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The main objective of this study is to present a method of determining viscoelastic deformation monitoring index of a Roller-compacted concrete (RCC) gravity dam in an alpine region. By focusing on a modified deformation monitoring model considering frost heave and back analyzed mechanical parameters of the dam, the working state of viscoelasticity for the dam is illustrated followed by an investigation and designation of adverse load cases using orthogonal test method. Water pressure component is then calculated by finite element method, while temperature, time effect, and frost heave components are obtained through deformation statistical model considering frost heave. The viscoelastic deformation monitoring index is eventually determined by small probability and maximum entropy methods. The results show that (a) with the abnormal probability 1% the dam deformation monitoring index for small probability and maximum entropy methods is 23.703 mm and 22.981 mm, respectively; thus the maximum measured displacement of the dam is less than deformation monitoring index, which indicates that the dam is currently in a state of safety operation and (b) the obtained deformation monitoring index using orthogonal test method is more accurate due to the full consideration of more random factors; the method gained from this study will likely be of use to diagnose the working state for those RCC dams in alpine regions.

A Roller-compacted concrete (RCC) dam is constructed with the Roller-compacted placement method in thin layers of dry lean concrete, composed of mixed sand aggregate and cement [

The deformation monitoring index of dams may be primarily determined using two approaches. Initially, the deformation monitoring index is obtained through the mining of dam deformation information using mathematical model on the basis of the existing monitoring effect quantity. Prior studies on monitoring index determined by mathematical model have focused on the methods of confidence interval, small probability, and statistical model [

On the other side, the deformation extreme value can also be determined on the basis of the structural numerical techniques of the dam body and its foundation. Numerous scholars have attempted, in terms of finite element numerical techniques, to assemble the adverse loads of dams that may occur during operation period, which makes up for the shortage of the adverse load combination cases of monitoring data series observed by precise instruments. For instance, Wu et al. [

Prior studies on monitoring index have focused on adverse load combinations that offer a simple combination by the accumulation of adverse loads rather than forming a full consideration on the actual situations (e.g., loads, boundary conditions, and uncertain parameters). For instance, the Canadian Turkstra combination rule is customarily used in the engineering field, which holds that the maximum effect value of the load combination manifests when a variable load reaches the maximum value in the design benchmark period and the other variable loads are in the form of instantaneous value [

In this study, a typical RCC gravity dam in an alpine region is taken as a case, and the typical water retaining dam block is selected as an analysis object. A combination sample of adverse cases is designed using orthogonal test method; the total effect quantity (i.e., deformation) sample is obtained through statistical model and finite element method, and then the viscoelastic deformation monitoring index for the dam in an alpine region is eventually determined based on the small probability and maximum entropy methods.

Orthogonal test design, as a highly efficient way capable of dealing with multifactor tests, is commonly adopted to arrange and analyze datasets by means of selecting a reasonable orthogonal table based on levels and factors [

In the case of an RCC dam in an alpine region, the dam crest displacement is affected by water pressure, temperature, time effect, and frost heave [

Additionally,

The basic loads consist of water pressure, uplift pressure, sediment pressure, and other loads regarding the permanent cases during the operation period of dams. Some analysis is conducted by selecting and combining these loads which have a strong influence on structure deformation. Due to the complexity of load combination under adverse cases, in this study, the water pressure and uplift pressure are recognized as the investigated loads, and then the orthogonal test method, according to the range of loads and levels as well as factors, is introduced to assemble loads under adverse cases. Combined with (

To be specific, effect quantities consist of water pressure component, temperature component, time effect component, and frost heave component in this study. Water pressure component is calculated using the finite element method, and the transversely isotropic mechanical parameters in the finite element model are obtained from inversion; while the temperature component is calculated through statistical model expression form, as shown in (

As the abnormality of a dam is regarded as a small probability event, the abnormal probability

According to the principle of maximum entropy, when the probability distribution reaches the minimum deviation under the given constraint condition of sample information, the entropy

Additionally,

According to a set of sample information

Hence, according to (

The Lagrange multiplier coefficients of the aforementioned formula are estimated by optimization algorithm.

The probability of abnormal behavior for dams is rather low, the abnormal probability

The flow diagram of implementation for viscoelastic deformation monitoring index of dams is shown as Figure

Flow diagram of implementation for viscoelastic deformation monitoring index.

Compared with the measured data

^{9} m^{3}, and reservoir’s normal storage water level and dead water level are 739.00 m and 680.00 m, respectively. The power station has a total installed capacity of 140 MW, and the annual generating capacity reaches 5.19 × 10^{8} KWh.

The project is mainly composed of dam, water diversion system, power plant, and other hydraulic structures. The main dam is composed of a full section Roller-compacted concrete (RCC) gravity dam with a length of 1489 m, a maximum height of 121.50 m, and a dam crest elevation of 745.50 m. Seen from the scale of water conservancy, the safety grade of the project is grade I or larger

Layout of an RCC gravity dam project.

Cross-sectional monitoring layout of the typical water retaining dam block (elevation: m).

Comparison between the measured and the fitted displacement of monitoring point for dam crest.

The separated displacement components of monitoring point for dam crest.

On the basis of the water pressure component separated by the deformation statistical model considering frost heave, the physical and mechanical parameters of the dam and its foundation are back analyzed by uniform design method, BP neural network, and finite element method [

There are several discrepancies between the parameters obtained by the inversion and the design parameters. The maximum difference is the horizontal equivalent elastic modulus, and the inversion value is 1.12 times of the designed value; the ratio of horizontal equivalent elastic modulus to vertical equivalent elastic modulus is 1.45, which is in accordance with the general variation law of RCC (i.e., 1-2).

Prior to selecting adverse cases, the factor having a strong influence or greater variability on a dam is considered as a random variable. According to actual engineering, with the potential impact of the temperature on RCC in alpine regions, the running state of a dam is affected by hydrostatic pressure along upstream and downstream of dams. Furthermore, stability and strength of the dam will be unfavorable if the uplift pressure is too large. Thus the upstream and downstream water level, temperature load, and uplift pressure are perceived as the main influencing factors. The water pressure component is calculated by the inversion results of parameters; the temperature component is calculated by the quasi-stable temperature field and statistical model. In addition, there is no available measured data about the uplift pressure; thus the reduction coefficient of uplift pressure is only analyzed herein.

It is seen from the analysis that the upstream reservoir water level, the downstream water level, the temperature load, and the uplift pressure are considered as the main loads that affect dam deformation. Therefore, according to the orthogonal test design table, four influential factors of upstream water level, downstream level, temperature load, and reduction coefficient of uplift pressure are selected, and four levels are set for each factor, as shown in Table

Factors and levels diagram of adverse loads.

Levels | Factors | |||
---|---|---|---|---|

Upstream water level (m) | Downstream water level (m) | Temperature load (°C) | Reduction coefficient of uplift pressure | |

1 | 737.50 | 641.02 | | 0.19 |

2 | 739.50 | 642.74 | | 0.23 |

3 | 741.50 | 644.46 | 8.9 | 0.27 |

4 | 743.50 | 646.18 | 18.4 | 0.31 |

The orthogonal table L_{16}(4^{5}) is selected to constitute 16 sets of load combinations including 4 factors and 4 levels, as shown in Table

The orthogonal design table L_{16}(4^{5}).

Number | A | B | C | D | E |
---|---|---|---|---|---|

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

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

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

4 | 1 | 4 | 4 | 4 | 4 |

5 | 2 | 1 | 2 | 3 | 4 |

6 | 2 | 2 | 1 | 4 | 3 |

7 | 2 | 3 | 4 | 1 | 2 |

8 | 2 | 4 | 3 | 2 | 1 |

9 | 3 | 1 | 3 | 4 | 2 |

10 | 3 | 2 | 4 | 3 | 1 |

11 | 3 | 3 | 1 | 2 | 4 |

12 | 3 | 4 | 2 | 1 | 3 |

13 | 4 | 1 | 4 | 2 | 3 |

14 | 4 | 2 | 3 | 1 | 4 |

15 | 4 | 3 | 2 | 4 | 1 |

16 | 4 | 4 | 1 | 3 | 2 |

As presented in Table

The calculation range of the model is twice the height of dam along the upstream and downstream as well as the depth of dam foundation. The positive direction of

The mesh division of dam and its foundation is conducted using hexahedral eight-node isoparametric element and a small amount of degraded tetrahedron or pentahedral elements. The monitoring points are arranged on the nodes as soon as possible when the mesh is divided. Simultaneously, the mesh generation in the vicinity of gallery is conducted using the local mesh refinement method. The total number of element in the finite element model is 13620, with the dam body containing 10540 elements, and the number of nodes is 17274. The finite element model of the typical water retaining dam block is shown in Figure

3D finite element model of the typical water retaining dam block. (a) Dam-foundation model and (b) Dam body model.

The adverse load combinations and components.

Number | A (m) | B (m) | C (°C) | D | Water pressure component (mm) | Temperature component (mm) | Time effect component (mm) | Frost heave component (mm) |
---|---|---|---|---|---|---|---|---|

1 | 737.50 | 641.02 | | 0.19 | 5.34 | 0.26 | 0.61 | 1.21 |

2 | 737.50 | 642.74 | | 0.23 | 5.37 | 0.14 | 0.61 | 0.22 |

3 | 737.50 | 644.46 | | 0.27 | 5.40 | 1.73 | 0.61 | 0.00 |

4 | 737.50 | 646.18 | | 0.31 | 5.43 | 0.99 | 0.61 | 0.00 |

5 | 739.50 | 641.02 | | 0.27 | 6.15 | 0.14 | 0.57 | 0.22 |

6 | 739.50 | 642.74 | | 0.31 | 6.18 | 0.26 | 0.57 | 1.21 |

7 | 739.50 | 644.46 | | 0.19 | 6.05 | 0.99 | 0.57 | 0.00 |

8 | 739.50 | 646.18 | | 0.23 | 6.08 | 1.73 | 0.57 | 0.00 |

9 | 741.50 | 641.02 | | 0.31 | 6.97 | 1.73 | 1.13 | 0.00 |

10 | 741.50 | 642.74 | | 0.27 | 6.92 | 0.99 | 1.13 | 0.00 |

11 | 741.50 | 644.46 | | 0.23 | 6.86 | 0.26 | 1.13 | 1.21 |

12 | 741.50 | 646.18 | | 0.19 | 6.81 | 0.14 | 1.13 | 0.22 |

13 | 743.50 | 641.02 | | 0.23 | 7.67 | 0.99 | 1.13 | 0.00 |

14 | 743.50 | 642.74 | | 0.19 | 7.61 | 1.73 | 1.13 | 0.00 |

15 | 743.50 | 644.46 | | 0.31 | 7.74 | 0.14 | 1.13 | 0.22 |

16 | 743.50 | 646.18 | | 0.27 | 7.69 | 0.26 | 1.13 | 1.21 |

The total displacement of dam crest under different cases.

Number | A (m) | B (m) | C (°C) | D | Total displacement (mm) |
---|---|---|---|---|---|

1 | 737.50 | 641.02 | | 0.19 | 19.68 |

2 | 737.50 | 642.74 | | 0.23 | 18.60 |

3 | 737.50 | 644.46 | | 0.27 | 20.00 |

4 | 737.50 | 646.18 | | 0.31 | 19.29 |

5 | 739.50 | 641.02 | | 0.27 | 19.34 |

6 | 739.50 | 642.74 | | 0.31 | 20.48 |

7 | 739.50 | 644.46 | | 0.19 | 19.87 |

8 | 739.50 | 646.18 | | 0.23 | 20.64 |

9 | 741.50 | 641.02 | | 0.31 | 22.09 |

10 | 741.50 | 642.74 | | 0.27 | 21.30 |

11 | 741.50 | 644.46 | | 0.23 | 21.72 |

12 | 741.50 | 646.18 | | 0.19 | 20.56 |

13 | 743.50 | 641.02 | | 0.23 | 22.05 |

14 | 743.50 | 642.74 | | 0.19 | 22.73 |

15 | 743.50 | 644.46 | | 0.31 | 21.49 |

16 | 743.50 | 646.18 | | 0.27 | 22.55 |

The following conclusions can be obtained from Table

(i) When the high water level is at elevation of 737.50 m, 739.50 m, 741.50 m, and 743.50 m, with the changes of temperature load and uplift pressure, the deformation monitoring index of dam crest is also unidentical. The mean values of the four cases are 19.39 mm, 20.08 mm, 21.42 mm, and 22.21 mm, respectively. From the analysis of the measured data, such as water level of 737.58 m that appeared on July 7, 2013 when it was in hot season, the monitoring displacement value of 17.20 mm which is less than the deformation monitoring index of 19.39 mm, and the actual operation of the project shows that the dam is in a state of safety operation. Also high water level of 739.5 m appeared on August 6, 2013; the actual monitoring value of 17.89 mm is less than deformation monitoring index of 20.08 mm; thus it is demonstrated that the dam does not present adverse situation. To summarize, the dam is currently in a safe condition.

(ii) As presented in Table

Based on the total displacement sample of 16 sets of adverse load combination cases (Table

When the measured value

It is seen from the statistical principle and structural importance (rank or grade) that empirical analysis shows that the event is impossible to occur when the abnormal probability (

List of numerical eigenvalues and function coefficients.

Observation | Eigenvalues | Results | Coefficients | Results |
---|---|---|---|---|

PL5-3 | | 1.0000 | | |

| | | | |

| 0.9385 | | | |

| | | | |

| 1.6258 | | |

The maximum entropy probability density function of displacement for dam crest is written as follows:

It can be assumed that the abnormal probability is 1% or 5% by focusing on the importance of engineering (rank or grade). Considering (

List of deformation monitoring indexes (Unit: mm).

Observation | Eigenvalues | Small probability method | Maximum entropy method | |||
---|---|---|---|---|---|---|

| | | | | | |

PL5-3 | 20.7744 | 1.2589 | 23.703 | 22.845 | 22.981 | 22.671 |

The diagnosis of running state for an RCC gravity dam in an alpine region is conducted via the comparison between the deformation monitoring index determined by small probability and maximum entropy method (Table

In this study, an RCC gravity dam project is taken as a case; the method of determining viscoelastic deformation monitoring index of RCC dams in alpine regions is proposed. The following conclusions can be drawn from this study:

The authors declare that there are no conflicts of interest regarding the publication of this article.

This research is supported by National Natural Science Foundation of China (nos. 51779130 and 51209124).