bank of the reservoir site area is relatively high,200 and the underground water level on the right bank is relatively low and basically equal to the river bed water level. This is mainly due to the existenceflow of a deep gully near the downstream of0 the dam axis of the right abutment, which is close to the dam axis and has a large channel x (m) angle with the dam axis, whichflow makesriver the mountain body of the right abutment thin and the underground-200 water level low. The groundwater level on the left and right banks of the upstream reservoir is also slightly higher than the river level, but the natural groundwater watershed on both sides of the reservoir-400 does not exist, which is consistent with the actual situation.

-1600 -1400 -1200 -1000 -800 -600 -400 -200 y (m) 0 200 Figure 12. Groundwater level contours (unit: m). Figure 12. Groundwater level contours (unit: m). Figure 13 is the water head distribution diagram of each typical section of the natural model. 200 AsFigure can be13 seen is the from water the figure,head distribution the groundwater diagram level generallyof each typical decreases section gradually of the from natural the left model. and As can beright seen banks from to the riverfigure, channel the groundwater and from the upstreamlevel generally to the downstream. decreasesflow gradually The groundwater from the flows left and from the left and right banks to the river channel and from the upstream channel to the downstream right banks to the river channel and from the upstream to the downstream. The groundwater flows channel.0 According to the contour map of the underground water level and the potential distribution frommap the left of each and section,right banks the underground to the riverchannel channel water level and in from the junction the upstream area and channel the mountains to the downstream onx both(m) flow river channel.sides According of the reservoir to the is relativelycontour map low, andof the the underground hydraulic gradient water is level very small.and the Therefore, potential there distribution is no -200 map watershedof each section, in the calculation the underground range. water level in the junction area and the mountains on both sides of the reservoir is relatively low, and the hydraulic gradient is very small. Therefore, there is no watershed in the calculation range. -400

-1600 -1400 -1200 -1000 -800 -600 -400 -200 0 200

Figure 12. Groundwater level contours (unit: m).

Figure 13 is the water head distribution diagram of each typical section of the natural model. As can be seen from the figure, the groundwater level generally decreases gradually from the left and right banks to the river channel and from the upstream to the downstream. The groundwater flows from the left and right banks to the river channel and from the upstream channel to the downstream channel. According to the contour map of the underground water level and the potential distribution map of each section, the underground water level in the junction area and the mountains on both sides of the reservoir is relatively low, and the hydraulic gradient is very small. Therefore, there is no watershed in the calculation range.

WaterWater 20202020,, 1212,, 734x FOR PEER REVIEW 1313 of of 17

(a) free surface free surface

1614.20 1610.60 1611.80 1615.40 1613.00 1611.80 1616.60

(b) free surface 1634.55 1630.91 1627.27 1623.64 1620.00 1616.36 1612.73 1609.09 1605.45 1601.82 1598.18

(c) free surface 1632.73 1629.09 1614.55 1607.27 1625.45 1621.82 1603.64 1618.18 1610.91 1600.00 1596.36 1592.73

Figure 13. Water head distribution of typical sections (unit: m): (a) Cross section of upstream channel Figure 13. Water head distribution of typical sections (unit: m): (a) Cross section of upstream channel (x = 500 m), (b) river profile (y = 150 m), and (c) profile of the maximum dam height (y = 100 m). (x = −500 m), (b) river profile (y = −−150 m), and (c) profile of the maximum dam height (y = 100 m). 5.3. Seepage Analysis of Recommended Anti-Seepage Scheme for Reservoir Site 5.3. Seepage Analysis of Recommended Anti-Seepage Scheme for Reservoir Site 5.3.1. Model and Parameters 5.3.1.There Model are and several Parameters deep fault fracture zones in the riverbed of the reservoir site of the Shangmo waterThere supply are project, several anddeep the fault fissures fractu ofre the zones rock in masses the riverbed in the of abutment the reservoir are extremely site of the developed, Shangmo whichwater supply results inproject, large and permeability the fissures coe offfi cientsthe rock of themasses rock in masses. the abutment The recommended are extremely anti-seepage developed, schemewhich results of the in reservoir large permeability site adopts thecoefficients full anti-seepage of the rock form masses. that combined The recommended the anti-seepage and concretescheme of slab. the Thereservoir composite site adopts the full an areti-seepage laid on form the upstream that comb damined slope the geomembrane of the gravel dam and andconcrete the riverbed slab. The surface, composite and geomembranes the concrete slabs are are laid arranged on the upstream in the mountain dam slope areas ofon the both gravel sides dam of theand reservoir the riverbed bank surface, below theand checked the concrete flood slabs level. are arranged in the mountain areas on both sides of the reservoirBased on bank the seepagebelow the model checked ofthe flood reservoir level. in a natural period, the structures of excavation, damBased body, geomembrane,on the seepage andmodel concrete of the slabreservoir are supplemented in a natural period, to form the the stru reservoirctures of model excavation, of the recommendeddam body, geomembrane, scheme. The and geomembrane concrete slab is are simulated supplemented by a certain to form thickness the reservoir of seepage model medium. of the Therecommended other structures scheme. are simulatedThe geomembrane according is to simulate their actuald by sizes. a certain The seepagethickness model of seepage of the medium. reservoir WatersiteThe area other2020, of12 structures, the x FOR recommended PEER are REVIEW simulated anti-seepage according scheme to thei isr actual shown sizes. in Figure The seepage14. model of the reservoir14 of 17 site area of the recommended anti-seepage scheme is shown in Figure 14. The rock parameters of the recommended scheme adopt the parameters of the natural period model, as listed in Table 3. The permeability coefficients of the dam body, geomembrane, concrete panel, and other materials are presented in Table 4. The normal water storage level is 1632.27 m, and there is no water downstream. The seepage boundary conditions of the model are as follows: (1) The known head boundary includes the riverbed, banks, and the dam below the normal water level, and the left and right boundary (known groundwater level) of the model. (2) The seepage boundary is the surface on the left and right bank of the reservoir and the dam above normal water level, which is the boundary that is in contact with the atmosphere. (3) The impermeable boundary includes the intercepting boundary on both upstream and downstream sides of the model and the bottom surface of the model.

FigureFigure 14. 14. ModelModel of of the the reservoir reservoir si sitete area area of of the the recommen recommendedded anti-seepage scheme. The rock parameters of the recommended scheme adopt the parameters of the natural period Table 4. Seepage parameters of main material zones. model, as listed in Table3. The permeability coe fficients of the dam body, geomembrane, concrete Zone Permeability Coefficient (cm/s) dam gravel 2.0 × 10−1

inverted filter 1.0 × 10−5 core material 1.0 × 10−5 concrete panel 1.0 × 10−7 drainage 1.0 × 10−1 geomembrane 1.0 × 10−9

5.3.2. Results and Discussions Figure 15 shows the contour map of the groundwater level in the reservoir site area of the recommended scheme. As can be seen in the figure, the water storage of the reservoir is affected by the seepage resistance of the geomembrane and the concrete slab, and the infiltration surface drops suddenly at the anti-seepage parts of the geomembrane and the concrete slab. Therefore, the water storage of the reservoir has little influence on the distribution of the groundwater level in the reservoir area. The movement trend of the groundwater is that the two banks supply water to the river channel, and seepage flows from the mountain on both banks of the upstream to the stratum below the bottom of the downstream reservoir. The water storage of the reservoir would leak to the outside of the reservoir through geomembranes at the bottom of the reservoir and concrete slabs on both sides of the reservoir. y (m)

concrete slab 200 dam

0 x (m) geomembrane river channel -200 flow dam axis -400

-1600 -1400 -1200 -1000 -800 -600 -400 -200 0 200 Figure 15. Groundwater level contours of the reservoir site for a recommended anti-seepage scheme (unit: m).

Water 2020, 12, x FOR PEER REVIEW 14 of 17

Water 2020, 12, 734 14 of 17 panel, and other materials are presented in Table4. The normal water storage level is 1632.27 m, and there is no water downstream. The seepage boundary conditions of the model are as follows: (1) The known head boundary includes the riverbed, banks, and the dam below the normal water level, and the left and right boundary (known groundwater level) of the model. (2) The seepage boundary is the surface on the left and right bank of the reservoir and the dam above normal water level, which is the boundary that is in contact with the atmosphere. (3) The impermeable boundary includes the intercepting boundary on both upstream and downstream sides of the model and the bottom surface of the model.Figure 14. Model of the reservoir site area of the recommended anti-seepage scheme. Table 4. Seepage parameters of main material zones. Table 4. Seepage parameters of main material zones. Zone Permeability Coefficient (cm/s) Zone Permeability Coefficient (cm/s) 1 dam gravel 2.0 10− −1 dam gravel 2.0× × 105 inverted filter 1.0 10− −5 inverted filter 1.0× × 105 core material 1.0 10− × −5 core materialconcrete panel 1.0 1.0 10× 107 × − concrete paneldrainage 1.0 1.0 10× 101 −7 × − drainagegeomembrane 1.0 1.0 10× 109 −1 × − geomembrane 1.0 × 10−9 5.3.2. Results and Discussions 5.3.2. Results and Discussions Figure 15 shows the contour map of the groundwater level in the reservoir site area of the recommendedFigure 15 scheme.shows the As contour can be seen map in of the the figure, groundwa the waterter level storage in the of the reservoir reservoir site is area affected of the by therecommended seepage resistance scheme. of As the can geomembrane be seen in the and figure, the concretethe water slab, storage and of the the infiltration reservoir surfaceis affected drops by suddenlythe seepage at resistance the anti-seepage of the geomembrane parts of the geomembrane and the concrete and theslab, concrete and the slab. infiltration Therefore, surface the waterdrops storagesuddenly of at the the reservoir anti-seepage has little parts influence of the ongeomembr the distributionane and of the the concrete groundwater slab. Therefore, level in the the reservoir water area.storage The of movement the reservoir trend has of thelittle groundwater influence on isthat the thedistribution two banks of supply the groundwater water to the river level channel, in the andreservoir seepage area. flows The from movement the mountain trend of on the both groundwater banks of the is upstream that the totwo the banks stratum supply below water the bottom to the ofriver the channel, downstream and seepage reservoir. flows The from water the storage mountain of theon reservoirboth banks would of the leak upstream to the to outside the stratum of the reservoirbelow the through bottom of geomembranes the downstream at thereservoir. bottom The of the water reservoir storage and of the concrete reservoir slabs would on both leak sides to the of theoutside reservoir. of the reservoir through geomembranes at the bottom of the reservoir and concrete slabs on both sides of the reservoir. y (m)

concrete slab 200 dam

0 x (m) geomembrane river channel -200 flow dam axis -400

-1600 -1400 -1200 -1000 -800 -600 -400 -200 0 200 Figure 15. Groundwater level contours of the reservoirreservoir site for a recommended anti-seepage scheme (unit:(unit: m).

The water head distribution of typical sections in the reservoir site area under the recommended scheme is presented in Figure 16. The figure shows the seepage gradient of the rock masses on both sides of the reservoir bank is small and uniform. The free surface in the rockfill area of the dam body is slightly higher than the dam foundation surface, and its maximum seepage gradient is 0.032, which Water 2020, 12, x FOR PEER REVIEW 15 of 17

The water head distribution of typical sections in the reservoir site area under the recommended scheme is presented in Figure 16. The figure shows the seepage gradient of the rock masses on both sides of the reservoir bank is small and uniform. The free surface in the rockfill area of the dam body is slightly higher than the dam foundation surface, and its maximum seepage gradient is 0.032, which occurs at the exit point of the downstream dam slope. The seepage gradient of the left bank rock mass at the exit of the downstream side of the dam body is 0.263, and the maximum seepage gradient of the fault fracture zone is 0.0345. The water head is mainly reduced by the effects of the geomembrane Waterand concrete2020, 12, 734 slab. The maximum seepage gradient of the geomembrane and concrete slab is 322.7015 of 17 and 161.35, respectively. The seepage gradient of each zone of the reservoir area is within the allowable range, which meets the requirements of seepage stability. occurs at the exit point of the downstream dam slope. The seepage gradient of the left bank rock mass In the natural period, the seepage flow rate through the dam axis section is 2.794 m3/s, and that at the exit of the downstream side of the dam body is 0.263, and the maximum seepage gradient of the is 2.801 m3/s for the recommended anti-seepage scheme. Therefore, the leakage of the reservoir under fault fracture zone is 0.0345. The water head is mainly reduced by the effects of the geomembrane and the recommended scheme is 0.007 m3/s, which is far less than the multi-year average runoff of 0.355 concrete slab. The maximum seepage gradient of the geomembrane and concrete slab is 322.70 and m3/s at the reservoir site. This shows that the recommended anti-seepage scheme can effectively solve 161.35, respectively. The seepage gradient of each zone of the reservoir area is within the allowable the problem of large leakage in the reservoir area and ensures the normal storage and operation of range, which meets the requirements of seepage stability. the reservoir.

Figure 16. Water head distribution of typical sections under the recommended anti-seepage scheme Figure 16. Water head distribution of typical sections under the recommended anti-seepage scheme (unit: m): (a) Cross section of dam axis (x = 0 m). (b) Profile of the maximum dam height (y = 100 m). (unit: m): (a) Cross section of dam axis (x = 0 m). (b) Profile of the maximum dam height (y = 100 m). In the natural period, the seepage flow rate through the dam axis section is 2.794 m3/s, and that is 6.2.801 Conclusions m3/s for the recommended anti-seepage scheme. Therefore, the leakage of the reservoir under the recommendedIn this paper, scheme a comprehensive is 0.007 m3/s, whichback analysis is far less method than the of multi-yearseepage parameters average runo for ffrockof 0.355masses m3 is/s proposed,at the reservoir which site. includes This showstwo different that the scales. recommended One is the anti-seepage inversion of scheme permeability can eff ectivelycoefficient solve of fracturedthe problem rock of mass large near leakage the insingle the reservoirborehole areaon the and basis ensures of the the unsteady normal storagepressure and water operation test. The of secondthe reservoir. is the back analysis of rock permeability of dam foundation and abutment in the whole reservoir site area by using the flexible tolerance method. Lastly, the permeability coefficients of the rock6. Conclusions masses of each zone in the entire reservoir area are taken as the seepage parameters for one waterIn supply this paper, engineering. a comprehensive The knowledge back analysisgained from method this research of seepage is summarized parameters foras follows. rock masses is proposed,(1) Back analysis which includes results of two the di boreholefferent scales.show that One the is equivalent the inversion permeability of permeability coefficients coeffi ofcient the rockof fractured masses in rock the massdepth near of 16 the m below single the borehole road su onrface the at basis the position of the unsteady of borehole pressure ZK0 of water Shangmo test. Thereservoir second is is1.12 the × back10−3 cm/s. analysis The of maximum rock permeability error of the of dammeasured foundation leakage and and abutment calculated in thevalues whole in eachreservoir period site are area 3.43% by usingand 4.67%. the flexible Moreover, tolerance the RMSE method. and Lastly, R2 of the the measured permeability and coecalculatedfficients values of the arerock 1.33 masses × 10− of4 m each3/s and zone 0.9976, in the respectively, entire reservoir which area indicates are taken the as inversion the seepage values parameters can match for onewell water with thesupply measured engineering. data. The knowledge gained from this research is summarized as follows. (2)(1) BackThe inversion analysis results method of theof boreholethe permeability show that coefficient the equivalent is applied permeability to other coe boreholes.fficients of The the equivalentrock masses permeability in the depth coefficients of 16 m below of the the rock road masses surface at thedifferent position depths of borehole aroundZK0 the ZK2 of Shangmo to ZK8 boreholesreservoir iswere 1.12 between10 3 cm 0.047/s. The cm/s maximum to 0.750 cm/s. error It of shows the measured that the leakagerock masses and calculatedin the reservoir values site in × − areaeach have period high are permeability. 3.43% and 4.67%. The Moreover,seepage parameters the RMSE andof each R2 of rock the mass measured zone andin the calculated reservoir values area 4 3 are 1.33 10− m /s and 0.9976, respectively, which indicates the inversion values can match well with × the measured data. (2) The inversion method of the permeability coefficient is applied to other boreholes. The equivalent permeability coefficients of the rock masses at different depths around the ZK2 to ZK8 boreholes were between 0.047 cm/s to 0.750 cm/s. It shows that the rock masses in the reservoir site area have high permeability. The seepage parameters of each rock mass zone in the reservoir area were obtained by using the flexible tolerance method. The results show that the maximum error Water 2020, 12, 734 16 of 17 between the calculated value of the groundwater level and measured value is 0.41 m, and the relative − error is 4.36%, which meets the engineering precision requirements. − (3) The proposed approach was used to analyze the three-dimensional seepage field of the Shangmo water supply project. The groundwater level in the junction area and the mountains on both sides of the Shangmo reservoir is low, and the seepage gradient is small. There is no watershed within the scope of the reservoir site area. The full anti-seepage scheme combined the geomembrane and the concrete slab, which can effectively solve the problem of large leakage in the reservoir area. This indicates that the comprehensive permeability coefficient inversion method proposed in this paper is appropriate for the seepage analysis of the field with the fractured rock masses or developed faults and fissures.

Author Contributions: L.G. and Z.S. designed the framework and wrote the manuscript. L.G. and G.C. collected the data. L.G. mainly responsible for the simulation analysis. Z.S. and G.C. verified the results of our work. L.G., Z.S. and G.C. discussed the results and contributed to the final manuscript. All authors have read and agreed to the published version of the manuscript. Funding: The National Natural Science Foundation of China (No.51609073), the Fundamental Research Funds for the Central Universities (No. 2018B11514), the Open Program of Safety and Disaster Prevention Engineering Technology Research Center of the Ministry of Water Resources (2018001), and the Priority Academic Program Development of Jiangsu Higher Education Institutions (YS11001) funded this research. Conflicts of Interest: The authors declare no conflict of interest.

References

1. Chen, S.H.; Xue, L.L.; Xu, G.S.; Shahrour, I. Composite element method for the seepage analysis of rock masses containing fractures and drainage holes. Int. J. Rock Mech. Min. Sci. 2010, 47, 762–770. [CrossRef] 2. Ikard, S.J.; Rittgers, J.; Revil, A.; Mooney, M.A. Geophysical investigation of seepage beneath an earthen dam. Groundwater 2014, 53, 238–250. [CrossRef][PubMed] 3. Lee, J.Y.; Choi, Y.K.; Kim, H.S.; Yun, S.T. Hydrologic characteristics of a large rockfill dam: Implications for water leakage. Eng. Geol. 2005, 80, 43–59. [CrossRef] 4. Xiang, Y.; Wang, L.; Wu, S.H.; Yuan, H.; Wang, Z.J. Seepage analysis of the fractured rock mass in the foundation of the main dam of the Xiaolangdi water control project. Environ. Earth Sci. 2015, 74, 4453–4468. [CrossRef] 5. Chen, Y.F.; Zhou, C.B.; Zheng, H. A numerical solution to seepage problems with complex drainage systems. Comput. Geotech. 2008, 35, 383–393. [CrossRef] 6. Levasseur, S.; Collin, F.; Charlier, R.; Kondo, D. A micro-macro approach of permeability evolution in rocks excavation damaged zones. Comput. Geotech. 2013, 49, 245–252. [CrossRef] 7. Li, Y.; Chen, Y.F.; Jiang, Q.H.; Hu, R.; Zhou, C.B. Performance assessment and optimization of seepage control system: A numerical case study for Kala underground powerhouse. Comput. Geotech. 2014, 55, 306–315. [CrossRef] 8. Oda, M. Permeability tensor for discontinuous rock masses. Geotechnique 1985, 35, 483–495. [CrossRef] 9. Oda, M. An equivalent continuum model for coupled stress and fluid analysis in jointed rock masses. Water Resour. Res. 1986, 22, 1845–1856. [CrossRef] 10. He, J.; Chen, S.H.; Shahrour, I. Back analysis of equivalent permeability tensor for fractured rock masses from packer tests. Rock Mech. Rock Eng. 2011, 44, 491–496. [CrossRef] 11. He, J.; Chen, S.H. A revised solution of equivalent permeability tensor for discontinuous fractures. J. Hydrodyn. 2012, 24, 711–717. [CrossRef] 12. Wines, D.R.; Lilly, P.A. Measurement and analysis of rock mass discontinuity spacing and frequency in part of the Fimiston Open Pit operation in Kalgoorlie, Western Australia: A case study. Int. J. Rock Mech. Min. Sci. 2002, 39, 589–602. [CrossRef] 13. Louis, C.; Maini, Y.N. Determination of in Situ Hydraulic Parameters in Jointed Rock. In Proceedings of the 2nd International Congress on Rock Mechanics, ISRM, Belgrade, Serbia, 21–26 September 1970; pp. 235–245. 14. Singhal, B.B.; Gupta, R.P. Applied of Fractured Rocks; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1999. Water 2020, 12, 734 17 of 17

15. Hsieb, P.; Neumann, S.P.; Simpson, E.S.; Stiles, G. Field determination of the three dimensional hydraulic conductivity tensor of anisotropic media: 1. theory. Water Resour. Res. 1985, 21, 1655–1665. 16. Hsieb, P.; Neumann, S.P.; Simpson, E.S.; Stiles, G. Field determination of the three dimensional hydraulic conductivity tensor of anisotropic media: 2. methodology with application to fractured rocks. Water Resour. Res. 1985, 21, 1667–1676. 17. Nappi, M.; Esposito, L.; Piscopo, V.; Rega, G. Hydraulic characterisation of some arenaceous rocks of Molise (SouthernItaly) through outcropping measurements and Lugeon tests. Eng. Geol. 2005, 81, 54–64. [CrossRef] 18. Sánchez, M.A.; Foyo, A.; Tomillo, C. Application of the Lugeon test in hydrologic studies. Environ. Eng. Sci. 2006, 12, 125–136. [CrossRef] 19. Liu, X.S.; She, C.X.; Zhang, L.J. Back analysis of seepage with ANN based on alternative and interative algorithm. Chin. J. Rock Eng. 2004, 23, 1470–1475. 20. Vahid, N.; Ali, B. Integration of artificial neural networks with radial basis function interpolation in earthfill dam seepage modeling. J. Comput. Civ. Eng. 2013, 27, 183–195. 21. Whitley, D.; Starkweather, T.; Bogart, C. Genetic algorithms and neural networks: Optimizing connections and connectivity. Parallel Comput. 1990, 14, 347–361. [CrossRef] 22. Lin, T.H.; Chiu, S.H.; Tsai, K.C. Supervised feature ranking using a genetic algorithm optimized artificial neural network. J. Chem. Inf. Model. 2006, 46, 1604–1614. [CrossRef] 23. Ren, J.; Shen, Z.Z.; Yang, J.; Yu, C.Z. Back analysis of the 3D seepage problem and its engineering applications. Environ. Earth Sci. 2016, 75, 1–8. [CrossRef] 24. Angulo, B.; Morales, T.; Uriarte, J.A.; Antiguedad, I. Hydraulic conductivity characterization of a recharge area using water injection tests and electrical . Eng. Geol. 2011, 117, 90–96. [CrossRef] 25. Moon, J.S. Representativeness of jointed rock mass hydraulic conductivity obtained from packer tests for tunnel inflow rate estimate. Int. J. Rock Mech. Min. Sci. 2011, 48, 836–844. [CrossRef] 26. Trottier, N.; Delay, F.; Bildstein, O.; Ackerer, P. Inversion of a dual-continuum approach to flow in a karstified limestone: Insight into aquifer heterogeneity revealed by well-test interferences. J. Hydrol. 2014, 508, 157–169. [CrossRef] 27. Shen, Z.Z.; Xu, L.Q.; Cui, J.; Jia, J. A New Interpolation Meshing Method for Calculating Seepage Flux of Well. In Proceedings of the 3rd International Conference on Bioinformatics and Biomedical Engineering, Beijing, China, 11–16 June 2009; pp. 5834–5837. 28. Shen, Z.Z.; Zhao, J.; Wu, L.L. A flexible tolerance method of inverting the percolation parameter. Water Resour. Power 1999, 3, 5–8. 29. Vafakhah, M. Comparison of cokriging and adaptive neuro-fuzzy inference system models for suspended sediment load forecasting. Arab. J. Geosci. 2013, 6, 3003–3018. [CrossRef]

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).