A series of super-high arch dams (height over 200 m) have been constructed or are being planned in China. Most of them are distributed in the mountainous areas in southwest China (Figure 1
), and therefore are subject to complex engineering challenges, such as high seismic intensity, high slope, huge water thrust, and so forth. The geological conditions are also very complex, for example, the deep-cutting valley, high ground stress, and some unfavorable geological conditions, such as atypical faults, dislocation interfaces, altered rock masses, and weak rock masses [1
]. The complex geological conditions may lead to the crack of dam concrete or foundation, which eventually leads to dam failure [4
]. Therefore, the construction of super-high arch dams still faces many challenges. Cracks may initiate in the outlets [5
], heel [6
], surface, and interior of dam concrete blocks [2
], then propagate and coalescence along horizontal or vertical directions in concrete blocks. The main cracking factors include temperature variations, heat from concrete hydration, shrinkage and creep, dam foundation uncoordinated deformation, earthquake, and seepage effect [4
Some research studies have been done related to the cracking mechanism on concrete blocks of dams experimentally and theoretically. Study on thermal mechanics of the concrete dam includes the temperature variation of the external environment and heat from concrete hydration. When the temperature gradient changes dramatically inside the dam, the thermal stresses will concentrate and cause the cracks to initiate under cold wave conditions [7
], in cold areas [8
], under unfavorable solar radiation [9
], and in dry, hot valley regions [10
]. Temperature load is the main cracking factor of the Karaj arch dam [11
]. The nonlinear analysis of concrete arch dams is necessary to check the stability of cracks in high tensile stress areas. Maken et al. [12
] investigated the mechanical properties and showed that stress relaxation is affected by the concrete temperature. They used a finite-element modeling procedure for assessing the thermal mechanical behaviors of concrete dams, and successfully reproduced the oblique cracks present on the downstream face of Daniel Johnson dam. The distribution of stresses in roller-compacted concrete dams is greatly affected by the starting date of the roller-compacted concrete placement schedule [13
]. Self-weight and weak foundation [14
], uneven settlement of arch dam foundation, and earthquake [16
] can also lead to the cracking of arch dams. Hariri-Ardebili et al. [18
] assessed seismic cracks in three types of concrete dams, namely gravity, buttress, and arch, using an improved 3D coaxial rotating smeared crack model. The cracking factors of arch dams often interact with each other in a nonlinear manner, and therefore cannot be considered separately.
The concrete dam cracking problems have been studied by different methods in the past 30 years as follows. (1) The finite element method (FEM) is widely used in the numerical simulation of dam cracking, including the FEM based on elastoplastic mechanics, the FEM based on fracture mechanics [19
], and the FEM based on damage mechanics [21
]. Based on linear elastic crack mechanics and three-dimensional boundary element modeling, Feng et al. [23
] presented a procedure to analyze the cracks in arch dams. Chen et al. [24
] introduced the existing constitutive model of large, light, reinforced concrete structures and the deficiency of the design procedure, and they also presented a three-dimensional nonlinear cracking response simulation procedure for outlet structures. The overall stability of arch dams is analyzed by the three-dimensional numerical simulation [25
]. Sato et al. [26
] simulated the thermal stress of a concrete dam by three-dimensional linear elastic FEM, and the autogenous shrinkage strain was added to the thermal strain. (2) Dam geomechanical model tests were widely carried out in the United States, Switzerland, Yugoslavia, Russia, Germany, Italy, Japan, and Sweden in the 1970s and 1980s [27
]. The geomechanical model mainly refers to the model that reflects the specific engineering geological structure in a small range, such as the faults, fractures, and weak zones in the dam foundation, and it follows the similarity theory [28
]. Lin et al. [2
] analyzed the cracking characteristics of the Xiaowan arch dam surfaces and rock mass failure process of the abutments. They judged the alteration zones, weak rock masses, and other faults in the abutments that caused the arch dam to crack and proposed the method of foundation reinforcement. (3) Many scholars also focus on different numerical methods to simulate dam cracking processes, for example, element-free method [29
], interface stress element method, and boundary element method [30
]. Prototype monitoring is also widely used in arch dam cracking analysis. However, there are still many areas for improvement in the analysis of cracking of arch dams. Linear finite element is not capable of revealing the actual state of the structure. As a popular simulation method, the nonlinear numerical method has no uniform standard for the selection of material constitutive models and parameters and the setting of boundary conditions. Although the geomechanical model of rupture test is straightforward, the loading control, boundary condition simulation, and error analysis of measurement data need to be further investigated. The cracking theory of arch dams has not been fully studied, especially for the location and propagation of cracks.
This study first summarizes the main analysis methods, cracking types, and factors of arch dams according to the cracking cases. In order to analyze the cracking and overall stability of the Xulong high arch dam, a nonlinear constitutive model and overall stability criterion are employed, and numerical simulation on the overall stability, cracking analysis of dam outlets, and arch abutments are performed. This study aims at proposing effective reinforcement methods and prevention methods for arch dam cracking. Through the analysis of the yielding region and stress before and after the reinforcement, the reinforcement methods of the Xulong arch dam are determined. Based on the analysis of the first and third principal stresses and yielding region of the arch dam, a method for crack prevention based on five stress zones of arch dams is proposed.
5. Overall Stability and Reinforcement Analysis of Xulong Arch Dam
5.1. Overall Stability Analysis
The overall stability analysis of the Xulong arch dam adopts the methods in Section 3.1
and obtains three safety factors,
= 8.5. The capacity curve of the maximum displacement along river direction of the arch crown is illustrated in Figure 10
. With 2 to 2.5 times overloading, cracks initiate at the dam heel. At the bottom of the dam to EL 2220 m, local yielding occurs on the upstream of the left and right abutments. Therefore, the safety factor of crack initiation is estimated to be 2~2.5.
When five times overloading, cracks initiate at the foundation surface and propagate from the upstream to the downstream between EL 2095 m and EL 2258 m. The maximum crack depth is about 0.5 times the thickness of the dam. The local region of the dam toe and the outlets of the downstream begin to yield and gradually propagate to the surrounding region. The yield region of the foundation surface between the dam heel and toe tends to coalesce and the capacity curve starts to be nonlinear at five times overloading (Figure 10
). Therefore, the safety factor of structural nonlinear behavior initiation of the dam is judged as 5.
When eight times overloading, the yielding region is not fully connected to form a movement mechanism, so the structure can still provide support (Figure 11
a,b). When nine times overloading, the foundation surface forms two connected yielding regions and a movement mechanism (Figure 11
c,d). The displacement along river direction of the arch crown increases faster at eight and nine times overloading (Figure 10
). The overall stability of arch dam–foundation is lost. Therefore, the ultimate undertaking coefficient of the arch dam is judged as 8.5.
The displacement distributions of the dam are basically consistent in different overloading times (Figure 12
). The maximum displacement along the river direction of the arch crown is around the dam crest and increases with the increase of overloading.
The arch thrust distribution characteristics of several high arch dams are compared in Figure 13
. The middle and lower elevation arch thrusts of the dam are huge and the upper elevation arch thrust is small. The Xulong and other arch dams have the same thrust distribution characteristic. The large arch thrust region is consistent with the large yielding region. The distribution characteristics of the yielding region and arch thrust can be used as a validation of the five stress zones in Section 5.2
5.2. Discussion on Dam Stress Zones
Based on past analytical experience and the analysis of the stress, displacement, and yielding region of the Xulong arch dam, five stress zones of the arch dam are proposed as follows. Figure 14
is a schematic diagram of the five stress zones. The five stress zones can better guide the crack prevention of the arch dam.
(1) Three-way compression zone of upstream surface
This zone ranges from about 1/5 to 4/5 dam height, and the zone width is close to the height. The stress state in this zone indicates the structural state of the arch dam and it is important to control the compression stress in this zone. In general, the maximum compression stress is around the arch crown beam at 1/3 elevation of the arch dam. The compression stress results of the finite element analysis are around 6.2~8.0 MPa.
(2) Tensile and compressive zone of upstream arch abutment
The stress state may be tensile stress in the direction of both beam and arch or one of the directions is tensile stress. When upstream water pressure is considered, it is the state of double-tension single-compression or double-compression single-tension. More attention should be paid to control the tensile stress of this area to prevent cracking. The calculation results show that the tensile stress of the left arch abutment of the Xulong dam reaches 1.18 MPa of case 1. It is suggested to control the tensile stress of this area to less than 1.5 MPa when the FEM is adopted.
(3) Tensile stress zone of upstream dam heel
Based on the analysis of several super-high arch dams in China, it is suggested that the tensile stress should be strictly controlled within 1.4 MPa if the tensile stress of arch dams is based on FEM simulation. The dam heel tensile stress of the Xulong arch dam is 0.9 MPa. Although the upstream bottom joint can reduce the tensile stress of the dam heel, attention should be paid to the effect of hydraulic fracturing. The upstream bottom joint cannot affect the construction of the curtain grouting. The high tensile stress is related to the discontinuous geometric shape of the arch dam heel. The cracking of the dam heel should be paid more attention to.
(4) Compression stress zone of downstream arch abutment
This zone ranges from the bottom to the middle height of the dam. Normally, the largest compression stress is in this zone and it is important to control it. The compression stress of the left arch abutment of the Xulong dam reaches 8.88 MPa of case 10. It is suggested to control the compression stress of this zone to less than 14 MPa when the FEM is adopted.
(5) Tensile stress zone of downstream surface
The arch dam’s downstream surface between the upper to middle elevation is a tensile zone, and the tensile stress is in the direction of the beam. The tensile stress may be large here due to the pier. When the upstream water level is low, this tensile stress zone will shift to the left and right arch abutments. The results of the geomechanical model test also show that the cracking of the downstream arch abutment basically extends to the center of the dam along the normal of the foundation surface, which is the failure of the tension and shear [2
5.3. Abutment Reinforcement Suggestion
Based on the analysis of the overall stability, stress, and displacement of the arch dam, it is considered that the fault f57, xenolith, fault f26, and biotite enrichment zone have a great effect on the stress distribution of the arch abutments.
In order to improve the stress state of the dam abutments and decrease the cracking risk during long-term operation, it is recommended to use a shearing-resistance wall in the fault f57, to replace the biotite enrichment zone with concrete, and to perform consolidation grouting or anchoring on the excavated exposed weak structural zone. Figure 15
illustrates the shearing-resistance tunnel for the left arch abutment and the concrete replacement for the right arch abutment.
Through numerical simulation, the tensile stress and yielding zone changes of the arch abutments are obtained before and after reinforcement (Figure 16
and Figure 17
). The first principal stresses of the left and right arch abutments decrease by about 0.13 and 0.17 MPa, respectively. The reinforcement of the abutments reduces the first principal stress and improves the stress state of the arch abutments, thereby reducing the cracking risk. The reinforcement method also improves the comprehensive shear strength of the side-slip surface and ensures a certain safety margin for the anti-sliding of the arch abutments.