The primary aim of this research was to analyze the seismic performance of the Guoduo gravity dam. A nonlinear FEM method was implemented to study the deformation, stress, and overall stability of dam under both static and dynamic loading conditions, including both normal and overloading conditions. A dam seismic failure risk control method is proposed based on the cracking mechanism induced by the dynamic load to ensure dam safety and stability. Numerical simulation revealed that (1) under normal static and dynamic loading the symmetry of the displacement distributions is good, showing that the dam abutments and riverbed foundation have good overall stiffness. The stress distribution is a safe one for operation under both normal water loading and seismic loading. (2) Attention should be paid to the reinforcement design of outlets of the diversion dam monoliths, and enhance the capability of sustaining that tensile stress of dam monoliths. (3) The shape of the dam profile has a significant effect on the dynamic response of the dam. (4) By employing the “overload safety factor method,” the overall seismic fortification is as follows:
During the last 30 years, over 2000 dams have been constructed for irrigation, energy production, flood control, and recreation purposes in China. Almost 500 large dams have been built on the fringes of the active seismic zone in southwestern provinces in China. Since the failure of dams incurs great losses to society [
During the development of structural seismic theory and analysis methods [
In the last 30 years, much research aimed at studying the seismic fortification of dams has been carried out. Bouaanani and Renaud [
The primary aim of the authors’ research was to analyze and understand the seismic performance of the Guoduo dam under complex geological conditions. The deformation, stress, cracking risk, and overall seismic stability of the Guoduo were analyzed using a 3D finite element method, under various dynamic and static loadings, and a description is given below. A dam seismic failure risk control method is proposed based on the cracking mechanism induced by the dynamic load to ensure dam safety and stability.
The Guoduo hydropower station (Figure
Geoconditions and vertical profile of the Gouduo gravity dam.
Snapshot of the Guoduo gravity dam under construction
Vertical profile of the Guoduo dam in the downstream side
The dam site valley is wide “V” shape, and the slope topographies are relatively good. The left bank terrain slopes at 35°~40°, and the right abutment is steep, with consideration necessary for a 40°~45° slope. The main hydraulic structure plane and profile layout are illustrated in Figure
Physicalmechanical parameters of the concrete dam, the rock mass, and faults.
Material  Density (t/m^{3})  Permit load (MPa)  Elastic modulus (GPa)  Poisson’s ratio  Effective shear  


 
Dam (concrete)  2.40  2.0  22  0.167  0.90  1.2 
III2A  2.61  3.4  8.8  0.32  0.70  0.80 
III1A  2.70  5.0  17.0  0.30  0.90  1.00 
IV2B  2.63  2.0  6.0  0.30  0.50  0.70 
IV1B  2.68  3.5  9.0  0.28  0.80  0.90 
Weak rock layer of right bank  2.4  1.0  1.5  0.30  0.05  0.40 
Fault f2  2.4  1.0  1.5  0.30  0.05  0.35 
Fault f3  2.4  1.0  1.5  0.30  0.05  0.35 
Fault f4  2.4  1.0  1.5  0.30  0.05  0.35 
Fault f5  2.4  1.0  1.5  0.30  0.05  0.35 
Fault f7  2.4  1.0  1.5  0.30  0.05  0.35 
Rock mass classification for the Guoduo dam foundation.
Class  Rock mass structure  Rock mass description  Weathering  Uniaxial compression strength (MPa) 

III1A 
Thick layered structure surface, steep dip structural plane in abutment  Hard rock, intact and massive, high strength, antislip deformation resistance controlled by the structural planes. Weak rock mass is affected by weathering and unloading; local rock mass is poor  Fresh to slightly 
Rb > 60 MPa 


IV1B 
Interbedded or lamellar structure; some structures may cause dam foundation and abutment instability  Rock masses are relatively poor intact, antislip deformation resistance controlled by the structural planes and rock mass of chimeric ability. The rock mass cannot be directly used as dam foundation and must be effectively reinforced before used locally  Fresh to slightly 
Rb = 30–60 Mpa 


IVC  Interbedded or lamellar structure; some structures obviously cause dam foundation and abutment instability  Soft rock, rock intact, low strength, antislip, and deformation resistance performance are poor. The rock mass cannot be used as dam foundation and is excavated  Fresh to slightly  Rb < 30 MPa 
The dam site has a better than 10% probability in 50 years of a bedrock horizontal peak acceleration of 0.09 g. The horizontal seismic acceleration criterion was of the Guoduo’s hydraulic structure 0.09 g. Dynamic loads generated by seismic disturbances must be considered in the design of concrete dams situated in recognized seismic highrisk regions. The possibility of seismic activity should also be considered for dams located outside those regions, particularly when sited in close proximity to potentially active geological fault complexes.
The 3D nonlinear finite element dynamic analysis code, ABAQUS [
The 3D finite element analysis adopts DruckerPrager (DP) yield criterion, which can be expressed in
The stress adjustment process in the nonlinear finite element analysis with the DP criterion can be listed as follows: stress and strain at the initial point are set to be
Figure
Schematic mesh model of Guoduo gravity dam.
Overall 3D mesh
Dam downstream
In this study, the main loadings considered were as follows:
selfweight load;
upstream, downstream water pressure, the normal upstream water being at EL 3418 m, corresponding to the downstream tail water at EL 3360.91 m;
sediment pressure, silt elevation of 3378.38 m, density,
the seismic loading horizontal design earthquake acceleration that was 0.09 g. The vertical design earthquake acceleration was 2/3 of the horizontal design acceleration. Standard spectra were used, respectively, to generate the three directions of the artificial seismic waves (Figure
the earthquake dynamic water pressure that is calculated using the Westergaard dynamic water pressure formula [
Inversed seismic waves and the response spectrum.
According to the specifications for seismic design of hydraulic structures (DL50732000) [
The 3D finite element nonlinear dynamic analysis program for the Guoduo gravity dam was executed as follows:
Summary of the analysis cases studied in the 3D finite element modelling.
Analysis case number  Loading combination 

1  Static loadings, selfweight + upstream normal water loading + silt load + downstream water load (3D linear elastic) 
2  Static and dynamic loadings, Case 1 + design seismic load, horizontal seismic acceleration, 0.09 g (3D linear elastic, response analysis) 
3  Static loadings, selfweight + upstream normal water loading + silt load + downstream water load (3D nonlinear) 
4  Static and dynamic loadings, Case 3 + design seismic load, horizontal seismic acceleration, 0.09 g (3D linear elastic, time history analysis) 
5  Static and dynamic loadings, Case 3 + design seismic load, horizontal seismic acceleration, 0.18 g (3D linear elastic, time history analysis) 
6  Static and dynamic loadings, Case 3 + design seismic load, horizontal seismic acceleration, 0.27 g (3D linear elastic, time history analysis) 
7  Static and dynamic loadings, Case 3 + design seismic load, horizontal seismic acceleration, 0.36 g (3D linear elastic, time history analysis) 
In this section, the linear elastic 3D analysis results for the Guoduo gravity dam for Cases 1 and 2 are discussed. Typical dam monolith analyses include the right hand side dam monoliths, the overflow dam monoliths, the diversion dam monoliths, and the left hand side dam monoliths. Four typical profiles are
Table
Threedimensional stress and displacement results of the five typical dam monoliths (Case 1).
Max.  Min.  

Left dam monoliths  Overflow dam monoliths  Sand sluicing dam monoliths  Diversion dam monoliths  Right dam monoliths  Left dam monoliths  Overflow dam monoliths  Sand sluicing dam monoliths  Diversion dam monoliths  Right dam monoliths  
Case 1  Displacement (cm)  

0.392  0.648  0.657 

0.575 

0.112  0.14  0.0879  0.0896  

−0.164  −0.261  −0.282  −0.173 

−0.343 

−0.626  −0.596  −0.559  
Horizontal principal stress (MPa) 

0.532  0.308  1.283  2.221  −2.481  −3.16  −2.449 

−2.709 
Note:
The stress and displacement results of all the typical dam profiles under analysis Cases 1 and 2.
Max.  Min.  

Diversion dam monolith (0 + 65.40)  Diversion dam monolith (0 + 97.00)  Overflow dam monolith (0 + 127.00)  Right dam monolith (0 + 159.00)  Diversion dam monolith (0 + 65.40)  Diversion dam monolith (0 + 97.00)  Overflow dam monolith (0 + 127.00)  Right dam monolith (0 + 159.00)  
Case 1  Displacement (cm) 

0.652  0.697  0.648  0.575  0.128  0.143  0.124  0.141 

−0.23  −0.259  −0.293  −0.259  −0.49  −0.57  −0.679  −0.559  
Principal stress/MPa  0.3  0.2  −0.3  0.4  −1.1  −1.0  −1.0  −1.4  


Case 2  Displacement (cm) 

1.62  1.707  1.597  1.492  −0.376  −0.358  −0.324  −0.356 

0.1  0.084  −0.048  −0.029  −0.805  −0.858  −0.915  −0.833  
Principal stress/MPa  2.0  2.0  1.0  1.8  −1.2  −1.2  −1.0  −1.6  


Case 4  Displacement (cm) 

2.36  2.33  2.32  2.30  −1.72  −1.73  −1.70  −1.72 

1.09  1.08  0.96  1.10  −1.96  −1.97  −1.96  −1.98  
Principal stress/MPa  2.0  1.5  1.8  1.4  2.0  −2.0  −1.8  −1.5 
Note:
Dam displacement contour in various directions under analysis Case 1 (unit: m).
Upstream displacement distribution in river direction
Downstream displacement distribution in river direction
Upstream displacement distribution in vertical riverbed direction
For challenging problems in dam design, it is vitally important to investigate clearly the stress distributions in both the dam and its foundation, especially in the tensile zone upstream at the heel of the gravity dam, close to the downstream toe of the dam, and at the damfoundation contact surface. For analysis Case 1, stress characteristic values for the typical dam monoliths are illustrated in Tables
For all typical dam monoliths, under analysis Case 1, the maximum principal stress and compression stress level were about 2.308 MPa and 3.232 MPa at the left hand side dam monolith and the toe of diversion dam monoliths, respectively. For all typical dam profiles, under analysis Cases 1 and 2, the maximum principal tensile stresses were about 0.4 MPa
For analysis Case 4, Table
The maximum displacement (along the river direction) (Figure
The maximum displacements along the river and in the settlement directions for analysis Case 2 increased by 1.4 and 1.3 times, respectively, when compared with the results of the linear elastic static working condition (analysis Case 1). The maximum displacements along the river and settlement direction under analysis Case 4 increased by about 2 and 1.1 times, respectively, compared with the results for analysis Case 1.
Dam displacement contour in various directions under analysis Case 4 (unit: m).
Upstream displacement distribution in river direction
Downstream displacement distribution in river direction
Upstream displacement distribution in vertical riverbed direction
For analysis Case 4, the 3D stress distribution for the Guoduo dam is shown in Figure
Principal stress contour of dam upstream/downstream under analysis Case 4 (unit: Pa).
Max. principal stress of upstream surface
Max. principal stress of downstream surface
Min. principal stress of upstream surface
Min. principal stress of downstream surface
Principal stress of typical section under analysis Case 4 (unit: Pa).
Max. principal stress of
Min. principal stress of
Max. principal stress of
Min. principal stress of
Max. principal stress of
Min. principal stress of
Max. principal stress of
Min. principal stress of
The overall upstream surface sustained the compression pressure, the maximum tensile principal stress level in the typical dam monoliths being about 1.5 MPa (the left hand side dam monolith downstream side), and the maximum compressive stress is about 3.0 MPa (the wall corner of the sand sluicing dam monolith). For all the typical dam profiles, for analysis Cases 4, the maximum principal stresses are about 2 MPa
Based on the numerical analysis Case 4, the tension and compression stress distributions are similar to those
This section describes an analysis of the ultimate seismic capacity of the dam using the “overload safety factor method,” based on nonlinear finite element analysis. For different analysis cases (Table
The maximum equivalent plastic strain of the typical dam monoliths. (Analysis Cases 4–7).
Diversion dam monoliths (0 + 65.40)  Diversion dam monoliths (0 + 97.00)  Overflow dam monoliths (0 + 127.00)  The right dam monoliths (0 + 159.00)  

Case 4  Working statues  Elastic  


Case 5  The maximum equivalent plastic strain 




Location  Downstream surface  


Case 6  The maximum plastic strain 




Location  Downstream surface  


Case 7  The maximum plastic strain 




Location  Downstream surface 
Dam upstream/downstream yield zone under various analysis cases.
Upstream, under analysis Case 4
Downstream, under analysis Case 4
Upstream, under analysis Case 5
Downstream, under analysis Case 5
Upstream, under analysis Case 6
Downstream, under analysis Case 6
Upstream, under analysis Case 7
Downstream, under analysis Case 7
The numerical results show the following.
For analysis Case 4, the dam and foundation remained within the elastic range.
For analysis Case 5, the seismic horizontal acceleration was more than twice as big with yielding appearing in the diversion pipe, flushing hole, pier and beam junctions, pier wall, and the top of the plan. The equivalent plastic strain value was
For analysis Cases 5 and 6, the seismic horizontal acceleration was more than twice and three times, respectively. The maximum plastic strain values were
For each overloading step increment above seismic horizontal acceleration (hereafter
Based on numerical analysis, under overloading (dynamic loading), the yielded zones appeared at the stress concentration areas, such as the dam heel, the dam joint face, and bank slope surfaces of the bank upstream and downstream. A large yielded zone appeared in the back tube and planthouse (Figures
This study analyzed and understood the seismic performance of the Guoduo dam. The geological conditions affecting seismic performance of the Guoduo dam are first discussed below. The deformation, stress, cracking risk, and overall seismic stability of the Guoduo were analyzed using a 3D finite element method, under various dynamic and static loadings and a description is given below. The following conclusions can be drawn.
For analysis Cases 1, 2, and 4, the symmetry of the displacement distributions is good, which shows that the dam abutments and riverbed foundation have good overall stiffness. The maximum displacements (along the river direction) of the dam were 0.697 cm, 1.707 cm, and 2.36 cm at
Based on the numerical analysis, the tension and compression stresses distribution is homogeneous, and the stress levels of the key components, such as dam heel and dam toe, are within safe limits for dam operation under normal water loading. A local tensile stress occurs at the upper dam foundation junction, the outlets of the diversion dam monoliths, and the parts in bending of the sand sluicing, diversion dam monoliths. Attention, therefore, must be paid to the reinforcement design for these sections to enhance the capability of sustaining tensile stresses. A reinforcement design should control the local cracking risk by selecting the appropriate concrete materials, using small diameter reinforcing bars, and improving temperature control measures for pouring mass concrete during construction.
The shape of the dam profile has a significant effect on the dynamic response of the dam. Numerical results show that highly stressed areas easily occur where there is a sudden change of geometry. In addition, after considering the interaction between the planthouse and diversion dam monoliths, although the planthouse can enhance the overall stiffness and stability of the dam, the high stiffness low down on the dam easily causes stress concentration at the dam downstream surface. This situation is not helpful to the safety of the dam body under strong earthquake action.
Based on numerical simulation, by employing the “overload safety factor method,” the overall seismic fortification factors are as follows:
The authors declare that there is no conflict of interests regarding the publication of this paper.
This research work was supported by National Natural Science Foundation of China (nos. 11272178 and 51339003), National Basic Research Program of China (973 Program) Grant no. 2011CB013503, and Tsinghua University Initiative Scientific Research Program. The authors are very grateful to Guiyang Hydroelectric Investigation and Design Institute for supporting this study.