A monitoring model for the stress on a super-high arch dam during pre-impoundment construction

This paper presents a proposed model for monitoring the stress on a super-high arch dam during construction. Using mathematics, mechanics, and dam engineering principles, the mathematical expressions of the self-weight component of the dam prior to and following the sealing of the bottom of the arch were derived. The visco-elastoplastic constitutive model of dam concrete during construction was identified and used to develop a stress monitoring model for a super-high arch dam. Based on in-situ stress monitoring data collected during the construction of a super-high arch dam, the stress monitoring model was applied to a super-high arch dam accounting for future impoundment, and the key components of the monitoring model were isolated. The results show that the model has high fitting accuracy and incorporates an appropriate selection of factors affecting dam stress. The hydrograph of each component conforms to the structural characteristics of superhigh arch dams during construction. This model overcomes the limitations of applying the complete self-weight of the dam body on the cantilever beam and was validated using data from a super-high arch dam construction project. Thus, this paper provides evidence for a safety monitoring model for super-high arch dams during construction.


INTRODUCTION
construction that considers the pre-impoundment stage is urgently needed (Ma et al. ).
The construction and initial impoundment of the dam are associated with more frequent accidents compared with other dam operations. Thus, there is a greater failure probability and greater risk of events that directly affect the safety of the structure at these stages (Zhang et  which results in the formation of a complete system after transverse joint grouting. Second, the self-weight of the dam body in the subsequent phases of construction will contribute to the load distribution of the arch beam. Therefore, the self-weight of subsequent pouring cannot be directly used as an influencing factor in the stress monitoring model. In order to elucidate the stress law changes of super-high arch dams during construction, this study aimed to consider the actual working conditions of the dam during pre-impoundment construction. In this work, prototype monitoring data from multi-source temporal and spatial monitoring, such as the amount of environmental stress, was comprehensively considered. This data was integrated with results from previous studies of mechanical characteristics and numerical analysis to develop a stress monitoring model for the pre-impoundment stage of superhigh arch dam construction. Finally, the model was validated using a case study of stress monitoring analysis in super-high arch dam construction. A crown cantilever of unit thickness was considered as the study object ( Figure 1). The self-weight of the concrete and the vertical normal stress at e hthe horizontal section of the measuring point Pincrease with dam height. In general, the maximum and minimum normal stresses appear on the up-and downstream edges of the dam, respectively. The calculation of point P is based on the stress values of two points, C and D. Assuming that the vertical normal stress of the horizontal section at a point is linearly distributed, the stress at points C and D is calculated by the eccentric compression formula for material mechanics, as follows:

DEVELOPMENT OF A STRESS MONITORING MODEL FOR SUPER-HIGH ARCH DAM PRE-IMPOUNDMENT CONSTRUCTION
In Equation (1), e C and e D are the vertical normal stresses of the up-and downstream edges, respectively, of the horizontal section at point P, W is the concrete self-weight above the horizontal section of point P, M is the moment of the concrete self-weight above the horizontal section from P to the centroid of the section, and T 2 is the thickness of the dam at P.
Integrating the configuration parameters of the arch dam, the vertical normal stress e C and e D can be calculated by Equation (1).
In Equation (2), r c is the concrete density, Z is the overall height of the dam, z 1 is the un-poured height of the dam, z 2 is the distance from the horizontal section of the measuring point P to the top of the poured section of the dam, T 1 is the thickness of the top of the poured dam, a 1 and a 2 are the configuration parameters of the arch dam, and the other parameters are the same as for Equation (1) as described above.
Therefore, the vertical normal stress at the measuring point is Figure 1 | Schematic diagram of stress calculation at measuring point.
In Equation (3), L is the horizontal distance from the measuring point to the surface of the upstream dam, r c , a 1 , a 2 , Z, L and T 2 are constant for a fixed measuring point, and the other parameters are as described above.
Therefore, the expression of the self-weight component prior to sealing the arch is The The expression of the self-weight component of stress in the upper portion of the dam after sealing the bottom of the arch is the sum of the stress generated by the self-weight before sealing the arch and the stress of the newly poured concrete self-weight after sealing the arch, as follows: Temperature component A thermometer inside the arch dam can be used to collect temperature data from an arch dam during construction.
The temperature stress was calculated using previously reported temperature data (Li et al. ) and can be expressed as: In Equation (8), T i is the temperature change of the ith thermometer (equal to the instantaneous value minus the initial value), and m 2 is the number of the thermometer.
The temperature of the dam interior changes with the harmonic change of the surrounding water and air temperatures (Gu & Wu ). Therefore, when there are no thermometers in the dam or the thermometers fail, the temperature component can be expressed as In Equation (9), i ¼ 1 represents an annual cycle whereas i ¼ 2 represents a semiannual cycle, i is generally 1 or 2, b 1i and b 2i are the regression coefficients, and t is the cumulative number of days from the start of monitoring.

Water pressure component
In general, the water pressure component of stress can be expressed by an nth-order polynomial of the water level H 1 . For a gravity dam, n ¼ 3 whereas n ¼ 4 for an arch dam or multiple arch dam. Accordingly, the water pressure component of stress can be expressed as: where a i is the regression coefficient for i ¼ 1-4.

Aging component
The (1) At a low stress level, σ min (σ s1 , σ s2 ), σ s1 and σ s2 are defined as the plastic yield stress in the unified mechanical constitutive model. Field observations and laboratory tests show that the dam concrete first demonstrates instantaneous linear elastic strain under loading followed by creep deformation until a stable value is achieved.
At any time, the total strain of the concrete is In Equation (11), ε e is the elastic deformation, ε c (t) is the creep deformation, and C(t, τ) is the creep degree, which represents the creep under unit stress and describes the creep characteristics of the material. The creep degree C(t, τ) can be expressed as: In Equation (12), c is the general volume of creep, and λ is the speed of creep development.
Thus, Equation (11) can be rewritten as: In Equation (13) Therefore, the attenuated rheological strain of the concrete is equal to the lag rebound strain.
(2) At a high stress level, σ ! max (σ s1 , σ s2 ), the concrete will undergo a process of accelerated rheology similar to rock. The accelerated rheological stage appears earlier than the low stress level in the stress curve.
Therefore, the rheological curve of concrete integrates both attenuated rheology and stationary creep.
According to the rheological characteristics of concrete at different stress levels, the attenuated rheological deformation of dam concrete is equal to the lag rebound strain at high or low stress levels. Therefore, the Nishihara model was adopted as a constitutive model of dam concrete, as this model can comprehensively describe the deformation of dam concrete under various loads (Figure 2).

The constitutive equation for dam concrete is
In Equation (14), σ s2 is the plastic yield stress, E MC is the elastic modulus, E KC is the viscoelastic modulus, η KC is the viscosity coefficient, and the other parameters are as described above.
The right side of Equation (14) includes instantaneous deformation and creep deformation. Considering that the dam concrete has just been poured and the stress level is unlikely to reach the yield limit, σ σ s2 ; creep deformation can therefore be expressed as: Equation (15) can be rewritten as: Equation (16) defines the creep stress as a function of t and ε c ,, and E MC , E KC , η KC are constant. Therefore, Equation (16) can be rewritten as: The stress monitoring model at the stage of ongoing dam construction following the sealing of the bottom of the arch is the sum of the self-weight, water pressure, temperature, and aging components. The comprehensive expression for stress monitoring of the super-high arch dam is therefore as follows: or

CASE STUDY
In order to validate the effectiveness and accuracy of the    Table 3.
The hydrograph of the self-weight component in Figure 5 indicates that the self-weight of the concrete has the most significant influence on the stress on the dam, and the   Finally, the hydrograph of the aging component in