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

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

_{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.

## 1. Introduction

## 2. Duncan–Chang E-B Model

_{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.

_{1}is the maximum principal stress and σ

_{3}is the minimum principal stress.

_{a}is the normal atmospheric pressure.

_{b}and m are initial bulk modulus base and bulk modulus index, respectively.

_{ur}and n

_{ur}were the elastic modulus base and elastic modulus index under unloading and reloading separately, respectively.

_{3}. Therefore, the internal friction angle could be calculated by the following formula:

_{0}is the initial internal friction angle; Δφ is the reduction value of friction angle φ when the confining pressure increases by one logarithmic period.

_{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].

## 3. Orthogonal Test Method

#### 3.1. Principle of Orthogonal Test Design

_{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.

#### 3.2. Analysis of Orthogonal Test

#### 3.2.1. Range Analysis Method

_{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]:

_{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; $\overline{Y}$ is the average value of all test results.

#### 3.2.2. Analysis of Variance (ANOVA) Method

_{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]:

_{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]:

_{T}, S

_{j}, and S

_{e}were assumed to be S

_{T}, S

_{j}, and S

_{e}, respectively, then:

_{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]:

_{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.

## 4. Case Study

#### 4.1. Study Site

^{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.

#### 4.2. Establishment of Finite Element Model

#### 4.3. Model Parameters

#### 4.4. Boundary Conditions and Step Loading

#### 4.5. Deformation Analysis Based on the Established Model

#### 4.5.1. Horizontal Displacement of Dam Rockfill

#### 4.5.2. Vertical Displacement of Dam Rockfill

#### 4.5.3. Tensile Strain of Asphalt Concrete Face

#### 4.6. Sensitivity Analysis

#### 4.6.1. Orthogonal Test Design and Results

_{f}, φ, Δφ, 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}, Δφ, R

_{f}, K, n, K

_{b}, and m.

_{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 Table 5, Table 6 and Table 7.

#### 4.6.2. Sensitivity Analysis Based on Range Analysis Method

#### Range Analysis for Main Rockfill Zone

_{f}> φ

_{0}> K > K

_{b}> n > Δφ > 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 > Δφ; 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 K

_{b}> R

_{f}> φ

_{0}> K > n > m > Δφ.

#### Range Analysis for Secondary Rockfill Zone

_{b}> K > R

_{f}> φ

_{0}> Δφ > 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}> Δφ > 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 > Δφ > n > R

_{f}.

#### Range Analysis for Reservoir Bottom Backfill Zone

_{f}> K > K

_{b}> n > φ

_{0}> m > Δφ; 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 > Δφ > 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}> Δφ > n > m.

#### 4.6.3. Sensitivity Analysis Based on ANOVA Method

_{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

_{b}and R

_{f}on the test index H was reduced by 1.5 times, as seen in Figure 11.

_{f}> φ

_{0}> K > K

_{b}> n > Δφ > 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, Δφ, 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 > Δφ. The influences of K

_{b}, R

_{f}, K, and φ were highly significant, and the sensitivities were high; the influences of n, m, and Δφ 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 > Δφ. 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 Δφ were not significant, and the sensitivities were low.

#### ANOVA for Secondary Rockfill Zone

_{b}on the test index u, H, and ε was reduced three times in Figure 12.

_{b}> K > R

_{f}> φ

_{0}> Δφ > 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}, Δφ, 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}> Δφ > 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}, Δφ, 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 > Δφ > n > R

_{f}. The influence of K

_{b}was highly significant, and the sensitivity was high; the influences of K, φ

_{0}, m, Δφ, n, and R

_{f}were not significant, and the sensitivities were low.

#### ANOVA for Reservoir Bottom Backfill Zone

_{b}and m on the test index u was reduced ten times in Figure 13 and two times of K

_{b}on the test index H.

_{f}> K > K

_{b}> n > φ

_{0}> m > Δφ. The influences of R

_{f}, K, and K

_{b}were highly significant, and the sensitivities were high; the influences of φ

_{0}, n, and m were generally significant, and the sensitivities were medium; the influences of φ

_{0}, Δφ, 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 reservoir bottom backfill zone parameters from high to low was K

_{b}> R

_{f}> K > Δφ > φ

_{0}> n > m. The influences of K

_{b}, K, and R

_{f}were highly significant, and the sensitivities were high; the influences of Δφ and φ

_{0}were generally significant, and the sensitivities were medium; the influence of n and m 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 reservoir bottom backfill zone parameters from high to low was K

_{b}> R

_{f}> K > φ

_{0}> Δφ > n > m. The influence of K

_{b}was highly significant, and the sensitivity was high; the influences of K, φ

_{0}, m, Δφ, n, and R

_{f}were not significant, and the sensitivities were low.

#### 4.6.4. Comparison of Sensitivity Results of Range Analysis and ANOVA

## 5. Conclusions

_{f}> φ

_{0}> K > K

_{b}> n > Δφ > 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}> Δφ > 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 > Δφ, the sensitivity degrees of R

_{f}, K and K

_{b}were highly significant, and the sensitivities were high.

_{b}> R

_{f}> K > φ

_{0}> n > m > Δφ, 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}> Δφ > 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 > Δφ > φ

_{0}> n > m, the sensitivities of K

_{b}, K and R

_{f}were high.

_{b}> R

_{f}> φ

_{0}> K > n > m > Δφ, 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 > Δφ > 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}> Δφ > n > m, the sensitivity of K

_{b}was the highest.

_{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.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Three-dimensional finite element mesh of the calculation zone: (

**a**) reservoir basin; (

**b**) reservoir bottom backfill area; (

**c**) asphalt concrete face; (

**d**) dam rock area.

**Figure 5.**Distribution of horizontal displacement along the river (unit: mm): (

**a**) after completion; (

**b**) after impoundment.

**Figure 6.**Distribution of vertical displacement (unit: mm): (

**a**) after completion; (

**b**) after impoundment.

Test Number | Column Number | |||||||
---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |

1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

2 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 |

3 | 1 | 1 | 3 | 3 | 3 | 3 | 3 | 3 |

4 | 1 | 2 | 1 | 1 | 2 | 2 | 3 | 3 |

5 | 1 | 2 | 2 | 2 | 3 | 3 | 1 | 1 |

6 | 1 | 2 | 3 | 3 | 1 | 1 | 2 | 2 |

7 | 1 | 3 | 1 | 2 | 1 | 3 | 2 | 3 |

8 | 1 | 3 | 2 | 3 | 2 | 1 | 3 | 1 |

9 | 1 | 3 | 3 | 1 | 3 | 2 | 1 | 2 |

10 | 2 | 1 | 1 | 3 | 3 | 2 | 2 | 1 |

11 | 2 | 1 | 2 | 1 | 1 | 3 | 3 | 2 |

12 | 2 | 1 | 3 | 2 | 2 | 1 | 1 | 3 |

13 | 2 | 2 | 1 | 2 | 3 | 1 | 3 | 2 |

14 | 2 | 2 | 2 | 3 | 1 | 2 | 1 | 3 |

15 | 2 | 2 | 3 | 1 | 2 | 3 | 2 | 1 |

16 | 2 | 3 | 1 | 3 | 2 | 3 | 1 | 2 |

17 | 2 | 3 | 2 | 1 | 3 | 1 | 2 | 3 |

18 | 2 | 3 | 3 | 2 | 1 | 2 | 3 | 1 |

Material | ρ/(g·cm^{−3}) | φ_{0}/° | ∆φ/° | K_{b} | m | K | n | R_{f} |
---|---|---|---|---|---|---|---|---|

Cushion material | 2.24 | 2.24 | 11.1 | 498.2 | 0.23 | 1241.2 | 0.30 | 0.74 |

Transition material | 2.21 | 56.4 | 12.1 | 526.7 | 0.03 | 1324.3 | 0.25 | 0.72 |

Main rockfill | 2.18 | 55.6 | 13.0 | 294.9 | 0.03 | 969.0 | 0.25 | 0.71 |

Secondary rockfill | 2.17 | 55.0 | 13.1 | 237.2 | 0.12 | 813.4 | 0.23 | 0.70 |

Rockfill behind the dam | 2.16 | 53.4 | 12.4 | 162.8 | 0.15 | 747.2 | 0.23 | 0.70 |

Reservoir bottom backfill | 2.16 | 53.4 | 12.4 | 162.8 | 0.15 | 747.2 | 0.23 | 0.70 |

Asphalt concrete | 2.40 | 30.0 | 4.20 | 1292.1 | 0.40 | 825.9 | 0.55 | 0.47 |

Material | Volumetric Weight γ/kN∙m^{−3} | Elastic Modulus E/GPa | Poisson’s Ratio ν |
---|---|---|---|

Concrete wave wall | 24.0 | 28.0 | 0.167 |

Strongly weathered bedrock | 26.6 | 20.0 | 0.250 |

Weakly weathered bedrock | 28.4 | 50.0 | 0.250 |

Zone | Factor Level | φ_{0} (°) | Δφ (°) | K_{b} | m | K | n | R_{f} |
---|---|---|---|---|---|---|---|---|

Main rockfill | 1 | 44.48 | 10.40 | 235.92 | 0.024 | 775.20 | 0.200 | 0.568 |

2 | 55.60 | 13.00 | 294.90 | 0.030 | 969.00 | 0.250 | 0.710 | |

3 | 66.72 | 15.60 | 353.88 | 0.036 | 1162.80 | 0.300 | 0.852 | |

Secondary rockfill | 1 | 44.00 | 10.48 | 189.76 | 0.096 | 650.72 | 0.184 | 0.560 |

2 | 55.00 | 13.10 | 237.20 | 0.120 | 813.40 | 0.230 | 0.700 | |

3 | 66.00 | 15.72 | 284.64 | 0.144 | 976.08 | 0.276 | 0.840 | |

Reservoir bottom backfill | 1 | 42.72 | 9.920 | 130.24 | 0.120 | 597.76 | 0.184 | 0.560 |

2 | 53.40 | 12.40 | 162.80 | 0.150 | 747.20 | 0.230 | 0.700 | |

3 | 64.08 | 14.88 | 195.36 | 0.180 | 896.64 | 0.276 | 0.840 |

Scheme | Empty Column | φ_{0} (°) | Δφ (°) | K_{b} | m | K | n | R_{f} | u/cm | H/cm | ε/% |
---|---|---|---|---|---|---|---|---|---|---|---|

1 | 1 | 44.48 | 10.4 | 235.92 | 0.024 | 775.2 | 0.20 | 0.568 | 5.751 | −54.952 | −0.348 |

2 | 1 | 44.48 | 13.0 | 294.90 | 0.030 | 969.0 | 0.25 | 0.710 | 6.849 | −49.394 | −0.408 |

3 | 1 | 44.48 | 15.6 | 353.88 | 0.036 | 1162.8 | 0.30 | 0.852 | 8.080 | −45.835 | −0.464 |

4 | 1 | 55.60 | 10.4 | 235.92 | 0.030 | 969.0 | 0.30 | 0.852 | 6.288 | −55.851 | −0.362 |

5 | 1 | 55.60 | 13.0 | 294.90 | 0.036 | 1162.8 | 0.20 | 0.568 | 4.298 | −41.551 | −0.371 |

6 | 1 | 55.60 | 15.6 | 353.88 | 0.024 | 775.2 | 0.25 | 0.710 | 8.404 | −45.892 | −0.451 |

7 | 1 | 66.72 | 10.4 | 294.90 | 0.024 | 1162.8 | 0.25 | 0.852 | 6.064 | −47.026 | −0.400 |

8 | 1 | 66.72 | 13.0 | 353.88 | 0.030 | 775.2 | 0.30 | 0.568 | 3.565 | −39.789 | −0.415 |

9 | 1 | 66.72 | 15.6 | 235.92 | 0.036 | 969.0 | 0.20 | 0.710 | 5.257 | −52.364 | −0.349 |

10 | 2 | 44.48 | 10.4 | 353.88 | 0.036 | 969.0 | 0.25 | 0.568 | 5.958 | −40.957 | −0.471 |

11 | 2 | 44.48 | 13.0 | 235.92 | 0.024 | 1162.8 | 0.30 | 0.710 | 5.285 | −51.644 | −0.351 |

12 | 2 | 44.48 | 15.6 | 294.90 | 0.030 | 775.2 | 0.20 | 0.852 | 10.698 | −57.170 | −0.456 |

13 | 2 | 55.60 | 10.4 | 294.90 | 0.036 | 775.2 | 0.30 | 0.710 | 6.982 | −48.559 | −0.404 |

14 | 2 | 55.60 | 13.0 | 353.88 | 0.024 | 969.0 | 0.20 | 0.852 | 8.621 | −46.753 | −0.467 |

15 | 2 | 55.60 | 15.6 | 235.92 | 0.030 | 1162.8 | 0.25 | 0.568 | 4.035 | −43.388 | −0.347 |

16 | 2 | 66.72 | 10.4 | 353.88 | 0.030 | 1162.8 | 0.20 | 0.710 | 5.789 | −40.488 | −0.418 |

17 | 2 | 66.72 | 13.0 | 235.92 | 0.036 | 775.2 | 0.25 | 0.852 | 7.472 | −58.165 | −0.379 |

18 | 2 | 66.72 | 15.6 | 294.90 | 0.024 | 969.0 | 0.30 | 0.568 | 4.334 | −41.853 | −0.369 |

Scheme | Empty Column | φ_{0} (°) | Δφ (°) | K_{b} | m | K | n | R_{f} | u/cm | H/cm | ε/% |
---|---|---|---|---|---|---|---|---|---|---|---|

1 | 1 | 44 | 10.48 | 189.76 | 0.096 | 650.72 | 0.184 | 0.56 | 7.253 | −49.164 | −0.402 |

2 | 1 | 44 | 13.10 | 237.20 | 0.120 | 813.40 | 0.230 | 0.70 | 6.120 | −47.333 | −0.395 |

3 | 1 | 44 | 15.72 | 284.64 | 0.144 | 976.08 | 0.276 | 0.84 | 5.077 | −45.942 | −0.389 |

4 | 1 | 55 | 10.48 | 189.76 | 0.120 | 813.40 | 0.276 | 0.84 | 6.934 | −49.052 | −0.401 |

5 | 1 | 55 | 13.10 | 237.20 | 0.144 | 976.08 | 0.184 | 0.56 | 6.601 | −46.128 | −0.394 |

6 | 1 | 55 | 15.72 | 284.64 | 0.096 | 650.72 | 0.230 | 0.70 | 4.150 | −46.209 | −0.386 |

7 | 1 | 66 | 10.48 | 237.20 | 0.096 | 976.08 | 0.230 | 0.84 | 6.018 | −47.180 | −0.394 |

8 | 1 | 66 | 13.10 | 284.64 | 0.120 | 650.72 | 0.276 | 0.56 | 4.408 | −45.656 | −0.385 |

9 | 1 | 66 | 15.72 | 189.76 | 0.144 | 813.40 | 0.184 | 0.70 | 7.065 | −48.570 | −0.400 |

10 | 2 | 44 | 10.48 | 284.64 | 0.144 | 813.40 | 0.230 | 0.56 | 5.314 | −45.503 | −0.388 |

11 | 2 | 44 | 13.10 | 189.76 | 0.096 | 976.08 | 0.276 | 0.70 | 7.555 | −48.173 | −0.401 |

12 | 2 | 44 | 15.72 | 237.20 | 0.120 | 650.72 | 0.184 | 0.84 | 4.715 | −47.923 | −0.392 |

13 | 2 | 55 | 10.48 | 237.20 | 0.144 | 650.72 | 0.276 | 0.70 | 5.208 | −47.175 | −0.391 |

14 | 2 | 55 | 13.10 | 284.64 | 0.096 | 813.40 | 0.184 | 0.84 | 4.462 | −46.276 | −0.388 |

15 | 2 | 55 | 15.72 | 189.76 | 0.120 | 976.08 | 0.230 | 0.56 | 7.091 | −46.712 | −0.396 |

16 | 2 | 66 | 10.48 | 284.64 | 0.120 | 976.08 | 0.184 | 0.70 | 5.295 | −45.533 | −0.388 |

17 | 2 | 66 | 13.10 | 189.76 | 0.144 | 650.72 | 0.23 | 0.84 | 5.874 | −49.213 | −0.397 |

18 | 2 | 66 | 15.72 | 237.2 | 0.096 | 813.4 | 0.276 | 0.56 | 6.453 | −46.663 | −0.394 |

Scheme | Empty Column | φ_{0} (°) | Δφ (°) | K_{b} | m | K | n | R_{f} | u/cm | H/cm | ε/% |
---|---|---|---|---|---|---|---|---|---|---|---|

1 | 1 | 42.72 | 9.92 | 130.24 | 0.12 | 597.76 | 0.184 | 0.56 | 5.916 | −47.179 | −0.466 |

2 | 1 | 42.72 | 12.40 | 162.80 | 0.15 | 747.20 | 0.230 | 0.70 | 6.069 | −47.133 | −0.394 |

3 | 1 | 42.72 | 14.88 | 195.36 | 0.18 | 896.64 | 0.276 | 0.84 | 6.226 | −47.075 | −0.330 |

4 | 1 | 53.40 | 9.92 | 130.24 | 0.15 | 747.20 | 0.276 | 0.84 | 6.131 | −47.146 | −0.502 |

5 | 1 | 53.40 | 12.40 | 162.80 | 0.18 | 896.64 | 0.184 | 0.56 | 5.865 | −47.116 | −0.331 |

6 | 1 | 53.40 | 14.88 | 195.36 | 0.12 | 597.76 | 0.230 | 0.70 | 6.270 | −47.027 | −0.335 |

7 | 1 | 64.08 | 9.92 | 162.80 | 0.12 | 896.64 | 0.230 | 0.84 | 6.183 | −47.116 | −0.413 |

8 | 1 | 64.08 | 12.40 | 195.36 | 0.15 | 597.76 | 0.276 | 0.56 | 6.147 | −47.067 | −0.328 |

9 | 1 | 64.08 | 14.88 | 130.24 | 0.18 | 747.20 | 0.184 | 0.70 | 6.014 | −47.159 | −0.472 |

10 | 2 | 42.72 | 9.92 | 195.36 | 0.18 | 747.20 | 0.230 | 0.56 | 6.030 | −47.126 | −0.323 |

11 | 2 | 42.72 | 12.40 | 130.24 | 0.12 | 896.64 | 0.276 | 0.70 | 5.845 | −47.178 | −0.411 |

12 | 2 | 42.72 | 14.88 | 162.80 | 0.15 | 597.76 | 0.184 | 0.84 | 6.354 | −47.040 | −0.405 |

13 | 2 | 53.40 | 9.92 | 162.80 | 0.18 | 597.76 | 0.276 | 0.70 | 6.192 | −47.099 | −0.389 |

14 | 2 | 53.40 | 12.40 | 195.36 | 0.12 | 747.20 | 0.184 | 0.84 | 6.316 | −47.044 | −0.335 |

15 | 2 | 53.40 | 14.88 | 130.24 | 0.15 | 896.64 | 0.230 | 0.56 | 5.840 | −47.150 | −0.329 |

16 | 2 | 64.08 | 9.92 | 195.36 | 0.15 | 896.64 | 0.184 | 0.70 | 6.110 | −47.101 | −0.335 |

17 | 2 | 64.08 | 12.40 | 130.24 | 0.18 | 597.76 | 0.230 | 0.84 | 6.312 | −47.091 | −0.497 |

18 | 2 | 64.08 | 14.88 | 162.80 | 0.12 | 747.20 | 0.276 | 0.56 | 5.918 | −47.154 | −0.374 |

**Table 8.**Range analysis results of influencing factors of each test index for the main rockfill zone.

Test Index | Factor | φ_{0} (°) | Δφ (°) | K_{b} | m | K | n | R_{f} |
---|---|---|---|---|---|---|---|---|

u | K_{1j} | 0.7852 | −0.1797 | −0.6370 | 0.0915 | 0.8270 | 0.4173 | −1.6615 |

K_{2j} | 0.1197 | −0.3033 | 0.2192 | −0.1143 | −0.1005 | 0.1453 | 0.1093 | |

K_{3j} | −0.9048 | 0.4830 | 0.4178 | 0.0228 | −0.7265 | −0.5627 | 1.5522 | |

R_{j} | 1.6900 | 0.7863 | 1.0548 | 0.2058 | 1.5535 | 0.9800 | 3.2137 | |

H | K_{1j} | −2.1236 | −0.1038 | −4.8589 | −0.1516 | −2.8861 | −1.0113 | 4.1201 |

K_{2j} | 0.8694 | −0.0143 | 0.2762 | 0.1884 | 0.0064 | 0.3981 | −0.1884 | |

K_{3j} | 1.2542 | 0.1181 | 4.5827 | −0.0368 | 2.8797 | 0.6132 | −3.9316 | |

R_{j} | 3.3778 | 0.2219 | 9.4416 | 0.3400 | 5.7658 | 1.6245 | 8.0517 | |

ε | K_{1j} | 0.1481 | −0.0124 | −0.4579 | −0.0421 | 0.0730 | −0.0021 | −0.1484 |

K_{2j} | −0.0148 | −0.0308 | −0.0190 | −0.0066 | 0.0260 | 0.0759 | −0.0476 | |

K_{3j} | −0.1333 | 0.0432 | 0.4599 | 0.0487 | −0.0991 | −0.0738 | 0.1961 | |

R_{j} | 0.2814 | 0.0740 | 0.9178 | 0.0908 | 0.1721 | 0.1497 | 0.3445 |

**Table 9.**Range analysis results of influencing factors on each test index for the secondary rockfill zone.

Test Index | Factor | φ_{0} (°) | Δφ (°) | K_{b} | m | K | n | R_{f} |
---|---|---|---|---|---|---|---|---|

u | K_{1j} | 0.1394 | 0.1374 | 1.0957 | 0.1156 | −0.5983 | 0.0322 | 0.3204 |

K_{2j} | −0.1253 | −0.0296 | −0.0138 | −0.10578 | 0.1917 | −0.1051 | 0.0324 | |

K_{3j} | −0.0141 | −0.1078 | −1.0819 | −0.0098 | 0.4066 | 0.0729 | −0.3529 | |

R_{j} | 0.2647 | 0.2452 | 2.1776 | 0.2214 | 1.0049 | 0.1780 | 0.6733 | |

H | K_{1j} | −0.2060 | −0.1342 | −1.3471 | −0.1439 | −0.4231 | −0.1321 | 0.4959 |

K_{2j} | 0.2082 | 0.0038 | 0.0666 | 0.0988 | −0.0992 | 0.1086 | −0.0319 | |

K_{3j} | −0.0022 | 0.1304 | 1.2804 | 0.0451 | 0.5223 | 0.0234 | −0.4641 | |

R_{j} | 0.4142 | 0.2646 | 2.6275 | 0.2427 | 0.9454 | 0.2407 | 0.9600 | |

ε | K_{1j} | 0.0122 | 0.0062 | 0.0619 | 0.0072 | −0.0121 | 0.0047 | −0.0029 |

K_{2j} | −0.0078 | −0.0013 | −0.0016 | −0.0054 | 0.0086 | −0.0061 | 0.0019 | |

K_{3j} | −0.0044 | −0.0049 | −0.0603 | −0.0018 | 0.0036 | 0.0014 | 0.0011 | |

R_{j} | 0.0200 | 0.0111 | 0.1222 | 0.0126 | 0.0207 | 0.0108 | 0.0048 |

**Table 10.**Range analysis results of influencing factors of each test index for the reservoir bottom backfill zone.

Test Index | Factor | φ_{0} (°) | Δφ (°) | K_{b} | m | K | n | R_{f} |
---|---|---|---|---|---|---|---|---|

u | K_{1j} | −0.0232 | −0.0029 | −0.0869 | −0.0219 | 0.1019 | −0.0007 | −0.1439 |

K_{2j} | 0.0058 | −0.0042 | 0.0003 | 0.0119 | −0.0169 | 0.0208 | −0.0132 | |

K_{3j} | 0.0174 | 0.0071 | 0.0866 | 0.0010 | −0.0851 | −0.0201 | 0.1571 | |

R_{j} | 0.0406 | 0.0113 | 0.1735 | 0.0338 | 0.1870 | 0.0409 | 0.3010 | |

H | K_{1j} | −0.0232 | −0.0029 | −0.0869 | −0.0219 | 0.1019 | −0.0007 | −0.1439 |

K_{2j} | 0.0058 | −0.0042 | 0.0003 | 0.0119 | −0.0169 | 0.0208 | −0.0132 | |

K_{3j} | 0.0174 | 0.0071 | 0.0866 | 0.0010 | −0.0851 | −0.0201 | 0.1571 | |

R_{j} | 0.0406 | 0.0113 | 0.1735 | 0.0338 | 0.1870 | 0.0409 | 0.3010 | |

ε | K_{1j} | 0.0109 | 0.1734 | 0.5892 | 0.0189 | 0.1622 | 0.0342 | −0.2856 |

K_{2j} | −0.1709 | −0.0439 | −0.0279 | −0.0503 | 0.1282 | −0.0528 | 0.0201 | |

K_{3j} | 0.1601 | −0.1294 | −0.5613 | 0.0314 | −0.2904 | 0.0186 | 0.2656 | |

R_{j} | 0.3310 | 0.3028 | 1.1505 | 0.0817 | 0.4526 | 0.0870 | 0.5512 |

Test Index | Source of Variance | Sum of Squares of Deviations S_{j} | Degree of Freedom f_{j} | Statistics F_{j} | Significance |
---|---|---|---|---|---|

u | φ_{0} | 8.6972 | 2 | 8.3728 | Generally significant |

Δφ | 2.1455 | 2 | 2.0655 | Not significant | |

K_{b} | 3.7703 | 2 | 3.6297 | Not significant | |

m | 0.13179 | 2 | 0.1269 | Not significant | |

K | 7.3310 | 2 | 7.0575 | Generally significant | |

n | 3.0713 | 2 | 2.9567 | Not significant | |

R_{f} | 31.091 | 2 | 29.931 | Highly significant | |

Random error | 1.55812 | 3 | – | – | |

H | φ_{0} | 41.032 | 2 | 16.032 | Highly significant |

Δφ | 0.1495 | 2 | 0.0584 | Not significant | |

K_{b} | 268.12 | 2 | 104.76 | Highly significant | |

m | 0.3590 | 2 | 0.1403 | Not significant | |

K | 99.735 | 2 | 38.969 | Highly significant | |

n | 9.3430 | 2 | 3.6501 | Not significant | |

R_{f} | 194.81 | 2 | 76.117 | Highly significant | |

Random error | 3.8390 | 3 | – | – | |

ε | φ_{0} | 0.2394 | 2 | 4.8606 | Not significant |

Δφ | 0.0178 | 2 | 0.3618 | Not significant | |

K_{b} | 2.5273 | 2 | 51.310 | Highly significant | |

m | 0.0251 | 2 | 0.5105 | Not significant | |

K | 0.0950 | 2 | 1.9294 | Not significant | |

n | 0.0672 | 2 | 1.3651 | Not significant | |

R_{f} | 0.3764 | 2 | 7.6426 | Generally significant | |

Random error | 0.0739 | 3 | – | – |

Test Index | Source of Variance | Sum of Squares of Deviations S_{j} | Degree of Freedom f_{j} | Statistics F_{j} | Significance |
---|---|---|---|---|---|

u | φ_{0} | 0.2119 | 2 | 1.1768 | Not significant |

Δφ | 0.1882 | 2 | 1.0450 | Not significant | |

K_{b} | 14.228 | 2 | 79.003 | Highly significant | |

m | 0.1478 | 2 | 0.8208 | Not significant | |

K | 3.3599 | 2 | 18.656 | Highly significant | |

n | 0.1044 | 2 | 0.5797 | Not significant | |

R_{f} | 1.3697 | 2 | 7.6051 | Generally significant | |

Random error | 0.2701 | 3 | – | – | |

H | φ_{0} | 0.5151 | 2 | 2.0988 | Not significant |

Δφ | 0.2103 | 2 | 0.8568 | Not significant | |

K_{b} | 20.751 | 2 | 84.557 | Highly significant | |

m | 0.19500 | 2 | 0.7945 | Not significant | |

K | 2.7696 | 2 | 11.286 | Generally significant | |

n | 0.1787 | 2 | 0.7282 | Not significant | |

R_{f} | 2.7740 | 2 | 11.303 | Generally significant | |

Random error | 0.3681 | 3 | – | – | |

ε | φ_{0} | 0.0014 | 2 | 2.3810 | Not significant |

Δφ | 0.0004 | 2 | 0.6719 | Not significant | |

K_{b} | 0.0448 | 2 | 77.415 | Highly significant | |

m | 0.0005 | 2 | 0.8810 | Not significant | |

K | 0.0014 | 2 | 2.4109 | Not significant | |

n | 0.0004 | 2 | 0.6384 | Not significant | |

R_{f} | 0.0001 | 2 | 0.1384 | Not significant | |

Random error | 0.0009 | 3 | – | – |

**Table 13.**ANOVA results of influencing factors of each test index for the reservoir bottom backfill zone.

Test Index | Source of Variance | Sum of Squares of Deviations S_{j} | Degree of Freedom f_{j} | Statistics F_{j} | Significance |
---|---|---|---|---|---|

u | φ_{0} | 0.0053 | 2 | 6.7039 | Generally significant |

Δφ | 0.0005 | 2 | 0.5866 | Not significant | |

K_{b} | 0.0903 | 2 | 115.06 | Highly significant | |

m | 0.0043 | 2 | 5.5092 | Generally significant | |

K | 0.1075 | 2 | 136.93 | Highly significant | |

n | 0.0050 | 2 | 6.3790 | Generally significant | |

R_{f} | 0.2734 | 2 | 348.30 | Highly significant | |

Random error | 0.0012 | 3 | – | – | |

H | φ_{0} | 0.0020 | 2 | 9.3796 | Generally significant |

Δφ | 0.0025 | 2 | 12.191 | Generally significant | |

K_{b} | 0.0179 | 2 | 85.571 | Highly significant | |

m | 0.0003 | 2 | 1.4848 | Not significant | |

K | 0.0068 | 2 | 32.442 | Highly significant | |

n | 0.0007 | 2 | 3.2408 | Not significant | |

R_{f} | 0.0068 | 2 | 32.337 | Highly significant | |

Random error | 0.0003 | 3 | – | – | |

ε | φ_{0} | 0.3298 | 2 | 1.8892 | Not significant |

Δφ | 0.2925 | 2 | 1.6758 | Not significant | |

K_{b} | 3.9780 | 2 | 22.791 | Highly significant | |

m | 0.0232 | 2 | 0.1330 | Not significant | |

K | 0.7627 | 2 | 4.3697 | Not significant | |

n | 0.0258 | 2 | 0.1478 | Not significant | |

R_{f} | 0.9150 | 2 | 5.2421 | Not significant | |

Random error | 0.2618 | 3 | – | – |

Zone | Analysis Method | u | H | ε |
---|---|---|---|---|

Main rockfill zone | Range analysis method | R_{f} > φ_{0} > K > K_{b} > n > Δφ > m | K_{b} > R_{f} > K > φ_{0} > n > m > Δφ | K_{b} > R_{f} > φ_{0} > K > n > m > Δφ |

ANVOA method | R_{f} > φ_{0} > K > K_{b} > n > Δφ > m | K_{b} > R_{f} > K > φ_{0} > n > m > Δφ | K_{b} > R_{f} > φ_{0} > K > n > m > Δφ | |

Secondary rockfill zone | Range analysis method | K_{b} > K > R_{f} > φ_{0} > Δφ > m > n | K_{b} > R_{f} > K > φ_{0} > Δφ > m > n | K_{b} > K > φ_{0} > m > Δφ > n > R_{f} |

ANVOA method | K_{b} > K > R_{f} > φ_{0} > Δφ > m > n | K_{b} > R_{f} > K > φ_{0} > Δφ > m > n | K_{b} > K > φ_{0} > m > Δφ > n > R_{f} | |

Reservoir bottom backfill zone | Range analysis method | R_{f} > K > K_{b} > n > φ_{0} > m > Δφ | K_{b} > R_{f} > K > Δφ > φ_{0} > n > m | K_{b} > R_{f} > K > φ_{0} > Δφ > n > m |

ANVOA method | R_{f} > K > K_{b} > n > φ_{0} > m > Δφ | K_{b} > R_{f} > K > Δφ > φ_{0} > n > m | K_{b} > R_{f} > K > φ_{0} > Δφ > n > m |

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## Share and Cite

**MDPI and ACS Style**

Ma, B.; Zhang, W.; Shen, Z.; Zhou, D.; Yao, H.; Wang, R. Identification of Sensitive Parameters for Deformation of Asphalt Concrete Face Rockfill Dam of Pumped Storage Power Station. *Water* **2022**, *14*, 2634.
https://doi.org/10.3390/w14172634

**AMA Style**

Ma B, Zhang W, Shen Z, Zhou D, Yao H, Wang R. Identification of Sensitive Parameters for Deformation of Asphalt Concrete Face Rockfill Dam of Pumped Storage Power Station. *Water*. 2022; 14(17):2634.
https://doi.org/10.3390/w14172634

**Chicago/Turabian Style**

Ma, Baotai, Wenbing Zhang, Zhenzhong Shen, Donghao Zhou, Haozheng Yao, and Runye Wang. 2022. "Identification of Sensitive Parameters for Deformation of Asphalt Concrete Face Rockfill Dam of Pumped Storage Power Station" *Water* 14, no. 17: 2634.
https://doi.org/10.3390/w14172634