Identiﬁcation of Sensitive Parameters for Deformation of Asphalt Concrete Face Rockﬁll Dam of Pumped Storage Power Station

: Pumped storage power station (PSPS) is an important clean energy project that plays an important role in ensuring the economical, safe, and stable operation of power systems and alleviating the contradiction of peak load regulation. Deformation analysis of the built and under construction PSPS dam was an important process of dam design and operation, which was of great signiﬁcance to ensure the safe operation of hydraulic structures in the reservoir site. Nevertheless, there were many parameters involved in the model for analyzing dam deformation, which brings a large workload to the inversion and application of model parameters. In this study, the asphalt concrete face rockﬁll dam (ACFRD) of a PSPS in Ningxia, China, was taken as an example, a dam deformation 3D ﬁnite element analysis model based on the Duncan–Chang E-B model was constructed, and the orthogonal test method was used. The model parameters of the main rockﬁll zone, secondary rockﬁll zone, and reservoir bottom backﬁll zone were taken as factors for the sensitivity analysis of horizontal displacement of dam H , vertical displacement u, and asphalt concrete face tensile strain ε . The results showed that initial bulk modulus base K b , damage ratio R f, and initial elastic modulus base K had a relatively higher sensitivity and had signiﬁcant impacts on the calculation results, while internal friction angle ϕ , fraction angle reduction ϕ , bulk modulus index m , and elastic modulus index n had a relatively lower sensitivity, which had no signiﬁcant impact on the calculation results. Therefore, when using the Duncan–Chang E-B model to analyze the deformations of a PSPS dam and asphalt concrete face, K b , R f , and K should be the focus. Parameters with a low sensitivity could be determined by engineering analogy so as to achieve the purpose of improving calculation efﬁciency under the premise of ensuring calculation accuracy. Meanwhile, these parameters should also be strictly controlled during construction. The results of this study could provide a reference for the design and safety assessment of ACFRD in PSPS.


Introduction
A pumped storage power station (PSPS) refers to pumping water from the lower reservoir to the upper reservoir during periods of low electrical demand. The electric energy is stored as the potential energy of water. Then, the stored water is discharged from the upper reservoir to the lower reservoir for power generation during periods of high electrical demand [1][2][3]. Owing to their role in power grid peak shaving, voltage regulation, energy storage, and power stability control, PSPSs have become an important type of hydropower project throughout the world [4]. As a large country with hydropower energy This research aimed to study the sensitivity of horizontal displacement of dam H, vertical displacement u, and asphalt concrete face tensile strain ε to model parameters in the analysis of PSPS dams and asphalt concrete face deformation with the Duncan-Chang E-B model. In this study, the ACFRD of a PSPS in Ningxia Province of China was taken as an example. According to the hydro-geological conditions and engineering design data of the project, a 3D finite element model of the dam's deformation based on the Duncan-Chang E-B model was established. The orthogonal test was adopted. The sensitivity of PSPS's ACFRD horizontal displacement H, vertical displacement u, and asphalt concrete face tensile strain ε to the main rockfill zone, secondary rockfill zone, and reservoir bottom backfill zone were studied to provide a theoretical basis for the selection of model parameters for PSPS's ACFRD deformation analysis.

Duncan-Chang E-B Model
To calculate the deformation, the Duncan-Chang E-B model [45] was used to simulate the stress-strain characteristics of the soil. The stress-strain relationship of materials to the Duncan-Chang E-B model was usually obtained by experimental or field triaxial compression tests, which could be approximated as a hyperbola. The Duncan-Chang E-B model could be expressed as follows: where E t is the tangential elastic modulus; E i is the initial shear modulus; S is the stress level, which reflects the ratio of practical principal stress difference and principal stress difference at failure; R f is the damage ratio, which is the ratio of principal stress difference asymptotic value to the actual failure principal stress difference; it was less than 1.0.
where σ 1 is the maximum principal stress and σ 3 is the minimum principal stress.
where K and n are the initial elastic modulus base, and elastic modulus index, respectively, which are experimentally determined; P a is the normal atmospheric pressure. According to the Mohr-Coulomb fracture criterion [46,47] ( where C is the cohesion and ϕ is the internal friction angle. By inserting Equations (2)-(4) into Equation (1), the expression of the tangential modulus could be obtained: The tangential bulk modulus could be calculated by where K b and m are initial bulk modulus base and bulk modulus index, respectively. The elastic module of the material under unloading or reloading could be expressed as [24] E ur = K ur P a σ 3 P a n ur (7) where K ur and n ur were the elastic modulus base and elastic modulus index under unloading and reloading separately, respectively. The Mohr envelope of the coarse aggregate showed obvious nonlinearity. The internal friction angle ϕ varied with the value of confining pressure σ 3 . Therefore, the internal friction angle could be calculated by the following formula: where ϕ 0 is the initial internal friction angle; ∆ϕ is the reduction value of friction angle ϕ when the confining pressure increases by one logarithmic period. Hence, the Duncan-Chang E-B model parameters used to describe the nonlinear constitutive relationship of dam or reservoir bottom filling materials mainly include C, ϕ, ∆ϕ, R f , K, K b , n, m, K ur , and n ur . It should be noted that the creep properties of rockfill, asphalt, concrete, and overburden were simulated by a viscous-elastic-plastic model [48,49].

Principle of Orthogonal Test Design
Orthogonal test design is a design method based on mathematical statistics and the orthogonality principle to select representative points from many test points. An orthogonal table is used to arrange and analyze multi-factor tests. Because of the characteristics of the "neat comparability" and "balanced dispersion" of the orthogonal table, using this method can effectively reduce the number of design tests and reflect the variation law of objective things.
An orthogonal table is key to the design of an orthogonal test. It is required to satisfy the following two conditions [43,44]: uniformity was ensured by the same occurrence of different levels of each column (factor); number pairs composed of different level combinations of any two columns (factors) have the same number of occurrences in the test, so as to ensure the uniformity of the distribution of test points. Only when the two conditions are satisfied can the test results be conveniently and comprehensively reflected. In orthogonal tests, the investigated results are called indicators, the parameters that may have an impact on the test indicators are called factors, and the specific test conditions for each factor to be compared in the test are called levels. The orthogonal table can be represented by the symbol L n (r c ). L is the code of the orthogonal table; n is the total number of tests; r is the level number of factors; c is the column number of the orthogonal table, that is, the maximum number of factors that can be arranged. Taking a test with seven factors and three levels as an example, the constructed orthogonal table is shown in Table 1. In Table 1, the first column of factors are two levels, and the last seven factors are three levels; the total number of tests is 18.

Analysis of Orthogonal Test
The orthogonal test results can be analyzed by: (a) range analysis and (b) variance analysis.

Range Analysis Method
In the range analysis method, the sensitivity degree of the factor is judged by range value R j , which is defined as the influence degree of the change of the factor level on the test indicator. The greater the range, the greater the influence of the change of the factor level on the test index [50]. The range value is obtained by statistical K ij of factors under various levels. The basic principle of the range analysis method can be described as follows [50]: where K ij is the average value of the factor j under level i; P ij is the test numbers of factor j under level i; Y k is the indicator number of the k th test; Y is the average value of all test results.

Analysis of Variance (ANOVA) Method
Range analysis can intuitively reflect the sensitivity order of each factor, but it cannot distinguish whether the fluctuation of test results is caused by the change of factor level or by test error, and there is no clear boundary standard to determine whether the factor is sensitive. Therefore, to distinguish the influence of factor level change and test error and clearly point out the sensitivity degree of the factor, and to further compare and verify the results of range analysis, the variance analysis method was adopted in this study to analyze the test results. The basic principle of the variance analysis method is as follows.
Suppose that L n (r c ) is used to arrange the test, and the results of the k th test are recorded as Y k (k = 1, 2, ···n), the sum of the test results Y k of the i th level of the jth factor is represented as T ij , where T represents the sum of the total test results and p ij is the number of tests of factor j under the i th level, then [44]: The total variance of n test results was recorded as S T , indicating the degree of difference between all test results; the quadratic sum of the variance of the j th column was recorded as S j , indicating the degree of difference between different levels of the factors listed in column j; the sum was marked as S e , indicating the different degree of test conditions during the test. The calculation formula could be expressed as [44]: The degrees of freedom of S T , S j , and S e were assumed to be S T , S j , and S e , respectively, then: In the calculation, the test results (Y 1 , Y 2 , ···Y n ) were independent and obeyed the normal distribution with the same variance σ 2 . The statistics of the F test could be constructed [44]: By comparing F j with the critical test value, F α (f j , f e ) was found in the F distribution table. The sensitivity of the model output results to the changes of various factors could be judged.

Study Site
The asphalt concrete face rockfill dam project of PSPS in this study was located at the western foot of the Niushou mountain on the right bank of the reservoir of the Qingtong gorge on the Yellow River in Ningxia, China. The upper reservoir of the PSPS is located in eastern Daxitian, the main peak of the Niushou mountain. The gully is in a "U" shape. The gully in the reservoir area is developed, and the bottom of the reservoir alternates ditches and beams. The gully needed to be backfilled with excavated materials from the reservoir basin to ensure that the reservoir bottom was flat; therefore, the foundation stiffness of the intense weathering rock mass and the weak weathering rock mass of the reservoir basin foundation and that of the backfilled and excavation area were quite different. The obvious foundation heterogeneity is prone to cause uneven deformation of the foundation. The reservoir bottom elevation of the upper reservoir of the PSPS is 1624 m; the normal water and dead water levels are 1654.00 and 1625.00 m, respectively; the maximum drawdown depth of the reservoir is 29 m; and the regulating reservoir capacity is 7.108 million m 3 , which is a daily regulating reservoir. The pivotal buildings of the project include ACFRD, reservoir basin anti-seepage system, and water inlet and outlet systems. According to the relevant provisions of "Standards for Classification of Hydro-power Projects and Design Safety" (DL5180-2003) and "Standards for Flood Control" (GB50201-2014) in China, this project is a second-class (2) type project according to its storage capacity. The construction of the reservoir was of great significance to the development of the local economy and electrical equipment. Figure 1 shows the geographical location and layout of the reservoir site.
The asphalt concrete face rockfill dam project of PSPS in this study was located at the western foot of the Niushou mountain on the right bank of the reservoir of the Qingtong gorge on the Yellow River in Ningxia, China. The upper reservoir of the PSPS is located in eastern Daxitian, the main peak of the Niushou mountain. The gully is in a "U" shape. The gully in the reservoir area is developed, and the bottom of the reservoir alternates ditches and beams. The gully needed to be backfilled with excavated materials from the reservoir basin to ensure that the reservoir bottom was flat; therefore, the foundation stiffness of the intense weathering rock mass and the weak weathering rock mass of the reservoir basin foundation and that of the backfilled and excavation area were quite different. The obvious foundation heterogeneity is prone to cause uneven deformation of the foundation. The reservoir bottom elevation of the upper reservoir of the PSPS is 1624 m; the normal water and dead water levels are 1654.00 and 1625.00 m, respectively; the maximum drawdown depth of the reservoir is 29 m; and the regulating reservoir capacity is 7.108 million m 3 , which is a daily regulating reservoir. The pivotal buildings of the project include ACFRD, reservoir basin anti-seepage system, and water inlet and outlet systems. According to the relevant provisions of "Standards for Classification of Hydro-power Projects and Design Safety" (DL5180-2003) and "Standards for Flood Control" (GB50201-2014) in China, this project is a second-class (2) type project according to its storage capacity. The construction of the reservoir was of great significance to the development of the local economy and electrical equipment. Figure 1 shows the geographical location and layout of the reservoir site.  The maximum dam height of the main dam in the project is 78 m with a crest elevation of 1660.2 m; the maximum depth of the reservoir bottom backfill zone is 38 m; the crest length is 549.80 m; the crest width is 10 m; the dam slope ratios of upstream and downstream are all 1:1.7. The zone of the dam from upstream to downstream can be divided into the cushion zone (thickness = 3 m), transition zone (thickness = 3 m), main rockfill zone, secondary rockfill zone, and rockfill behind the dam.
The asphalt concrete face with a simple section structure was adopted for seepage prevention in the reservoir basin. The thickness of the panel is 0.202 m. From top to bottom, there is a 2 mm thick asphalt mastic sealing layer, 10 cm thick asphalt concrete anti-seepage layer, and 10 cm thick flat cementation layer. The reservoir bottom and dam are connected by a thickened asphalt concrete arc. The cementation layer was laid between the gravel drainage cushion and the anti-seepage layer to ensure the stable combination of the asphalt concrete face and the cushion. A typical section of the dam along the river is shown in Figure 2.
tom, there is a 2 mm thick asphalt mastic sealing layer, 10 cm thick asphalt concrete antiseepage layer, and 10 cm thick flat cementation layer. The reservoir bottom and dam are connected by a thickened asphalt concrete arc. The cementation layer was laid between the gravel drainage cushion and the anti-seepage layer to ensure the stable combination of the asphalt concrete face and the cushion. A typical section of the dam along the river is shown in Figure 2.

Establishment of Finite Element Model
The actual deformation generally occurred in the semi-infinite domain below the ground, and the deformation calculation could only be conducted in a limited region; therefore, it was very important to determine the scope of the calculation domain for model generalization. The bottom and sides of the deformation calculation domain were truncated boundaries, which were often difficult to accurately determine. Therefore, in addition to including the design area concerned with the displacement field in the computational domain, the position of the truncation boundary should be taken as a position where the error of the adopted boundary conditions has little influence on the displacement field of the concerned area.
In view of the aforementioned principles, the calculation coordinate system and model interception range were defined as follows: the x direction of the model was perpendicular to the dam axis with the positive direction pointing downstream; the y direction was along the dam axis with the positive direction pointing to the left bank; the z-axis was vertically upward with the elevation as the coordinate. The truncated boundaries were 40 m outside the left dam abutment and 60 m outside the right dam abutment. The scope of the reservoir was 20 m within the main backfill area. The downstream truncated boundary was 2 m outside any material area behind the dam. The top elevation was taken as the actual terrain, and the bottom elevation was 1624 m.
According to the geological structure of the dam foundation and abutment on both banks, as well as the requirements of layered filling and loading, super element automatic or manual dissection was adopted to form the finite element mesh. The element model mesh had 20,207 nodes and 20,185 elements after discretization by the hexahedral cells. The nodes and elements for the asphalt concrete face are 1308 and 1244, respectively, and

Establishment of Finite Element Model
The actual deformation generally occurred in the semi-infinite domain below the ground, and the deformation calculation could only be conducted in a limited region; therefore, it was very important to determine the scope of the calculation domain for model generalization. The bottom and sides of the deformation calculation domain were truncated boundaries, which were often difficult to accurately determine. Therefore, in addition to including the design area concerned with the displacement field in the computational domain, the position of the truncation boundary should be taken as a position where the error of the adopted boundary conditions has little influence on the displacement field of the concerned area.
In view of the aforementioned principles, the calculation coordinate system and model interception range were defined as follows: the x direction of the model was perpendicular to the dam axis with the positive direction pointing downstream; the y direction was along the dam axis with the positive direction pointing to the left bank; the z-axis was vertically upward with the elevation as the coordinate. The truncated boundaries were 40 m outside the left dam abutment and 60 m outside the right dam abutment. The scope of the reservoir was 20 m within the main backfill area. The downstream truncated boundary was 2 m outside any material area behind the dam. The top elevation was taken as the actual terrain, and the bottom elevation was 1624 m.
According to the geological structure of the dam foundation and abutment on both banks, as well as the requirements of layered filling and loading, super element automatic or manual dissection was adopted to form the finite element mesh. The element model mesh had 20,207 nodes and 20,185 elements after discretization by the hexahedral cells. The nodes and elements for the asphalt concrete face are 1308 and 1244, respectively, and the maximum and minimum sizes are 10.6 m and 0.55 m, respectively. The three-dimensional finite element mesh of the computational zone is shown in Figure 3. It should be noted that in the subsequent description, the dam body refers to the combination of Figure 3b,d.
the maximum and minimum sizes are 10.6 m and 0.55 m, respectively. The three-dimensional finite element mesh of the computational zone is shown in Figure 3. It should be noted that in the subsequent description, the dam body refers to the combination of Figure  3b,d.

Model Parameters
During model calculation, the dam foundation overburden, dam material (e.g., asphalt concrete face, cushion, transition layer, main rockfill zone, secondary rockfill zone), reservoir bottom backfill zone, and rockfill behind the dam were all considered nonlinear materials [51,52]. The Duncan-Chang E-B model was used to describe the nonlinear constitutive relationship of materials. The calculation parameters are shown in Table 2. Both preventative water-wave concrete walls and bedrock were considered linear materials. A linear elastic model was used to describe the constitutive relationship of materials. The calculation parameters are shown in Table 3. All calculation parameters in this study were provided by the design department and geological exploration department of the project.

Model Parameters
During model calculation, the dam foundation overburden, dam material (e.g., asphalt concrete face, cushion, transition layer, main rockfill zone, secondary rockfill zone), reservoir bottom backfill zone, and rockfill behind the dam were all considered nonlinear materials [51,52]. The Duncan-Chang E-B model was used to describe the nonlinear constitutive relationship of materials. The calculation parameters are shown in Table 2. Both preventative water-wave concrete walls and bedrock were considered linear materials. A linear elastic model was used to describe the constitutive relationship of materials. The calculation parameters are shown in Table 3. All calculation parameters in this study were provided by the design department and geological exploration department of the project. It should be noted that the calculation parameters were obtained according to Chinese national industry standards. For instance, geotechnical parameters were obtained through laboratory tests in accordance with the "Standard for Geotechnical Testing Method in China" (GB/T 50123-2019), and asphalt concrete parameters were obtained through laboratory tests in accordance with the "Standard for Test Code for Hydraulic Bitumen Concrete in China" (DL/T 5362-2006).

Boundary Conditions and Step Loading
For boundary conditions, the bottom boundary of the model was a fixed constraint boundary, and the surrounding truncated boundary was constrained in the x and y directions. The purpose of staged loading was mainly to simulate the construction process and water storage process of the dam, reservoir bottom backfill, rockfill behind the dam, and asphalt concrete face. In staged loading, the mountains around the reservoir basin were loaded first, and then the geo-stress balance was conducted. Before loading the reservoir bottom backfill and dam materials, the node displacement was reset to zero, and the element stress was reserved to obtain the initial stress field of the foundation. The calculated displacements were all caused by construction. The whole dam construction and water storage process was divided into 24 levels, as shown in Figure 4. Each level of the load was loaded once, and the midpoint increment method was used to better simulate the loading process.
Weakly weathered bedrock 28.4 50.0 0.250 It should be noted that the calculation parameters were obtained according to Chinese national industry standards. For instance, geotechnical parameters were obtained through laboratory tests in accordance with the "Standard for Geotechnical Testing Method in China" (GB/T 50123-2019), and asphalt concrete parameters were obtained through laboratory tests in accordance with the "Standard for Test Code for Hydraulic Bitumen Concrete in China" (DL/T 5362-2006).

Boundary Conditions and Step Loading
For boundary conditions, the bottom boundary of the model was a fixed constraint boundary, and the surrounding truncated boundary was constrained in the x and y directions. The purpose of staged loading was mainly to simulate the construction process and water storage process of the dam, reservoir bottom backfill, rockfill behind the dam, and asphalt concrete face. In staged loading, the mountains around the reservoir basin were loaded first, and then the geo-stress balance was conducted. Before loading the reservoir bottom backfill and dam materials, the node displacement was reset to zero, and the element stress was reserved to obtain the initial stress field of the foundation. The calculated displacements were all caused by construction. The whole dam construction and water storage process was divided into 24 levels, as shown in Figure 4. Each level of the load was loaded once, and the midpoint increment method was used to better simulate the loading process. Step loading and water storage process of the model.

Horizontal Displacement of Dam Rockfill
Based on the proposed finite element model, the dam rockfill horizontal displacement distribution along the valley direction after completion and impoundment periods (as shown in Figure 5) were calculated. Notably, the horizontal displacement was positive to point to the downstream direction and negative to point to the upstream direction along the river valley. As shown in Figure 5a, after completion, limited by topographic conditions, the maximum horizontal displacement of the dam rockfill downstream along the valley appeared at the middle ridge of the main rockfill zone ((x, y, z) = (−32.2, 59.1, 1640.1)), and the maximum displacement was about 42.17 mm. The maximum displacement of the dam rockfill upstream along the valley was about 68.26 mm, which occurred 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25   According to the results of the typical cross-section displacement along the river valley, the reservoir bottom backfill zone had an impact on the main rockfill displacement. The maximum displacement of the typical surface to the upstream appeared near y = −30 m, and the displacement at this position decreased under the action of water pressure after impounding. Moreover, after completion, the displacement change of the reservoir bottom surface of the typical section was small, and there was a certain displacement difference on the dam slope. However, after impounding, the displacement difference on the reservoir bottom surface increased to about 60 mm. Although the displacement of the dam slope along the river increased after impounding, the displacement difference was not much different from after completion. Figure 6 shows the distribution of vertical displacements of dam rockfill after completion and impoundment. Notably, vertical displacement was positive when it was vertically upward and negative when it was vertically downward. As observed, after completion, the maximum vertical displacement of the dam rockfill (506.  According to the results of the typical cross-section displacement along the river valley, the reservoir bottom backfill zone had an impact on the main rockfill displacement. The maximum displacement of the typical surface to the upstream appeared near y = −30 m, and the displacement at this position decreased under the action of water pressure after impounding. Moreover, after completion, the displacement change of the reservoir bottom surface of the typical section was small, and there was a certain displacement difference on the dam slope. However, after impounding, the displacement difference on the reservoir bottom surface increased to about 60 mm. Although the displacement of the dam slope along the river increased after impounding, the displacement difference was not much different from after completion.  From a safety point of view, the internal structure of the anti-seepage material cannot be damaged. In terms of the safety of stress-strain curves of asphalt concrete, the linear section was generally regarded as the main working stage of asphalt concrete. According to the relevant provisions of "Standards for Design Code of Asphalt Concrete Facings and Cores for Embankment Dams" (SL 501-2010), the content of asphalt in the impervious layer of asphalt concrete face could be from 6.5-8.5%. According to much triaxial test data, if the stress when the volume changed from compression equilibrium to micro-expansion was regarded as failure stress [53], the tensile range of the asphalt concrete was 1.0~1.3 MPa. The test value of yield tensile strain for the asphalt concrete at 5 °C at the Sabigawa Dam, Japan at 0.5%. The allowable tensile strain of the modified asphalt concrete could reach 1%, but 0.5% was taken as the yield tensile strain for the asphalt concrete in engineering practice. Figure 7 shows the distribution of tensile strain of asphalt concrete face after impoundment. It should be noted that the negative value represents tensile strain, and the positive represents compressive. To clearly show the tensile strain, strain values above 0 were uniformly limited to one level here, i.e., the compressive strain is displayed in blue.

Tensile Strain of Asphalt Concrete Face
From a safety point of view, the internal structure of the anti-seepage material cannot be damaged. In terms of the safety of stress-strain curves of asphalt concrete, the linear section was generally regarded as the main working stage of asphalt concrete. According to the relevant provisions of "Standards for Design Code of Asphalt Concrete Facings and Cores for Embankment Dams" (SL 501-2010), the content of asphalt in the impervious layer of asphalt concrete face could be from 6.5-8.5%. According to much triaxial test data, if the stress when the volume changed from compression equilibrium to micro-expansion was regarded as failure stress [53], the tensile range of the asphalt concrete was 1.0~1.3 MPa. The test value of yield tensile strain for the asphalt concrete at 5 • C at the Sabigawa Dam, Japan at 0.5%. The allowable tensile strain of the modified asphalt concrete could reach 1%, but 0.5% was taken as the yield tensile strain for the asphalt concrete in engineering practice. Figure 7 shows the distribution of tensile strain of asphalt concrete face after impoundment. It should be noted that the negative value represents tensile strain, and the positive represents compressive. To clearly show the tensile strain, strain values above 0 were uniformly limited to one level here, i.e., the compressive strain is displayed in blue.
As shown in Figure 7, the tensile strain peak area appeared at the reverse arc section of the panel and the excavation-filling interface. Overall, the tensile strain of the reverse arc section of the panel was larger at the reservoir bottom backfill zone and tended to gradually decrease towards the middle ridge and the two banks. The tensile strain of most of the panel reverse arc section of the reservoir bottom backfill zone exceeded 0.3%, but the maximum tensile strain was only 0.445%, which did not exceed the specification value by 0.5%, so it was safe. For the excavation-filling interface, the maximum tensile strain was 0.483%, which did not exceed the allowable value of 0.5%. The tensile strain at other locations was not more than 0.05%. It is slightly larger at the left and right bank abutments but still within the allowable range of the specification value. Therefore, the whole asphalt concrete face was safe after impoundment.  Figure 7, the tensile strain peak area appeared at the reve of the panel and the excavation-filling interface. Overall, the tensile strain arc section of the panel was larger at the reservoir bottom backfill zone gradually decrease towards the middle ridge and the two banks. The tensile of the panel reverse arc section of the reservoir bottom backfill zone excee the maximum tensile strain was only 0.445%, which did not exceed the spec by 0.5%, so it was safe. For the excavation-filling interface, the maximum was 0.483%, which did not exceed the allowable value of 0.5%. The tensile locations was not more than 0.05%. It is slightly larger at the left and right ba but still within the allowable range of the specification value. Therefore, the concrete face was safe after impoundment.

Orthogonal Test Design and Results
There were 10 parameters involved in the Duncan-Chang E-B model n, Rf, φ, Δφ, Kb, m, c, Kur, and nur. In the process of filling and impounding, th was under a loading state. Parameters Kur and nur were not included in th and the rockfill was a granular material, so parameter c could be considere fore, the factors for sensitivity analysis were φ0, Δφ, Rf, K, n, Kb, and m.
Under the self-weight of the rockfill and water load, vertical and hor mation upstream and downstream had a great impact on the dam. At the sa sidering that the excessive asphalt concrete face tensile strain was the main cracking, the dam maximum vertical displacement u, maximum horizontal H, and asphalt concrete face tensile strain ε were selected as the main test rameter sensitivity analysis. Based on the above model calculation parame parameters were increased or decreased by 20% as the three level values of t test in this study. Table 4 shows the levels of various factors adopted in t

Orthogonal Test Design and Results
There were 10 parameters involved in the Duncan-Chang E-B model, including: K, n, R f , ϕ, ∆ϕ, K b , m, c, K ur , and n ur . In the process of filling and impounding, the rockfill zone was under a loading state. Parameters K ur and n ur were not included in the calculation, and the rockfill was a granular material, so parameter c could be considered zero. Therefore, the factors for sensitivity analysis were ϕ 0 , ∆ϕ, R f , K, n, K b , and m.
Under the self-weight of the rockfill and water load, vertical and horizontal deformation upstream and downstream had a great impact on the dam. At the same time, considering that the excessive asphalt concrete face tensile strain was the main cause of panel cracking, the dam maximum vertical displacement u, maximum horizontal displacement H, and asphalt concrete face tensile strain ε were selected as the main test indices of parameter sensitivity analysis. Based on the above model calculation parameters, the basic parameters were increased or decreased by 20% as the three level values of the orthogonal test in this study. Table 4 shows the levels of various factors adopted in the orthogonal test sensitivity analysis. According to the test factors and levels, the L 18 (2 × 3 7 ) orthogonal table was selected in this study. The first column in the table was set as empty and was not included in the calculation and analysis. The different levels of each factor were filled in accordingly. Assuming that the test factors were independent, the corresponding orthogonal table could be obtained by randomly filling the test factors in the last seven columns of the orthogonal table. Considering the possible differences in the sensitivity of test indicators to model parameters in different zones, the main rockfill, secondary rockfill, and reservoir bottom backfill zones were separately considered, and the maximum vertical displacement of the dam u, maximum horizontal displacement H, and tensile strain of asphalt concrete ε during the impoundment period under the orthogonal combination of the Duncan-Chang E-B model parameters of these three zones was calculated. The test scheme and results are shown in Tables 5-7. The range analysis method was used to process the results of each scheme in the three columns u, H, and ε and in the summary table of orthogonal test results in the main rockfill zone ( Table 5). The range analysis results are shown in Table 8. The range analysis results of each test index u, H, and ε in the main rockfill zone were organized, and then the range value histogram was drawn according to the range value of each test index according to each factor, as shown in Figure 8.
As shown in Table 8 and Figure 8, during the impoundment period, the sensitivity degree of maximum vertical displacement of dam u to indices of the Duncan-Chang E-B model of the main rockfill zone from high to low was R f > ϕ 0 > K > K b > n > ∆ϕ > m; the sensitivity of maximum horizontal displacement H to indices of the Duncan-Chang E-B model of main rockfill zone from high to low was K b > R f > K > ϕ 0 > n > m > ∆ϕ; the sensitivity of asphalt concrete face maximum tensile strain ε to indices of the Duncan-Chang E-B model of main rockfill zone from high to low was The range analysis results of each test index u, H, and ε in th organized, and then the range value histogram was drawn acco of each test index according to each factor, as shown in Figure 8. As shown in Table 8 and Figure 8, during the impoundme degree of maximum vertical displacement of dam u to indices o model of the main rockfill zone from high to low was Rf > φ0 > sensitivity of maximum horizontal displacement H to indices of model of main rockfill zone from high to low was Kb > Rf > K > φ0 > n of asphalt concrete face maximum tensile strain ε to indices of model of main rockfill zone from high to low was Kb > Rf > φ0 > K

Range Analysis for Secondary Rockfill Zone
The range analysis method was used to process the results of columns u, H, and ε in the summary table of the orthogonal test rockfill zone ( Table 6). The range analysis results are shown in T

Range Analysis for Secondary Rockfill Zone
The range analysis method was used to process the results of each scheme in the three columns u, H, and ε in the summary table of the orthogonal test results in the secondary rockfill zone ( Table 6). The range analysis results are shown in Table 9. Table 9. Range analysis results of influencing factors on each test index for the secondary rockfill zone.

Test Index
Factor The range analysis results of each test index u, H, and ε in the secondary rockfill zone were sorted out, and then the range value histogram was drawn according to the range value of each test index according to each factor, as shown in Figure 9. r 2022, 14, x FOR PEER REVIEW Figure 9. Sensitivity of each test index for the secondary rockfill zone.
As shown in Table 9 and Figure 9, during the impoundme degree of maximum vertical displacement of dam u to indexes o Duncan-Chang E-B model from high to low was Kb > K > Rf > φ0 > Δ of maximum horizontal displacement H to indexes of Duncanondary rockfill zone from high to low was Kb > Rf > K > φ0 > Δφ > maximum tensile strain of asphalt concrete face ε to indexes of D of secondary rockfill zone from high to low was Kb > K > φ0 > m >

Range Analysis for Reservoir Bottom Backfill Zone
The range analysis method was used to process the results of columns of u, H, and ε in the summary table of orthogonal tes bottom backfill zone (Table 7), and the range analysis results we   As shown in Table 9 and Figure 9, during the impoundment period, the sensitivity degree of maximum vertical displacement of dam u to indexes of secondary rockfill zone Duncan-Chang E-B model from high to low was K b > K > R f > ϕ 0 > ∆ϕ > m > n; the sensitivity of maximum horizontal displacement H to indexes of Duncan-Chang E-B model of secondary rockfill zone from high to low was K b > R f > K > ϕ 0 > ∆ϕ > m > n; the sensitivity of maximum tensile strain of asphalt concrete face ε to indexes of Duncan-Chang E-B model of secondary rockfill zone from high to low was K b > K > ϕ 0 > m > ∆ϕ > n > R f .

Range Analysis for Reservoir Bottom Backfill Zone
The range analysis method was used to process the results of each scheme in the three columns of u, H, and ε in the summary table of orthogonal test results in the reservoir bottom backfill zone (Table 7), and the range analysis results were shown in Table 10. Table 10. Range analysis results of influencing factors of each test index for the reservoir bottom backfill zone.

Test Index
Factor The range analysis results of each test index u, H, and ε in the reservoir bottom rockfill zone were sorted out, and then the range value histogram was drawn according to the range value of each test index according to each factor, as shown in Figure 10. Figure 10. Sensitivity of each test index for the reservoir bottom bac As shown in Table 10 and Figure 10, during the impoun of maximum vertical displacement of dam u to indexes of re Duncan-Chang E-B model from high to low was Rf > K > Kb > n of maximum horizontal displacement H to indexes of Duncan voir bottom backfill zone from high to low was Kb > Rf > K > Δ of maximum tensile strain of asphalt concrete face ε to ind model of reservoir bottom backfill zone from high to low wa 4.6.3. Sensitivity Analysis Based on ANOVA Method

022, 14, x FOR PEER REVIEW
For the variance analysis of the orthogonal test results, th selected α = 0.05 and α = 0.1. From the F distribution table, F0 5.46. The significance levels of the factors were judged by com the earlier values. The judgment criteria were when Fj > F0.0 factor was highly significant, and the sensitivity was high; w the influence of this factor was generally significant, and the s when Fj < F0.1 (2, 3), the influence of this factor was not signifi low. As shown in Table 10 and Figure 10, during the impoundment period, the sensitivity of maximum vertical displacement of dam u to indexes of reservoir bottom backfill zone Duncan-Chang E-B model from high to low was R f > K > K b > n > ϕ 0 > m > ∆ϕ; the sensitivity of maximum horizontal displacement H to indexes of Duncan-Chang E-B model of reservoir bottom backfill zone from high to low was K b > R f > K > ∆ϕ > ϕ 0 > n > m; the sensitivity of maximum tensile strain of asphalt concrete face ε to indexes of Duncan-Chang E-B model of reservoir bottom backfill zone from high to low was K b > R f > K > ϕ 0 > ∆ϕ > n > m.

Sensitivity Analysis Based on ANOVA Method
For the variance analysis of the orthogonal test results, the test level confidences were selected α = 0.05 and α = 0.1. From the F distribution table, F 0.05 (2, 3) = 16.0 and F 0.1 (2, 3) = 5.46. The significance levels of the factors were judged by comparing the calculated F j with the earlier values. The judgment criteria were when F j > F 0.05 (2,3), the influence of this factor was highly significant, and the sensitivity was high; when F 0.1 (2, 3) ≤ F j ≤ F 0.05 (2,3), the influence of this factor was generally significant, and the sensitivity was medium; and when F j < F 0.1 (2,3), the influence of this factor was not significant, and the sensitivity was low.

ANOVA for Main Rockfill Zone
The results of each scheme involved u, H, and ε in the main rockfill zone orthogonal test results (Table 5) were analyzed with the variance analysis method, and the variance analysis results are shown in Table 11. To reflect the results of the analysis, the ANOVA results for each test index were collated, and a sensitivity size bar chart was plotted from the F value of each test index ( Figure 11). Notably, for comparison convenience, the influence value F of K b and R f on the test index H was reduced by 1.5 times, as seen in Figure 11.
As shown in Table 11 and Figure 11, for the maximum vertical displacement of dam u, the sensitivity degree of the Duncan-Chang E-B model of the main rockfill zone parameters from high to low was R f > ϕ 0 > K > K b > n > ∆ϕ > m. The influence of R f was highly significant, and the sensitivity was high; the influences of ϕ 0 and K were generally significant, and the sensitivities were medium; the influences of K b , n, ∆ϕ, and m were not significant, and the sensitivities were low. For the maximum horizontal displacement of dam H, the sensitivity degree of Duncan-Chang E-B model of main rockfill zone parameters from high to low was K b > R f > K > ϕ 0 > n > m > ∆ϕ. The influences of K b , R f , K, and ϕ were highly significant, and the sensitivities were high; the influences of n, m, and ∆ϕ were not significant, and the sensitivities were low. For the tensile strain of asphalt concrete ε, the sensitivity degree of the Duncan-Chang E-B model of the main rockfill zone parameters from high to low was K b > R f > ϕ 0 > K > n > m > ∆ϕ. The influence of K b was highly significant, and the sensitivity was high; the influence of R f was generally significant, and the sensitivity was medium; the influences of ϕ 0 , K, n, m, and ∆ϕ were not significant, and the sensitivities were low.

ANOVA for Secondary Rockfill Zone
The results of each scheme involved u, H, and ε in the secondary rockfill zone's orthogonal test results (Table 6) were analyzed with the variance analysis method, and the variance analysis results are shown in Table 12.
To reflect the results of the analysis, the ANOVA results f collated, and a sensitivity size bar chart was plotted from the F (Figure 11). Notably, for comparison convenience, the influence the test index H was reduced by 1.5 times, as seen in Figure 11 Table 11 and Figure 11, for the maximum verti u, the sensitivity degree of the Duncan-Chang E-B model of the m eters from high to low was Rf > φ0   To obviously reflect the results of the analysis, the ANOVA results for each test index were collated, and a sensitivity size bar chart was plotted through the F value of each test index ( Figure 12). Notably, for comparison convenience, the influence value F of K b on the test index u, H, and ε was reduced three times in Figure 12.
Random error 0.0009 3 To obviously reflect the results of the analysis, the ANOVA r were collated, and a sensitivity size bar chart was plotted throug index ( Figure 12). Notably, for comparison convenience, the influ test index u, H, and ε was reduced three times in Figure 12.  Table 12 and Figure 12, for the maximum verti u, the sensitivity degree of the Duncan-Chang E-B model of the parameters from high to low was Kb > K > Rf > φ0 > Δφ > m > n. Th were highly significant, and the sensitivities were high; the influ significant, and the sensitivity was medium; the influences of φ significant, and the sensitivities were low. For the maximum ho dam H, the sensitivity degree of the Duncan-Chang E-B model zone parameters from high to low was Kb > Rf > K > φ0 > Δφ > m > n highly significant, and the sensitivity was high; the influences of significant, and the sensitivities were medium; the influences of φ significant, and the sensitivities were low. For the tensile strain o sensitivity degree of the Duncan-Chang E-B model of the second eters from high to low was Kb > K > φ0 > m > Δφ > n > Rf. The inf significant, and the sensitivity was high; the influences of K, φ0, m significant, and the sensitivities were low.

ANOVA for Reservoir Bottom Backfill Zone
The results of each scheme involved u, H, and ε in the reserv orthogonal test results (  As shown in Table 12 and Figure 12, for the maximum vertical displacement of dam u, the sensitivity degree of the Duncan-Chang E-B model of the secondary rockfill zone parameters from high to low was K b > K > R f > ϕ 0 > ∆ϕ > m > n. The influences of K b and K were highly significant, and the sensitivities were high; the influence of R f was generally significant, and the sensitivity was medium; the influences of ϕ 0 , ∆ϕ, m, and n were not significant, and the sensitivities were low. For the maximum horizontal displacement of dam H, the sensitivity degree of the Duncan-Chang E-B model of the secondary rockfill zone parameters from high to low was K b > R f > K > ϕ 0 > ∆ϕ > m > n. The influence of K b was highly significant, and the sensitivity was high; the influences of R f and K were generally significant, and the sensitivities were medium; the influences of ϕ 0 , ∆ϕ, m, and n were not significant, and the sensitivities were low. For the tensile strain of asphalt concrete ε, the sensitivity degree of the Duncan-Chang E-B model of the secondary rockfill zone parameters from high to low was K b > K > ϕ 0 > m > ∆ϕ > n > R f . The influence of K b was highly significant, and the sensitivity was high; the influences of K, ϕ 0 , m, ∆ϕ, n, and R f were not significant, and the sensitivities were low.

ANOVA for Reservoir Bottom Backfill Zone
The results of each scheme involved u, H, and ε in the reservoir bottom backfill zone orthogonal test results (Table 6) were analyzed with the variance analysis method, and the variance analysis results are shown in Table 13.  As shown in Table 13 and Figure 13, for the maximum vertic u, the sensitivity degree of the Duncan-Chang E-B model of the r zone parameters from high to low was Rf > K > Kb > n > φ0 > m > Δφ and Kb were highly significant, and the sensitivities were high; the m were generally significant, and the sensitivities were medium; m, and n were not significant, and the sensitivities were low. For t displacement of dam H, the sensitivity degree of the Duncan-C reservoir bottom backfill zone parameters from high to low was m. The influences of Kb, K, and Rf were highly significant, and the the influences of Δφ and φ0 were generally significant, and the sen the influence of n and m were not significant, and the sensitivities strain of asphalt concrete ε, the sensitivity degree of the Duncanreservoir bottom backfill zone parameters from high to low was m. The influence of Kb was highly significant, and the sensitivity of K, φ0, m, Δφ, n, and Rf were not significant, and the sensitivitie 4.6.4. Comparison of Sensitivity Results of Range Analysis and A To explore the analysis accuracy of deformation-sensitive pa phalt concrete face dam with an orthogonal test, the results obtain and variance analysis methods were compared, as shown in Table  by the variance analysis were consistent with those obtained by th reflected the rationality of the sensitivity analysis results in this s

Comparison of Sensitivity Results of Range Analysis and ANOVA
To explore the analysis accuracy of deformation-sensitive parameters of the PSPS asphalt concrete face dam with an orthogonal test, the results obtained by the range analysis and variance analysis methods were compared, as shown in Table 14. The results obtained by the variance analysis were consistent with those obtained by the range analysis, which reflected the rationality of the sensitivity analysis results in this study to some extent.
Secondary rockfill zone Range analysis method Reservoir bottom backfill zone Range analysis method

Conclusions
To determine the sensitivity of the deformation of the ACFRD of the PSPS to the Duncan-Chang E-B model parameters, a PSPS project in Ningxia, China, was taken as an example. Firstly, an ACFRD deformation finite element analysis model based on the Duncan-Chang E-B model was established, and the laws of dam horizontal displacement, vertical displacement, and asphalt concrete face tensile strain under the conditions of completion period and impoundment period were analyzed. Then, based on the orthogonal test, the sensitivities of ACFRD horizontal displacement, vertical displacement, and asphalt concrete face tensile strain to the Duncan-Chang E-B models of the main rockfill zone, secondary rockfill zone, and reservoir bottom backfill zone were studied. Finally, the results of the two orthogonal test sensitivity analysis methods (i.e., range analysis and ANOVA methods) were compared to demonstrate the rationality of the sensitivity analysis results. The major conclusions derived from this study could be summarized as follows: 1. The PSPS's ACFRD deformation finite element analysis model based on the Duncan-Chang E-B model could reasonably reflect the dam's horizontal displacement, vertical displacement, and the tensile strain of the asphalt concrete face during the completion and impoundment periods. The maximum vertical displacement of the dam appeared at about half the dam's height of the main rockfill zone in the impoundment period, which was consistent with the actual general law, indicating the rationality of the model calculation results. The maximum tensile strain of asphalt concrete face was 0.483%, which did not exceed the allowable value of 0.5% in the impoundment period. Therefore, during the operation of the dam, the asphalt concrete face was safe.
2. For the maximum vertical displacement of dam u, the sensitivity degree of the Duncan-Chang E-B model of the main rockfill zone parameters from high to low was R f > ϕ 0 > K > K b > n > ∆ϕ > m, the sensitivity degree of R f was the highest; the sensitivity degree of the Duncan-Chang E-B model of the secondary rockfill zone parameters from high to low was K b > K > R f > ϕ 0 > ∆ϕ > m > n, the sensitivity degrees of K b and K were high; the sensitivity degree of the Duncan-Chang E-B model of the reservoir bottom backfill zone parameters from high to low was R f > K > K b > n > ϕ 0 > m > ∆ϕ, the sensitivity degrees of R f , K and K b were highly significant, and the sensitivities were high.
3. For the maximum horizontal displacement of dam H, the sensitivity degree of the Duncan-Chang E-B model of the main rockfill zone parameters from high to low was K b > R f > K > ϕ 0 > n > m > ∆ϕ, and the sensitivities of K b , R f , K, and ϕ 0 were highly significant, and the sensitivities were high; the sensitivity of the Duncan-Chang E-B model of the secondary rockfill zone parameters from high to low was K b > R f > K > ϕ 0 > ∆ϕ > m > n, the sensitivity of K b was the highest; the sensitivity of the Duncan-Chang E-B model of the reservoir bottom backfill zone parameters from high to low was K b > R f > K > ∆ϕ > ϕ 0 > n > m, the sensitivities of K b , K and R f were high.
4. For the tensile strain of asphalt concrete ε, the sensitivity of the Duncan-Chang E-B model of main rockfill zone parameters from high to low was K b > R f > ϕ 0 > K > n > m > ∆ϕ, and the sensitivity of K b was highly significant, and the sensitivity was high; the sensitivity of the Duncan-Chang E-B model of secondary rockfill zone parameters from high to low was K b > K > ϕ 0 > m > ∆ϕ > n > R f , e the sensitivity of K b was the highest; the sensitivity of the Duncan-Chang E-B model of the reservoir bottom backfill zone parameters from high to low was K b > R f > K > ϕ 0 > ∆ϕ > n > m, the sensitivity of K b was the highest. 5. The results of the range analysis were consistent with that of the variance analysis, which reflected the reliability of the sensitivity analysis in this study. Therefore, K b , R f , and K should be focused when analyzing PSPS's ACFRD deformation with the Duncan-Chang E-B model, for which values were required to be accurate. For other parameters with low sensitivity, the engineering analogy method could be adopted to obtain the values. In this way, even if the measured data were missed, the calculation accuracy and efficiency could both be ensured. Furthermore, these sensitivity parameters should also be strictly controlled during the design and construction of ACFRD.
It should be noted that the mechanical properties of asphalt concrete are greatly affected by temperature changes. Therefore, for PSPS's ACFRD deformation analysis in extremely cold or hot environments, the effect of temperature needs to be considered during modeling.