Long-Term Settlement of High Concrete-Face Rockfill Dam by Field Monitoring and Numerical Simulation

Qinghai University, Xining, Qinghai Province 810016, China Department of Civil, Construction and Environmental Engineering, Iowa State University, 354 Town Engineering Building, Ames, IA 50011, USA Cold and Arid Regions Water Engineering Safety Research Center, Key Laboratory of Agricultural Soil and Water Engineering in Arid and Semiarid Areas of Ministry of Education, Northwest A&F University, Yangling 712100, China Construction Management Bureau of the Xujixia Water Conservancy Project in Haixi Prefecture, Delingha 817000, China College of Architecture and Civil Engineering, Beijing University of Technology, Beijing 100124, China


Introduction
Concrete-face rockfill dams (CFRDs) have been quickly developed in recent years because of the adaptability to terrain, low cost, and facilitated construction [1]. However, researchers have observed creep deformation of rockfills in the body of high CFRDs even under normal operating conditions [2][3][4][5][6]. e creep can cause differential and inconsistent deformation between rockfill and concrete-face, resulting in detachment of these two structural elements [7,8]. Without the support of rockfill, fractures may develop in concrete-face panels caused by panel's weight and external loads, which seriously affects the performance and fatigue life of CFRDs [9]. For example, the fractured concrete-faces have been reported in the Australian Cethana CFRD with a height of 110 m and the Chinese Tianshengqiao CFRD with a height of 178 m. If the fractures continue to develop, significant water leaks may occur [10,11], which may cause structural failure of the dams [12][13][14][15][16][17][18], such as Gouhou CFRD failure in August 1993 in Qinghai Province, China [19].
According to triaxial test results, theoretical models have been developed to characterize the creep behavior of rockfill materials.
eoretical models mainly use elastic elements (linear springs), viscous elements (Newton's stick pots), and plastic elements (friction parts) to form series and parallel connections to describe time-dependent stress-strain relationship of rockfill materials. Based on the combination and expansion of the above three elements, a variety of theoretical models for evaluating creep behavior of rockfill materials have been proposed [45,46], such as Merchant model, viscoelastic model, elastic-viscoplastic model, elastoplastic model, and Hardening Soil Creep (HSC) model [40,[47][48][49][50][51][52]. eoretical models are supported by rigorous mathematical theory, which is very important for investigating the mechanical characteristics of rockfill materials.
e results of large-scale triaxial tests can be used to determine theoretical model parameters. However, the largescale triaxial tests are subject to sample disturbance and size effects, and the theoretical model parameters are limited by undefined practical meaning [31,[53][54][55][56]. erefore, indoor creep test results often have a large divergence with actual creep measurements in the field [57,58]. As such, empirical models are developed by assessing field monitoring data of CFRDs. Statistical methods are used to analyze creep deformation curve to obtain empirical model functions, such as exponential decay function, hyperbolic type function, and power function [29,59,60]. In order to better understand the dam deformation property, it is necessary to conduct deformation monitoring analysis, empirical model, and back-analysis.
is case study focuses on the field monitoring results of Xujixia high CFRD (121.5 m) and developing a subroutine in ABAQUS using exponential decay-type empirical creep model to evaluate creep deformation of high CFRDs. e simulation parameters were determined based on displacement back-analysis (BP-MPGA/MPGA) considering the construction process and field compaction test results. e effectiveness of the proposed method is validated by field monitoring results of Xujixia high CFRD.  [61], which is expressed as follows:

Establishment of the Creep Model in ABAQUS
where ε cr is time-dependent creep strain, ε f is final creep deformation when t ⟶ ∞, a is the ratio of initial creep deformation when t � 0, and exp is the base of natural logarithm. erefore, strain rate can be computed as Assuming that creep deformation of the rockfill is related to confining pressure and stress level, total creep deformation of the rockfill can be divided into volume creep ε vf depending on confining pressure and shear creep ε sf depending on stress level. According to the rockfill and clay creep deformation test results, Shen et al. [62,63] determined that volumetric creep deformation and shear creep deformation could be simulated as Based on the rockfill creep deformation test results, Li et al. [64] updated equations (3) and (4) to incorporate the shear stress influence on final shear creep deformation to reflect the influence of particle breakage on creep deformation. e updated equations (3) and (4) are expressed as where b and d are two model parameters. b is equivalent to final volume creep at σ 3 � P a (atmospheric pressure), with a stress level D � (σ 1 − σ 3 )/(σ 1 − σ 3 ) f . Specifically, σ 1 is the major principal stress, and σ 3 is the minor principal stress. d is final shear creep at stress level D � 0.5. When FEM is used for creep analysis, the range of stress level significantly affects the results of creep calculation. erefore, stress level should be reasonably limited based on the actual situation, where a, b, c, d, m 1 , m 2 , and m 3 are model parameters.
Based on the Prandtl-Reuss flow rule, the uniaxial creep rate can be obtained after three-dimensional creep rate is degraded [65]. erefore, the creep rate of each component of strain tensor can be written as where S { } is the partial stress, I { } is the unit tensor, and σ s is the generalized shear stress. e volumetric deformation rate _ ε v and the shear deformation rate _ ε s are 2

Advances in Civil Engineering
CFRDs are filled in phases and zones; the loading process is complicated. e specific initial creep occurrence time of a cast layer and the subsequent creep occurrence time after the stress state changes are difficult to accurately determine. So, as an implementation of incremental creep routines in ABAQUS, relative time is used for creep calculations. us, the volume deformation rate and shear deformation rate can be changed to For rockfill materials subject to zero stress, ε vf � ε sf � 0 according to equations (3) and (4), where ε vf and ε sf are the accumulated volume and shear creep variables for time t, which can be calculated as in the following equations by integration: e creep strain increment tensor Δε cr { } can be obtained according to equations (6), (8), and (9): us, subroutine is written in FEM platform ABAQUS through the above incremental creep model ( Δε cr { }).

Implementation of Creep Model in ABAQUS.
e creep model in Section 2.1 is implemented in finite element program ABAQUS through the user-defined material subroutine (UMAT) as shown in Figure 1. erefore, the creep model needs to be written in incremental form, and the stress increment tensor Δσ(t n ) is expressed as where [D] is the elastic stiffness matrix, also called the Jacobian matrix; Δε el is the elastic strain increment tensor. e total strain increment includes an elastic strain increment tensor and a creep strain increment tensor. e elastic strain increment tensor is where Δε { } is the total strain increment tensor (DSTRAN); Δε cr { } is the creep strain increment tensor. e finite element calculation process is divided into filling stage during construction and creep stage during operation by analyzing step KSTEP. e calculation process of ABAQUS with UMAT-based creep model includes five steps: (1) determine initial stress state of creep; (2) determine the beginning of the creep stage; (3) determine the creep strain increment tensor; (4) determine the stress increment tensor; and (5) update the stress tensor, the Jacobian matrix, and state variable (STATEV). e subroutine compiled by Fortran is used to implement exponential decay-type empirical creep model. With FEM software ABAQUS, the stress and deformation simulation analysis, considering rockfill creep, was performed for the Xujixia CFRD.

The Xujixia CFRD
e Xujixia CFRD Project, as shown in Figure 2(a), is one of the 172 major water projects identified by the State Council of China. It is located about 6 km upstream of the Bayin River Canyon Exit and approximately 60 km northeast of Delingha City, Qinghai Province, China. Specifically, the maximum height of dam is 121.5 m, and the altitude of dam crest is 3472.0 m. e width of dam crest is 8 m, and the length of dam crest is 365.0 m. e upstream slope is 1:1.4, and the downstream composite slope is 1:1.85. e normal water storage level of reservoir is 3468.00 m, and the total storage capacity of reservoir is 162 million m3. e total volume of dam filling materials is 4,185,500 m 3 (see Table 1). e rockfill materials are primary rockfill (3B) and secondary rockfill (3C). e primary rockfill is a mixture of sandstone and sandy slate with low compressibility and high shear strength. e secondary rockfill is a mix of slate and riverbank gravel at the dam construction site.  Table 2. e dam is constructed in multiple phases as shown in Figure 2(d). e tests, as shown in Table 3, are performed on dam filling materials to determine the mechanical properties before and after compaction. e results are shown in Table 4 and Figure 3. After roller compaction, the maximum particle size of the rockfill is reduced from 800 mm to 600 mm. e percentage of the particles with a size of D < 5 mm increases from 15.73% to 16.38%. e fine particles with size of D < 0.075 mm increase from 0.84% to 1.61%. e dry density increases from the 1.92 g/ cm 3 to 2.18 g/cm 3 . ese index test results meet the design values. It is observed that the weak particles and sharp edges of the particles are broken during the compaction process.
Based on particle size distribution curves in Figure 3, the particle breakage of rockfill materials mainly occurs for particles in a size range of 300 mm-800 mm, resulting in the reduced particle size and increased percentage of fine Advances in Civil Engineering particles. ese broken particles are rearranged to fill the voids between large particles. erefore, the dry density, the compactness, and the compressive strength of rockfill are increased. After compaction, the porosity of rockfill material is 19.1%, and the permeability coefficient is 1.75 × 10 −1 cm/s. e settlement period of dam before water storage is mainly affected by the creep deformation of rockfill rather than the external water pressure. erefore, settlement monitoring data are used to evaluate the effectiveness of the creep subroutine in ABAQUS.

Duncan-Chang E-B Model and Creep
Model. e Duncan-Chang E-B model is used to characterize the nonlinear stress-strain relationship of the rockfill. e tangent modulus E t in the model can be expressed as Nonlinear volume change can be expressed as According to the Mohr-Coulomb criterion, the friction angle of dam rockfill can be expressed as e rockfill test samples in this paper are from main rockfill zone and secondary rockfill zone of the Xujixia CFRD. e samples are prepared according to the gradation after scaling and designed dry density. e rockfill sample has a diameter of 300 and a height of 600 mm. e maximum particle diameter is 60 mm. e consolidated drained triaxial tests are performed on rockfill samples using a ST-1500-type electrohydraulic servo Triaxial tester  ϕ 0 � the internal friction angle when the confining pressure is one atmosphere, Δϕ � the internal friction angle that changes with pressure, R f � the failure ratio, K � the tangent modulus coefficient, n � the tangent modulus index, K b � volume modulus coefficient, and m � bulk modulus index. static triaxial test system as shown in Figure 5. Four confining pressures, 500, 1000, 1500, and 2000 kPa, are used in tests. e initial values of Duncan-Chang E-B model parameters are obtained based on the testing results and used for subsequent parameter inversion [68,69].
e parameters of rockfill materials used in Xujixia CFRD were back-analyzed using neural network response surface method (BP-MPGA/MPGA). e inversion problem is transformed into a constraint problem. e optimization objective function is as follows:   Advances in Civil Engineering 11 1, 2, . . . , D), where X (D is the number of parameters to be inverted) is a group of rockfill model parameters to be inverted; U (X) ij and U real ij are the calculated displacement and the monitoring displacement, respectively, at the jth displacement in the ith time period; u is the number of external environmental factors affected by the measuring point; W (u) i is the weight of the external environmental factor u in the ith time period,  ij is the weight of the internal environmental factor v at the jth displacement in the ith time period,  (Table 5) and creep model parameters (Table 6) of rockfill materials of the dam are determined through backanalysis using neural network response surface method (BP-MPGA/MPGA).

Comparison of Calculation Results with Monitoring
Results.
e simulation and monitoring results are compared in Figure 6, which agree with each other very well. e settlement rate of each measurement point gradually slows down with time. e measurement points located in subrockfill area (such as CS1-1-04, CS1-2-05, CS1-3-07, CS1-4-05, and CS1-5-07) have larger creep values. Figure 7 shows the computed settlements in measured points with and without considering the dam creep. When considering creep, the calculated settlement is more consistent with the actual field monitoring results.

Creep Analysis for the Xujixia CFRD.
e simulated horizontal displacement and settlement with and without considering creep are shown in Figure 8. Considering creep in simulations, larger horizontal displacement is observed. Figures 9 and 10      Advances in Civil Engineering 13 gradually stabilized. Table 7 compares the simulation results with and without considering creep. In Figure 11, the maximum settlement is located in the middle and upper part of the sub-rockfill area of the dam after three years. e settlement of the dam has changed from 75.22 cm to 81.61 cm (0.67% < 1% of the dam height), which reaches a total increase of 8.5%. Both the simulation and monitoring results of Xujixia CFRD are consistent with similar projects in Table 8 and Figure 12. Figure 13 shows that the simulated maximum settlement of the dam at cross section D0 + 163.8 m agrees well with the measured values. Large settlement occurs rapidly during the construction stage and small settlement occurs in the long term due to creep deformation. ree settlements of measurement points of CS1-2-01, CS1-2-02, and CS1-3-03 are plotted in Figure 13. Large settlement occurs at points CS1-2-02 and S1-3-03, which are close to upstream of the dam due to the influence of water pressure.
e creep deformation at the main rockfill zone generally stabilized after 1-2 years after construction, resulting    in more compacted rockfill and increased strength of the dam body. By contrast, the secondary rockfill zone takes a longer time for creep to occur, which is due to the low strength of the rock in this zone. erefore, particle breakage, slippage, and filling of gaps continue to develop in the secondary rockfill zone.

Summary and Conclusions
An UMAT subroutine in ABAQUS was developed based on exponential decay empirical creep model. e creep parameters were obtained by quasilinearization method (BP-MPGA/MPGA) inversion. Numerical simulations were performed based on the Xujixia CFRD project to validate the UMAT subroutine. It was shown that the exponential decay-type empirical creep model was applicable for creep analysis of high CFRDs. Based on the results, the effects of rockfill creep on stress and deformation of the dam were analyzed.
By considering rockfill creep in FEM simulation, the major principal stress (σ 1 ) and the difference of principal stress (σ 1 − σ 3 ) were reduced. e stress distribution in the dam tended to be more uniform due to the stress relaxation after creep. By simulating dam body after water storage for three years, the maximum settlement of the Xujixia CFRD increased from 75.22 cm to 81.61 cm by considering dam body creep. Compared with similar projects (100-meter high CFRDs), the Xujixia CFRD has better deformation control effect. Due to the low strength of filling stone, the creep of secondary rockfill zone had a greater impact on stress and deformation distribution of the dam compared with primary rockfill zone.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest regarding the publication of this paper.