Overall Stability Analysis of Xiluodu High Arch Dam Based on Fine Three-Dimension Numerical Modeling

-e RFPA3D is used to establish a fine finite element model of 6.63 million elements, which realizes the fine simulation of the stability of the Xiluodu arch dam under layered, overall, multiworking conditions and multistress fields, and the cracking and failure process under overload.-e structural design scheme of the arch dam and the corresponding foundation treatment design are evaluated. -e model fully reflects the measures of dam shape structure design, angle fitting structure design, and foundation concrete replacement in the Xiluodu arch dam technical design stage. -e RFPA3D adopts the mesoelement elastic damage model, which considers the Mohr–Coulomb criterion of shear fracture and the maximum tensile failure criterion, and assumes that the mechanical properties of the element satisfy Weibull distribution to consider its heterogeneity. -e simulation results show that, under normal load conditions, the dam foundation surface after comprehensive reinforcement has better overall stability, the stress and deformation of the dam body have good symmetry, and the overload factor of crack initiation under overload calculation K1� 2P0 (P0 is normal water load), the nonlinear deformation overload factor K2� 3.5–4P0, and the limit load factorK3� 7.5–8.0P0, dam safety can be satisfied.-e RFPA3D is used to establish a superlarge finemodel to study the overall stability of the high arch dam, which provides an effective method for analysis and research of other large hydraulic projects in the world.


Introduction
A series of major projects related to national economic construction in China, such as water conservancy and hydropower industry, tend to be large-scale, comprehensive, and complex. A large number of dam foundation-bank structures that are complete, in process, or proposed are generally facing the challenges of construction and operational safety under complex, unpredictable, and extreme load conditions. Among super-high dams, the arch dams transfer loads to the dam foundations and abutments through the effect of the beam and the arching effect, so that the dam body is mainly compressed, and hence, the compressive performance of concrete materials can be fully realized. It has become an extremely beneficial dam type of super-high dams because of its advantages of high safety, strong seismic capacity, large dam discharge, and small concrete quantities [1][2][3][4][5]. However, as most of the load is transferred to the rock on both sides of the dam, high stability and strength of the rock are required. If the geological conditions of the foundation are not good or the symmetry is poor, the arch dam will be prone to stress concentration, dam instability, and other problems, which can result in cracking and even damage to the dam body. e safe operation of dams has a profound impact on social energy efficiency and the lives of downstream residents.
ere have been many incidents of arch dam damage in the world [6,7], which have greatly hindered the safe operation of the project. erefore, it is particularly important to reasonably evaluate the stability of the arch dams in the design.
Among various numerical simulation methods, the threedimensional nonlinear finite element method is widely used in the stability analysis of high arch dam; using a threedimensional nonlinear finite element method to calculate the deformation and stress of the arch dam can well simulate the constitutive relationship and load and boundary conditions of the complex rock and can better reflect the complexity of geological structure and the influence of engineering measures on dam structure. erefore, with the development of computer technology and the popularity of general finite element software, finite element analysis technology has been more and more widely used in solving complex hydropower engineering problems and achieved good engineering results. For example, Yang et al. [15] tried to solve large finite element equations by an iterative method in the three-dimensional finite element analysis of the Geheyan gravity arch dam in 1989 and obtained reasonable calculation results. Shen et al. [16] solved the minimum safety factor and the position of the corresponding potential sliding surface during the excavation of Xiaolangdi high slope by using the three-dimensional finite element analysis method, and the results were confirmed by actual construction. Chen et al. [17] and Chen et al. [18], respectively, carried out a finite element analysis on the abutment rock mass stability and the dam heel cracking risk of the Xiaowan high arch dam. Wang et al. [19] simulated and analyzed the stress state of the Ertan arch dam during operation. According to the results of numerical simulation and model test, Zhang et al. [20] analyzed the displacement and stress distribution, failure mechanism, and overall stability of the arch dam; the results are in good agreement. Pei et al. [21] simulated the construction process and impoundment process of the Lizhou RCC arch dam and analyzed the stress deformation behavior and development law of the dam body in the real working state during the impoundment process. ese applications show that the finite element numerical simulation analysis has obvious advantages in studying the stress, displacement, and failure characteristics of high arch dams and has become an effective way to study the dam design, reinforcement, and stability evaluation of high arch dams. e accuracy of finite element analysis will be affected by the selection of reasonable constitutive relations. Arch dams are usually built into geologically complex mountains and valleys and form an interactive system with dam foundation and dam abutments. As the main engineering materials, rock and concrete are heterogeneous quasi-brittle materials with complex mechanical properties. e researchers have made in-depth discussions on their constitutive relations from phenomenology and physical mechanisms, including strength theory, plastic constitutive theory, damage constitutive theory, and distributed fracture mechanics constitutive theory [22][23][24][25][26]. It has been widely recognized that the fracture and failure process of rock or concrete is actually the whole process of microcracks' generation and development until the formation of the transfixion zone under load. In the past, the constitutive relations of nonlinear finite elements only grasped the "nonlinear" characteristics of material deformation from the macrolevel and participated in the analysis and calculation as an element's attribute, which ignored the inhomogeneity of micromedium parameters, so there is no macromicro difference in the results. In fact, due to the extreme heterogeneity of these materials, their properties at the microlevel are very different from the macrolevel. In order to fully consider the nonlinearity and heterogeneity during the fracture process of rock or concrete, Tang et al. proposed a new numerical simulation method "RFPA (Rock Failure Process Analysis) Method" [27][28][29][30][31][32][33] based on the basic theory of finite element, to explain the structural fracture process with statistical damage theory, and the basic principle of strength reduction method [34,35] was introduced to analyze the stability of geotechnical engineering [36]. It is proved that the method can be used to deal with geotechnical engineering under complex geological conditions effectively.
In addition, the number of grids affects the accuracy of calculation results and the size of the calculation scale. In order to make the element size in numerical simulation reflect the basic microscopic properties of the medium, the RFPA3D code is used to establish the superlarge model of the Xiluodu high arch dam with full hexahedron element (6, 632, 192 elements, 6,893,485 nodes, more than 20 million degrees of freedom). e large-scale parallel computing cluster [37] is used to realize the fine simulation of the dam under layered, overall, multiworking conditions and multistress fields. On the basis of fully reflecting the geological conditions after the actual excavation of the Xiluodu arch dam, the corresponding structural design and foundation treatment measures, the deformation and stress characteristics of the dam body, and abutment rock mass under several different load combinations are studied. rough the application of overload, the overload coefficient, yield, and cracking conditions of each failure stage are obtained to analyze the overload capacity of the arch dam. According to the analysis results, the overall stability and safety of the arch dam under the structural design and foundation treatment design scheme are demonstrated, and the overall safety of the arch dam under the current implementation scheme is comprehensively evaluated, and the results provide a basis for the structural design and foundation treatment design of the Xiluodu high arch dam.

Engineering Background
e Xiluodu hydropower station is located in Xiluodu gorge, which is adjacent to Leibo County in Sichuan Province and Yongshan County in Yunnan Province.
is is the third cascade in the development plan of the Jinsha River section. e double-curvature arch dam is selected as the dam type (the centerline of the arch dam is N 48.2°W), with a crest elevation of 610.0 m, a foundation surface elevation of 332.0 m, and a maximum dam height of 278.0 m, which bears a huge water thrust of about 13 million tons, requiring the foundation to have the corresponding bearing capacity. e total amount of engineering concrete is 12.96 million m 3 , of which about 7 million m 3 is dam concrete. e normal water level of the reservoir is 600.00 m, and the corresponding downstream water level is 378.00 m (381.46 m for normal operation of 18 units); the dead water level is 540.00 m, and the corresponding downstream water level is 378.00 m; the total storage capacity is 11.57 billion m 3 , and the regulated storage capacity is 641.6 billion m 3 . is project is a giant hydropower station that mainly generates electricity and has comprehensive utilization benefits such as sand retaining, flood control, and improving downstream shipping.
ere are abundant mountains on both sides of the Xiluodu double-curvature arch dam, with a steep valley slope. e valley section is symmetrical "U", with the left bank slope of 40°～75°and the right bank slope of 55°～75°. e rock property of the dam site area is single, and the bedrock of the valley slope and the riverbed is the continental basic volcanic rock flow with the intermittently multistage eruption of Emeishan basalt (P2β), which is divided into 14 rock flow layers, generally 25-40 m thick. e representative lithology mainly includes porphyry basalt (1, 6 layers), microcrystalline basalt (2, 5, 9-14 layers), and phenocryst basalt (3, 4, 7, 8 layers), which are distributed in the lower part of the flow layer; basaltic breccia (agglomerate) lava and a small amount of volcanic breccia and basaltic tuff are distributed in the upper part of most flow layers; the lithology changes gradually from the top to the bottom.
Compared with the design requirements and acceptance standards, the rock mass quality of the riverbed under natural conditions is insufficient. erefore, it is necessary to strengthen consolidation grouting and adopt structural forms, expand the stress area of the foundation, and improve the homogeneity of rock mass and the stiffness of the foundation, so as to meet the requirements of dam construction.

Introduction to the Model.
A three-dimensional model is adopted in this calculation. Centered at the dam axis, the calculation range is as follows: the upstream length is about 1 times the height of the dam, the downstream length is about 2.5 times the height of the dam, the banks are near twice the height of the dam, and the simulated depth of the dam foundation is almost the same as the height of the dam. e mesh generation is carried out according to the drawings provided by the Chengdu Survey and Design Institute of China Hydropower Consulting Group, and the total simulation range is 1800 × 1000 × 660 m. Eight-node hexahedron elements are adopted in the grid, with a total number of 6,632,192 elements, a total number of 6,893,485 nodes, and a total number of 2,692,032 dam elements. e computational grid is shown in Figures 1 and 2.
Combined with the current situation of the Xiluodu foundation rock mass, the rock mass parameters are evaluated by the method of layered, segmented, zoned, and graded benchmarking, and on this basis, various rock masses, dislocation zones C9, C8, C7, Lc6, Lc5, C3, and C2, and weak interlayer P2βn are simulated, and the distribution characteristics are shown in Table 1 and Figure 3. e foundation concrete replacement and dam toe treatment are shown in Figure 4. Concrete replacement: the replacement and backfill treatment are carried out for the interlaminar dislocation zone on the banks of the dam foundation at EL 510-610 m, grade IV1 rock mass exposed above the EL 560 m, grade IV 1 and class III2 exposed below the EL 560 m, the staggered zone in the interlayer between the EL 400-510 m and the strongly weathered interlayer, the grade IV1 rock mass exposed on the foundation surface, and the grade III2 rock mass exposed at the middle elevation and lower elevation of the foundation surface. Because the broken rock mass and dislocation zone C3 are exposed at EL 330.00-350.00 m on the left bank of the dam foundation, it is grooved. e strongly weathered interlayer in the middle dislocation zone of the P2βn layer is treated with a composite replacement plug. e exposed IV 1 and III 2 rock masses on the riverbed are treated by displacement excavation. e minimum excavation elevation is EL 324.5 m, and the depth is about 7 m. e depth of replacement excavation shall be adjusted locally according to the geological exposure of the site. e RFPA3D adopts the mesoelement elastic damage model [28], which considers the Mohr-Coulomb criterion of shear fracture and the maximum tensile failure criterion, and assumes that the mechanical properties of the element satisfy Weibull distribution to consider its heterogeneity, so as to reveal the macroscopic nonlinearity of quasi-brittle materials such as rock or concrete from the simple elasticbrittle constitutive relation at the mesolevel. e elasticbrittle constitutive relation of primitive under uniaxial stress is shown in Figure 5.

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For quasi-brittle materials such as rock, especially in the case of special mesoscale, tensile damage mainly occurs in the element. erefore, if the mesoelement satisfies both the shear failure criterion and tensile failure criterion, the tensile criterion takes precedence.

Material Parameters.
e actual monitoring value of dam deformation is usually very different from the original design calculation value, and the mechanical parameters of the rock foundation in the reservoir area also vary greatly. ese factors have a great influence on the deformation of the dam body and rock foundation. erefore, it is necessary to use measured data, combined with numerical analysis and calculation, to carry out inverse analysis on the elastic modulus Ec of the dam body, the deformation modulus Er of the dam bedrock foundation, and the deformation modulus Eb of the reservoir rock foundation and deduce the actual deformation modulus by this method. Table 2 shows the mechanical parameters of Xiluodu materials.

Calculation Conditions.
In this paper, the RFPA3D code is used for finite element numerical calculation, and only the self-weight stress field is considered for crustal stress. As for water load, the upstream check flood level and corresponding downstream water level are 607.00 m and 414.61 m, and the upstream design flood level and corresponding downstream water level are 600.70 m and 409.78 m. e upstream silt elevation is 490.00 m, the floating bulk density of the silt is 0.5 t/m 3 , and the internal friction angle of the silt is 0°. e temperature load of the dam body is shown in Table 3, and the linear expansion coefficient of dam concrete is 1.0×10-5/°C. e calculation consists of 16 calculation conditions, as shown in Tables 4  and 5.

Dam Displacement Analysis.
In this paper, the displacement characteristics of the dam body along the river and transverse the river were analyzed, the working conditions include basic load conditions 4-11, and special load conditions 12-16. e results show that the overall stiffness of the dam foundation after reinforcement is good. Figure 6 shows the displacement distribution along the river of Xiluodu arch dam under conditions 4 and 6.
Taking working condition 4 as an example, the results show that the maximum displacement of the crown along the river was 104.356 mm, located at EL 585 m. e maximum displacement of the left arch abutment along the river was 27.612 mm, at the downstream surface EL 345 m. e maximum displacement of the right arch abutment along the river was 25.617 mm, at the downstream surface EL360 m. e maximum displacement of the arch dam foundation is 25.541 mm, which is located at the right arch abutment EL 440 m, and the relative displacement of the disturbed belt is relatively small. e transverse displacement of the downstream dam surface was toward the mountains. e upstream surface varied from EL 480 m to EL 440 m, and the displacement of the upper part points to the mountains, and the displacement below EL 475 m points to the dam in the transverse direction with the maximum displacement of 2.203 mm. Figure 6 shows the displacement characteristic curve of the arch dam under a normal load condition (condition 4). e displacement characteristics under each condition calculated by RFPA3D code are as follows: (1) Along the river, the maximum displacement of the Xiluodu arch dam under various working conditions was located at the downstream arch crown, the displacement of the two arch abutments was equal, the displacement of the left abutment was slightly larger than that of the right abutment, and the displacement symmetry of dam body was good. Under one to five times of normal water load, the relationship between displacement and overload coefficient is basically linear, which indicates that the deformation of dam structure can still keep a certain linear working state. Figure 7 shows the displacement comparison of the dam abutments and arch crown under 1-5 times normal water load (other loads are the same).
(2) Under different working conditions, the displacement characteristics of the downstream surface of the dam body on the transverse direction of the river were similar, and all of them were toward the mountains, so the dam body had good symmetry. Under the basic load combination, transverse displacement of the upstream surface changed at EL 400 m-EL 520 m, the upper abutments deformed toward the mountains, and the lower abutments deformed toward the dam, so it could be predicted that the compressive stress was larger in this part.
(3) e temperature effect is shown in Figure 8. Under the working condition of temperature rise, the deformation of the two arch abutments increased toward both the mountains and rivers, while the transverse deformation and deformation along the river at the arch crown decreased, which was beneficial to the stability of the arch crown and unfavorable to the stability of the arch abutments.
It can be seen from the calculation results that, under the basic load combinations, the dam surface was basically in a relatively uniform compression state. With the increase of load, the tensile stress first occurred at the dam crest. e maximum tensile stress on the downstream surface was -1.119 MPa under working condition 4, and the maximum tensile stress under other working conditions did not exceed -0.5 MPa. e compressive stress at the two arch abutments of the downstream surface was moderate, and the maximum compressive stress appeared at the arch abutments, mainly at EL 350 m-EL 380 m. e compressive stress at the left arch abutment and that at the right arch abutment were equivalent, and the compressive stress at the left arch abutment was slightly larger. e characteristic stress values of arch dams under different load combinations are shown in Tables 6 and 7.
As one of the main loads of arch dams, temperature load has an important influence on the distribution of the stress Advances in Civil Engineering 5 field, and the change of dam body temperature is an important reason for concrete cracks. By comparing and analyzing the characteristic stress law of arch dam under eight working conditions of 4, 5, 10, 11, and 13-16, the results show that due to the constraint of the abutment rock mass and foundation on the dam body, the temperature rise caused tension on the upstream surface of the arch dam, which makes the upstream surface more prone to cracks, and the downstream surface of the dam had a tendency of squeezing inward.

Displacement of Abutment Rock
Mass. e deformation of the dam abutment rock mass can reflect the stiffness harmony between the rock mass on both banks and the dam. Excessive deformation of the dam abutment will lead to unreasonable stress distribution of the dam body, which will affect the overall stability of the dam body. e calculation of the RFPA3D code shows that the displacement of the dam abutment rock mass along the river mainly occurred near the arch abutments, and the maximum displacement occurred in the middle and lower parts of the downstream arch abutments.
Taking the displacement of the dam abutment rock mass under normal load condition (condition 4) as an example, the displacement of the upstream dam abutments along the river decreased gradually from the bottom elevation to the top, while the displacement of the downstream dam abutments decreased from middle elevation to the top and the bottom, the displacement difference between the top and bottom elevation was small, and the maximum displacement difference was not greater than 12.5 mm. e transverse displacement of the two banks was basically symmetrical, which was larger in the middle elevation and decreased toward the top and bottom gradually. e maximum displacement of the left bank was 10.744 mm, located at EL 565 m, and the maximum displacement of the right bank was -9.835 mm, located at EL 525 m (as shown in Figures 9 and  10).

Foundation Stress.
e following can be obtained from the principal stress distribution of the foundation under working conditions 4 to 16 (Figures 11 and 12 show the principal stress distribution of the foundation under normal working conditions): (1) e calculation results of the basic load combinations (working conditions 4, 5, 10, and 11) show that        the foundation was basically in a compression state, the stress distribution on the two banks was basically symmetrical, the additional stress caused by the thrust of the dam body was mainly distributed in the area near the arch abutments, and the stress far away from the dam was controlled by the self-weight stress field of rock mass; only the dam heel of condition 5 had tensile stress.

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(2) e calculation results of the special load combination (working conditions [12][13][14][15][16] show that the foundation was basically under compression, the stress distribution on the two banks is basically symmetrical, the additional stress generated by the thrust of the dam body was mainly distributed in the vicinity of the arch abutments, and the stress far away from the dam was controlled by the self-weight stress field of rock mass; only the dam heel of condition 13 had tensile stress.

Point Safety Analysis of Foundation Surface
(1) After consolidation grouting, the average elastic modulus of the dam foundation was 12.3 GPa at 0-5 m and 13.3 GPa at 5-20 m. Combined with the Note. "-" means tensile stress and "+" means compressive stress.
Step 2-(0) Figure 9: Displacement of foundation along the river in working condition 4 (unit: mm). current situation of the foundation rock mass, the rock mass evaluation method of layered, segmented, zoned, and graded benchmarking proposed in the design reflected the characteristics of the foundation plane.
(2) Under normal load conditions, the KP of the riverbed was 1.2-3.5, the point safety degree was small, while the KP of both sides of the riverbed was 1.5-5.0. With the overload increase, the excess force of the riverbed gradually shifts to the sides. Overloading to 3P0, the whole downstream surface KP � 1.0-1.5, and the abutment rock mass yielded locally. Overloading to 4P0, the whole downstream surface KP was 1.0-1.5, the riverbed part could still bear large thrust, and a load of dam abutments turned to the riverbed area with higher safety; overloading to 5P0, KP � 1.2. (3) Because the foundation of the banks is mainly on class II rock, the riverbed of both banks can still maintain a high degree of safety in the process of overload. Until 3.5-4P0, both banks first yielded.

Arch Dam Cracking Failure Analysis.
In this paper, the RFPA3D code is used to analyze the cracking process of the dam under overload conditions to evaluate the safety of the arch dam. e dam failure under four overload conditions from working conditions 6 to 9 is mainly simulated. e water load is 2, 3, 4, and 5 times of normal water load, respectively, and other loads remain unchanged. e yield and cracking state of each elevation of the dam under overload conditions are shown in Table 8 and Figure 13. From the calculation results, the following can be seen: (1) Under normal load condition (1P0), the dam body did not yield and was in the normal elastic working state. e deformation and stress in the dam and abutment are basically symmetrical. e safety factors of the rock mass near the abutments of the Xiluodu arch dam were greater than 1.0, indicating that the abutments were in a stable state. e value of the stability safety factor of the rock mass near the dam abutments was the same, and that on the surface was lower than the internal rock mass.        Table 9 and Figure 7, with the increase of overload multiple, the variation characteristics of dam structure deformation and characteristic stress are basically linear, without obvious acceleration or sudden change, indicating that the structure could still maintain certain stability before 5P0.

Conclusions
In this paper, the RFPA3D code is used to establish the hexahedron elements of the Xiluodu superlarge model, which realizes the fine simulation of stress and deformation of the dam under layered, overall, multiworking conditions and multistress fields. Based on the calculation results, the following conclusions can be drawn: (1) Under various working conditions, the displacement distribution of the arch dam body was uniform and symmetrical, the displacement along the river of the arch abutments was equal, and the displacement of the left abutment was slightly larger than that of the right abutment, which stated that the displacement symmetry of dam body was good.
In the transverse river direction, the displacement characteristics of the downstream surface of the dam body have little difference, and they were all toward the mountains, so the symmetry of the dam body was good. It can be seen that the homogenization has performed well after the reinforcement treatment of dam abutment rock mass and dam foundation surface. e maximum displacement of the dam foundation is about 27.6 mm, which is equivalent to Ertan and Jinping arch dam, and smaller than the Xiaowan project.
(2) Under normal load, the abutment rock mass was basically under compression; without obvious concentrated stress, the dam body and dam foundation rock mass are in the linear elastic working state. ere is a tensile stress area at the upstream arch abutment and the replaced rock mass at the EL 400 m-EL 332 m, the maximum tensile stress is -1.1 MPa (right arch abutment at EL 380 m), and the tensile damage is very small, which will not affect the overall operation of the arch dam. e point safety factor of rock mass and dislocation zone along the bank is more than 1.2 and more than 1.5 in the deep.
(3) Under the condition of temperature rise, the deformation of the abutments increased toward both the mountain and river direction, while the deformation of the arch crown decreased toward both transverse direction and the river direction, which is beneficial to the stability of the arch crown and adverse to the stability of the arch abutments. e tension on the upstream surface made it easier to produce cracks.
(4) e calculation results of various working conditions show that the foundation surface at the dam heel had local yield, and the dam heel cracked. e left dam abutment of the downstream surface yielded at EL 480 m, and the dam body at EL 560 m-EL 440 m yielded locally. Besides, with the increase of the overload coefficient, the tensile stress failure points increased, and the overall failure zone also increased, but the failure range did not change greatly.
(5) Under overload conditions, the overall overload capacity of the dam abutment rock mass after comprehensive reinforcement was high. e rock mass quality had been improved in the interlayer Lc5 and Lc6 at EL 400-380 m on the left bank and in the dam area near EL 570-520 m on the right bank. (6) e overall overload safety degree of the Xiluodu arch dam is obtained as follows: the overload factor of crack initiation K1 � 2P0, the nonlinear deformation overload factor K2 � 3.5-4P0, and the limit load factor K3 � 7.5-8.0P0. e arch dam has a high degree of overload safety, and dam safety can be satisfied. (7) e numerical simulation reasonably reflects the stress, deformation, and failure characteristics of dam concrete structure, foundation replacement concrete, dam foundation consolidation grouting, and various rock masses (interlayer dislocation zone, weak structural plane, geological defects) of dam foundation and comprehensively reflects the interaction between arch dam and foundation. e simulation results verify the feasibility of concrete replacement and backfill engineering measures for the Xiluodu arch dam. e stress-strain state and overload capacity of the Xiluodu arch dam are good, which can meet the safety requirements of dam construction. e RFPA3D is used to establish a superlarge fine model to study the working state and overload capacity of the arch dam proposed in this paper, which can be used as a reference for the design and research of super-high arch dam.

Data Availability
e data used to support the findings of this study are included within the article.

Conflicts of Interest
e authors declare that they have no conflicts of interest.