Research on the Full Life Cycle Deformation, Stress Response, and Dynamic Fatigue Performance of Concrete Structures in Pump Stations

Abstract

Concrete structures are subjected to static and fatigue loads during long-term service, and temperature changes can cause changes in the volume of concrete, leading to stress changes and fatigue damage, which affect the mechanical properties and service life of a structure. In response to the current lack of three-dimensional analysis and the exploration of the mechanical behavior and damage evolution processes of concrete structures under variable temperature environmental conditions, this paper relies on the Fenghuangjing Pump Station project involving the Yangtze River and Huaihe River and constructs a concrete thermo-mechanical-fatigue-damage model based on the power exponent function damage constitutive model. By using multiple coupled simulation calculations to predict the performance of concrete structures; analyzing the stress, deformation, and fatigue damage of structures from construction to operation; comparing measured data; dynamically optimizing inversion to obtain concrete thermal parameters; proposing key control parameters; and warning indicators and thresholds, the research results can provide reference for the long-term safe operation of similar projects.

1. Introduction

Numerous engineering practices have proven that 80% of concrete structure cracks are caused by non-load stresses generated within the concrete material itself [1,2] or under changes in the environmental temperature [3,4] and humidity [5,6]. During long-term service, the pump station structure not only bears static loads [7,8], but also frequently experiences fatigue loads [9,10]. Among them, changes in daily and annual environmental temperatures from the construction period to the operation period can cause volume expansion or contraction in concrete structures, leading to changes in stress and causing fatigue damage. This will cause the internal stress field of a pump station structure to constantly change and be redistributed, leading to the continuous derivation and expansion of microcracks [11,12], resulting in a gradual deterioration of the mechanical properties of structural components [13,14] and increasing the risk of fatigue failure of the structure below the allowable stress [15,16]. The essence of fatigue failure is the process of the continuous accumulation of damage and gradual attenuation of the bearing capacity [17,18].

Numerical simulation, as an effective means of predicting the performance of concrete structures, is particularly important in analyzing the stress [19,20], deformation [21,22], and fatigue damage [23,24] of concrete structures. In terms of coupling algorithms and models, Wang [25] established a relatively new temperature damage model for concrete materials through experiments and calculations. Wang [26] also studied the method of obtaining parameters, describing concrete damage from experiments, and applied temperature damage to the simulation calculation of three-dimensional finite element temperature stress fields. Tang [27] believed that the failure process of concrete actually comprises the initiation and propagation of microcracks until macroscopic cracks are generated, leading to the instability and failure of concrete. A coupled hygro-thermo-mechanical peridynamic model has been proposed for concrete at high temperatures by Zhang [28]. The model can take into account the influences including water vapor diffusion, water vapor flow, and liquid water flow. However, there has not been much analysis of parameters such as the thermal expansion coefficient α, critical fracture energy G_f, and other parameters. The model by Zhang [29] is here employed to investigate the significance of pore pressures and thermally induced stresses for the spalling of concretes with different initial permeabilities and moisture contents through the numerical simulations of a wall and a square column exposed to fire. The numerical results reveal that thermally induced stresses constitute a primary factor in causing damage and hence spalling in concrete while pore pressures, at most, play a secondary role. In order to comprehensively predict the performance of concrete subjected to multiaxial compressive loads in fire, an orthotropic triaxial compression thermo-mechanical damage model for concrete was developed by Zhang [30]. A new numerical simulation framework was introduced by Wang [31] to analyze the long-term damage characteristics of ballastless tracks under cyclic environmental loading considering the thermal properties of the track and the nonlinearity of concrete. In terms of experimentation, the experiments by Seng [32] allowed researchers to demonstrate how the heat and moisture transport phenomena within a wall are coupled, particularly how a temperature difference can be a sufficient driving force for the release of moisture. The author’s work points out the impact of moisture adsorption on heat release and on the temperature changes within the wall. The findings by Zhu [33] demonstrated that temperature significantly impacts relative humidity development and that temperature and relative humidity are the primary determinants of early stress development in concrete. The effects of mineral admixtures and curing ages on the hydration process, mechanical properties, and permeability of concrete during the steam curing process were studied by Shi [34], and the pore structure, micromorphology, and interfacial transition zone (ITZ) were also determined by multi-scale image processing and scanning electron microscopy.

Although the above references have conducted extensive researches on the stress, de-formation, and damage of concrete structures, there is still a lack of three-dimensional analysis and the exploration of the mechanical behavior and damage evolution processes of early-age concrete structures in environments with changing temperature and humidity. In particular, the influences of damage on thermal diffusivity, the thermal conductivity coefficient, and elastic modulus still need to be studied. Therefore, the proposal and establishment of multi-field coupling algorithms and models for thermo-mechanical-damage are necessary.

Therefore, in order to comprehensively understand and deal with fatigue damage under multi-field coupling conditions from a three-dimensional perspective, this paper relies on the Fenghuangjing Pump Station project involving the Yangtze River and Huaihe River, establishes a concrete thermo-mechanical-fatigue-damage model based on the power exponent function damage constitutive model [26], and uses the Fortran language to develop a corresponding three-dimensional finite element simulation calculation program. The finite element mesh model of the pump station structure is subjected to thermo-mechanical-fatigue-damage multi-field coupling simulation calculation and the adiabatic temperature rise of the material is inverted to obtain a concrete structure prediction model. On this basis, the numerical simulation prediction and analysis of the entire process of the pump station structure are carried out to obtain performance response parameters such as the stress performance, deformation performance, and dynamic fatigue damage of the pump station structure throughout the entire life cycle from construction to operation. These parameters are compared with the response characteristics (monitoring values) of the physical structure, and key control structural parameters, warning indicators, and thresholds for long-term safe operation of the structure are proposed. Through exploring the above research content, the aim is to provide reference for ensuring the long-term safe and efficient operation of the structure.

2. Project Overview

Located on the north bank of the Yangtze River embankment in Liudu Town, Wuwei City, Anhui Province of China, the Fenghuangjing Pump Station project is the first diversion hub of the Xizhao Canal for the Yangtze-River-to-Huaihe-River Water Diversion Project, and it was also the last but crucial project to commence among the eight major hubs of the “Infrastructure Construction Project No.1” of the Yangtze-River-to-Huaihe-River Water Diversion Project in Anhui Province. The project aims to optimize the allocation of water resources through cross-basin water transfer, alleviate the problem of drought and water shortage in the Huai River Basin, improve the ecological environment of Chaohu Lake and the Huai River, and promote the coordinated development of the Yangtze River Economic Belt and the Huai River Ecological Economic Belt. The Fenghuangjing Pump Station is located south of the Jianghuai watershed, belonging to the Yangtze River Basin. It is in a warm temperate and northern subtropical humid monsoon climate zone with a mild climate, four distinct seasons, abundant sunshine, and long frost-free period. The dominant wind directions in this area are northeast (winter) and southwest (summer), with an average annual wind speed of 2 m/s.

3. Main Calculation Parameters

3.1. Temperature Data

In the simulation calculation, the formula for fitting the average monthly temperature of the concrete structure of the Fenghuangjing Pump Station into a cosine curve over many years is as follows [35] while considering a day–night temperature difference of ±10.0 °C.

$$T_a\left(t\right)=16.6+12.3\times cos\left[{\displaystyle \frac{\pi }{6}}\left(t-7.2\right)\right]$$

(1)

3.2. Main Thermodynamic Parameters

The main thermodynamic parameters of the foundation refer to the engineering data and similar projects [35]. Concrete specimens of the C30 target strength grade were prepared according to the Chinese standard JGJ55-2011 [36] the thermodynamic parameters of concrete (C30) were obtained from indoor tests, and the above parameters are detailed in

Table 1. Thermodynamic parameters of the foundation and concrete.

Category	Thermal Conductivity Coefficient $\mathit{\lambda }$/ (kJ·m−1·h−1·°C−1)	Specific Heat $\mathit{c}$/ (kJ·kg−1·°C−1)	Thermal Diffusivity $\mathit{a}$/ (m2·h−1)	Final Adiabatic Temperature Rise ${\mathit{\theta }}_0$/ °C	Linear Expansion Coefficient $\mathit{\alpha }$/ (10−6·°C−1)	Final Modulus of Elasticity E0/ (MPa)	Poisson’s Ratio $\mathit{\mu }$
Foundation	10.838	0.886	0.004780	/	6.8	300	0.2
C30	7.830	0.870	0.003524	41.6	8.1	30,000	0.167

.

$$\mathrm{Elastic} \mathrm{modulus} \mathrm{of} \mathrm{concrete} (\mathrm{GPa}): E\left(\tau \right)=39.6\times \left[1-e^{-0.39{\tau }^{0.496}}\right]$$

(2)

$$\mathrm{Concrete} \mathrm{compressive} \mathrm{strength} (\mathrm{MPa}): f_c\left(\tau \right)=47.5\times \left[1-e^{-0.49{\tau }^{0.497}}\right]$$

(3)

$$\mathrm{Concrete} \mathrm{tensile} \mathrm{strength} (\mathrm{MPa}): f_t\left(\tau \right)=2.96\times \left[1-e^{-0.46{\tau }^{0.496}}\right]$$

(4)

According to Reference [35], the creep degree of concrete is taken as follows:

$$C\left(t,\tau \right)=\left(f_1+g_1{\tau }^{-P_1}\right)[1-{e^{-{\tau }_1}}^{\left(t-\tau \right)}]+\left(f_2+g_2{\tau }^{-P_2}\right)\left[1-{e^{-{\tau }_2}}^{\left(t-\tau \right)}\right]$$

(5)

$$\mathrm{Adiabatic} \mathrm{temperature} \mathrm{rise} (°\mathrm{C}): \theta \left(\tau \right)=56.1\tau /\left(\tau +1.76\right)$$

(6)

3.3. Other Thermal Parameters

The numerical value of the surface heat release coefficient of concrete in the air is related to the wind speed. According to engineering data, the average wind speed in the construction area over the years was 2.0 m/s. Since the surface of concrete is smooth after demolding, the value is taken based on the smooth surface as follows.

When there is wind [35],

$$\beta =18.46+17.36v_a^{0.883}=18.46+17.36\times {2.09}^{0.883}=51.74 \mathrm{kJ}/({\mathrm{m}}^2·\mathrm{h}·°\mathrm{C}).$$

(7)

The surface of the foundation is considered rough and can be divided thus:

$$\beta =21.06+17.58v_a^{0.910}=21.06+17.58\times {2.09}^{0.910}=55.44 \mathrm{kJ}/({\mathrm{m}}^2·\mathrm{h}·°\mathrm{C})$$

(8)

4. Calculation Model and Boundary Conditions

4.1. Calculation Model

To ensure the accuracy of the calculation results, it is necessary to establish a calculation model that is as consistent as possible with the actual engineering situation. Considering the pouring process during the construction period, the entire pump station is divided into left and right sections, which are poured separately. The left and right sections have similar structures and are separated by transverse joints. They are poured at the same time. Therefore, in the simulation calculation analysis, the left section is taken as the research object for analysis.

Considering the efficiency of multi-field coupling simulation, this study only uses half of the symmetrical finite element model for simulating the pump station structure. The computational model mesh is shown in Figure 1, and the simulation range includes the pump station and the foundation within a certain range. The model is divided into a total of 137,209 three-dimensional hexahedral elements and 179,444 nodes. The Cartesian coordinate system used for calculation is defined thus: in addition to being parallel to the water, the flow direction is the X-axis, the dam axis is the Y-axis, and the elevation direction is the Z-axis.

4.2. Feature Points and Cross-Sections

In order to facilitate the observation of the maximum temperature and maximum tensile stress inside the concrete structure of the pump station, the maximum temperature and maximum tensile stress at each time within the time range have been calculated and concentrated into one graph each, namely the temperature envelope graph and the stress envelope graph. The characteristic section with high stress has been sliced (middle section), and the specific location of the characteristic section of the pump station is shown in Figure 2. The feature point selection model is located near the actual temperature measurement point, with the coordinate origin located at the center of the first hole on the baseplate of the left inlet channel of the pump station. The specific coordinates of the feature points are shown in

Table 2. Coordinates of the feature points (m).

Location Description	Coordinates
	X	Y	Z
Baseplate surface points	−19.55	−19.55	0.00
Internal points of the baseplate	−6.37	−7.37	−4.84

.

It should be noted that considering the efficiency of multi-field coupling simulation calculations, this paper only conducts thermo-mechanical-fatigue-damage multi-field coupling simulation calculations on the symmetrical finite element model of the pump station structure. The selection of characteristic sections is half of the overall finite element model, and the selection of feature points is consistent with the overall finite element model.

4.3. Initial and Boundary Conditions

Temperature boundary: The surface of the foundation serves as the heat dissipation surface while the bottom and sides are considered adiabatic boundaries. The symmetry plane of the thermo-mechanical-fatigue-damage multi-field coupling simulation calculation is the adiabatic boundary. Starting from the pouring date, we calculate the temperature field of the foundation 30 years ago to obtain the temperature of the foundation on the pouring date. The heat dissipation of each surface of concrete is determined according to different schemes.

Stress boundary: The bottom of the foundation is fully constrained and the surrounding areas are subjected to normal constraints. The symmetry plane of the thermo-mechanical-fatigue-damage multi-field coupling simulation is subjected to normal constraints.

4.4. Pouring Temperatures

According to the pouring plan, the pump station baseplate will be poured from the end of May to June. Considering the ambient temperature at that time and the measured warehousing temperature, 25 °C will be selected as the initial pouring temperature for the baseplate pouring for calculation and analysis.

Table 3. Actual pouring temperature of each layer of the pump station.

Serial Number	Pouring Layer	Pouring Temperature (°C)	Start Pouring Time
1	Cushion	19	May 2023
2	Baseplate	25	June 2023
3	Inlet channel layer (Elevation −6.37~−0.77 m)	26	September 2023
4	Outflow channel layer (Elevation −0.77~4.63 m)	21	October 2023
5	Mechanical and electrical layer (Elevation 4.63~9.3 m)	14	November 2023
6	Above an elevation of 9.3 m	10	December 2023

shows the pouring temperatures for each layer of the pump station.

5. Model Establishment, Dynamic Optimization, and Validation

This section is mainly based on using the power exponent function damage constitutive model to establish a concrete thermo-mechanical-fatigue-damage model. The finite element mesh model of the pump station structure is subjected to the multi-field coupled simulation calculation of thermo-mechanical-fatigue-damage. Based on actual monitoring data, various parameters such as the thermal parameters of the material (mainly adiabatic temperature rise in this article) are dynamically optimized and inverted to obtain a concrete structure prediction model. In addition, based on the calculation results of the concrete thermo-mechanical fatigue damage prediction model from the construction period to the operation period of the pump station concrete structure, a comparative analysis is conducted of the measured and calculated values of the monitoring data of the bottom plate of the key parts of the pump station to verify the rationality of the calculation results of the established thermo-mechanical-fatigue-damage model.

5.1. Model Establishment

5.1.1. Temperature Field Parameters

The occurrence of fatigue damage in concrete can have an impact on the thermal conductivity coefficient of concrete. Therefore, establishing a relationship between the thermal conductivity coefficient of concrete and fatigue damage can help make the calculation of temperature field more in line with the actual situation. According to Fourier’s law of the thermal conductivity coefficient [37], the thermal conductivity coefficient of fatigue damage variable D is considered as follows [25,26]:

$$\lambda \left(D\right)={\lambda }_0\left(1-D\right)$$

(9)

Here, λ(D) is the effective thermal conductivity coefficient of concrete, when fatigue damage D occurs, in W/(m·K); D is the fatigue damage variable, such that 0 ≤ D ≤ 1; and λ₀ is the initial thermal conductivity coefficient of concrete in W/(m·K).

Because the calculation of the thermal conductivity coefficient already takes into account the influence of fatigue damage, the above formula can be used to calculate the thermal diffusivity without considering the influence of fatigue damage.

The temperature field mainly considers the influence of damage on the thermal conductivity coefficient, and the specific values of other parameters in the temperature field can be found in Section 3.2 and Section 3.3.

5.1.2. Stress Field Parameters

The elastic modulus of concrete will continuously deteriorate with the accumulation of fatigue damage. According to the “strain equivalence assumption” of fatigue damage, the variation process of the elastic modulus of concrete with age under fatigue damage can be expressed as follows [26]:

$$E\left(\tau , D\right)=E_0\left[1-e^{-a{\tau }^b}\left(1-D\right)\right]$$

(10)

Here, D is the fatigue damage variable, $\overline{E}$ is the elastic modulus considering fatigue damage in GPa, and E is the elastic modulus of the non-destructive material in GPa.

The stress field mainly considers the influence of damage on the elastic modulus, and the specific values of other parameters of the stress field have been referred to in Section 3.2 and Section 3.3.

In summary, the multi-field coupled calculation process of thermo-mechanical fatigue damage in concrete is shown in Figure 3.

5.2. Dynamic Optimization

Considering the limited actual monitoring data and the complexity and computational efficiency of multi-field coupled multi parameter inversion, this section only inverts the adiabatic temperature rise of the pump station structure after one year of pouring. The inversion method adopts the classical genetic algorithm [38]. Due to its relatively mature basic theory and method, it will not be further elaborated here.

Based on the dynamic inversion results of actual monitoring data, the optimized fitting formula for the adiabatic temperature rise and age of pump station concrete is obtained as shown in Equation (11).

$$\theta \left(\tau \right)=56.3\tau /\left(\tau +1.69\right)$$

(11)

5.3. Model Validation

Based on the dynamic inversion results of actual monitoring data, the adiabatic temperature rise parameters were optimized, and a multi-field coupling prediction model for thermo-mechanical fatigue damage in concrete structures (hereinafter referred to as “Model 2”) was ultimately established. In order to verify the rationality of the calculation results of the established thermo-mechanical-fatigue-damage model, Figure 4, Figure 5, Figure 6 and Figure 7 show the temperature simulation calculation values of the feature points on the baseplate of the inlet channel of Model 2 and the temperature values measured by the embedded detection equipment over time. As mentioned earlier, on the one hand, considering the monitoring time limit, and on the other hand, due to the more significant changes in concrete damage during the construction period compared to the operation period, the actual measurement data of concrete during the construction period (covering temperature, displacement, damage, and stress) are presented separately for 30 days in this article while the corresponding data during the operation period are not listed separately. In contrast, the actual measurement data points during the construction period are more dense, which is more conducive to the observation and comparative analysis involving the actual measurement data and calculated values during the operation period. The coverage and time span of the actual measurement data comprise about one year. Figure 4, Figure 5, Figure 6 and Figure 7 also add the temperature simulation calculation values of the feature points on the baseplate of the inlet channel without considering fatigue damage (hereinafter referred to as “Model 1”), and comprehensively compare and analyze the above data, as follows.

As shown in Figure 4, Figure 5, Figure 6 and Figure 7, in terms of surface temperatures, considering the effect of fatigue damage, the calculated values of surface temperatures in the early stage of baseplate construction decreased compared to Model 1 (without considering fatigue damage), with the maximum differences being about 1 °C and 2 °C from the measured values, respectively. Compared to the calculated results of Model 1 (without considering fatigue damage), the maximum errors had decreased by about 1 °C and 1 °C, respectively. During operation, the calculated value of the baseplate surface temperature was also closer to the measured value compared to Model 1. In terms of internal temperature, considering the effect of fatigue damage, the calculated values of internal temperature in the early stage of baseplate construction had increased compared to Model 1 (without considering fatigue damage), with the maximum differences being about 2 °C and 1.5 °C from the measured values, respectively. Compared to the calculated results of Model 1 (without considering fatigue damage), the maximum errors had decreased by about 1 °C and 0.5 °C, respectively. During operation, the calculated temperature inside the baseplate was also closer to the measured value compared to Model 1.

Overall, considering the effect of fatigue damage, the degree of agreement between the measured and calculated values of the surface and internal temperatures of the pump station baseplate was relatively higher compared to Model 1 (without considering fatigue damage), with the maximum errors reduced by about 1 °C and 1 °C, respectively. This indicates that there are varying degrees of fatigue damage to the concrete structure of a pump station during both the construction and operation periods. Based on the previous analysis, the following conclusion has been further verified: fatigue damage can lead to a decrease in the internal thermal conductivity coefficient of concrete, manifested macroscopically as a slower rate of heat conduction from the inside to the surface; insufficient time for internal heat to diffuse to the surface, resulting in heat accumulation and increase; and the insufficient timely replenishment of internal heat to reduce the surface temperature.

In summary, fatigue damage can affect the thermal conduction process of concrete, thereby affecting the temperature distribution of concrete. At the same time, the calculation results of the established thermo-mechanical-fatigue-damage model have been verified to be reasonable and feasible. Therefore, in the simulation calculation process of concrete structure construction and operation, it is necessary to consider the impact of fatigue damage on the temperature, deformation, stress, etc. of the concrete structure, and then the simulation calculation results can more accurately predict the actual temperature, deformation, stress, and other changes.

6. Analysis of the Results

6.1. Analysis of the Influence of Fatigue Damage

The main purpose of this section is to clarify the performance response parameters of the pump station during the construction operation period, including the stress performance, deformation performance, and dynamic fatigue damage, based on the established concrete thermo-mechanical fatigue damage prediction model under the existing construction conditions and construction progress. The influence analysis of the temperature field, deformation, and stress field of the calculation results is also conducted.

Figure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15 and Figure 16 correspond to the envelope diagrams of the highest temperature, maximum displacement, maximum damage, and maximum stress in various parts of the pump station one year after the start of pouring the baseplate in May 2023 at a temperature of 25 °C (as shown in Section 4.4).

In terms of surface temperatures, as shown in Figure 8, when pouring from the bottom to the top, the peak surface temperatures of individual layers in the upper part show the same variation patterns with a change in the seasonal environmental temperature. Under the effect of fatigue damage, the overall surface temperatures of the pump station decrease relatively, and the highest surface temperatures of individual parts of the pump station decrease by 0.1 °C to 1.0 °C. The maximum temperature on the surface of the pump station baseplate is around 31 °C and the maximum temperature on the surface of the inlet channel pier wall is around 30 °C. The peak temperature of the baseplate surface of the inlet channel layer is around 33 °C. The peak temperature of the baseplate surface of the outflow channel layer is around 33 °C and the peak temperature of the pier wall surface of the outflow channel layer is around 29 °C. The peak temperature of the baseplate surface of the electromechanical layer is around 33 °C and the peak temperature of the top surface of the pump station is around 28 °C.

Overall, during the entire process from construction to operation and under the influence of fatigue damage, the surface temperature of the pump station slightly decreases by 0.1 °C to 1.0 °C. This was mainly due to the fact that the damage causes a decrease in the internal thermal conductivity coefficient of the concrete, manifested macroscopically as a slower thermal conductivity coefficient from the inside to the surface, and the surface temperature does not receive the timely replenishment of internal heat, resulting in a decrease.

In terms of internal temperature, as shown in Figure 9, considering the effect of fatigue damage, the highest temperatures inside individual parts of the pump station increase by 0.5 °C to 3 °C. Due to the large thickness of the baseplate and single-sided heat dissipation, the peak temperature inside the baseplate reaches around 58 °C, and the peak temperature inside the inlet channel pier wall reaches around 55 °C. The peak temperature inside the baseplate of the inlet channel reaches around 48 °C. The pouring temperature of the baseplate of the outlet channel is 4 °C lower than that of the pump station baseplate, and the thickness is 1 m, which is only half of the thickness of the pump station baseplate and has double-sided heat dissipation. The peak temperature is only about 48 °C while the peak temperature inside the outlet channel pier wall reaches about 49 °C. The upper part of the electromechanical layer pier wall, which is structurally similar, has a peak temperature of about 50 °C.

Overall, during the entire process from construction to operation and under the influence of fatigue damage, the internal temperatures of the pump station slightly increase by 0.5 °C to 3 °C. This is mainly due to the fact that the damage causes a decrease in the thermal conductivity coefficient inside the concrete, which manifests macroscopically as a slower thermal conductivity coefficient rate from the inside to the surface. The internal heat does not have time to diffuse to the surface, resulting in heat accumulation and an increase.

In terms of maximum deformation, as shown in Figure 10, Figure 11 and Figure 12, most parts of the pump station structure have relatively large displacement differences in the three directions of water flow, vertical water flow, and vertical direction. After considering the fatigue damage effect, the overall displacement of the pump station in the direction of water flow is positive while the displacement in the direction of vertical water flow and vertical direction is negative, that is, downward displacement. The maximum displacements of the pump station structure in the three directions of water flow, vertical water flow, and vertical direction are 0.75 cm, 0.31 cm, and −1.83 cm, respectively, located on the upstream side of the inlet channel baseplate, the left side of the baseplate in the direction of water flow, and the downstream side of the baseplate.

Overall, the vertical displacement values on the surface of the pump station are greater than those along and perpendicular to the water flow direction. The main reason is that the foundation is relatively soft, and the overall settlement during the construction period of the pump station structure is relatively large compared to the displacement caused by temperature loads. Due to the consideration of fatigue damage, the overall temperature difference between the inside and outside of the pump station increases relatively, and the maximum displacements in all directions of the pump station change by −0.21 cm to 0.23 cm relative to Model 1.

In terms of surface damage, as shown in Figure 13, during the entire process from construction to operation of the pump station structure and under fatigue damage, the maximum damage to the pump station surface mainly occurs on the baseplate surface (damage of about 0.47) and the outer surface of the side wall (damage of 0.51–0.81). It should be noted that considering an initial damage of 0.15, the larger the damage value (maximum value of 1) is, the more microcracks are generated in the concrete, the lower the structural strength is, and the lower the safety is.

As shown in Figure 14, in terms of internal damage, during the entire process from construction to operation of the pump station structure and under fatigue damage, the damage to the baseplates on both sides of the pump station is above 0.26, the damage to other areas of the baseplate is around 0.23, the damage to the inlet channel baseplate is around 0.51, the damage to the outlet channel baseplate is around 0.42, the maximum damage to the inlet channel pier wall is between 0.29 and 0.44, the maximum damage to the outlet channel pier wall is between 0.34 and 0.51, and the maximum damage to the mechanical and electrical layer pier wall is between 0.31 and 0.46.

As shown in Figure 15, in terms of surface stress, the maximum surface stress of the pump station structure during the entire process from construction to operation and under fatigue damage mainly occurs on the baseplate surface at about 1.6 MPa and the outer surface of the side walls at 1.1~1.4 MPa.

As shown in Figure 16, in terms of internal stress, during the entire process from construction to operation of the pump station structure and under fatigue damage, the stress on the baseplates on both sides of the pump station is above 1.5 MPa, the stress on other areas of the baseplate is around 1.3 MPa, the stress on the baseplate of the inlet channel is around 1.5 MPa, the stress on the baseplate of the outlet channel is around 1.6 MPa, the maximum stress on the inlet channel pier wall is between 2.2 MPa and 2.7 MPa, the maximum stress on the outlet channel pier wall is between 1.6 MPa and 1.9 MPa, and the maximum stress on the mechanical and electrical layer pier wall is between 1.8 MPa and 2.2 MPa.

6.2. The Variation Law of Characteristic Parameters over Time

The main purpose of this section is to analyze the calculation results based on the established concrete thermo-mechanical fatigue damage prediction model and clarify the temperature, deformation, fatigue damage, and stress development and variation laws of typical parts of the pump station from the construction period to the operation period.

6.2.1. Time Dependent Variations of Characteristic Parameters

Figure 17, Figure 18, Figure 19, Figure 20, Figure 21, Figure 22, Figure 23, Figure 24, Figure 25 and Figure 26 show the temperature, displacement, stress history, and temperature difference changes of the feature points on the baseplate of the inlet channel. The surface feature points are located on the surface of the baseplate and the internal feature points are located at the center elevation of the baseplate. The specific coordinate positions are shown in Section 4.2. It should be noted that the temperature simulation calculation values and actual monitoring values have been analyzed in Section 5.2, and no comparative analysis will be conducted in this section. The focus will be on analyzing the temperature, displacement, fatigue damage, and stress changes over time in typical parts of the pump station.

As shown in Figure 17 and Figure 18, in terms of surface temperature, the surface points reach a peak temperature of 30.67 °C within 2 days after pouring, displaying a decrease of about 1.0 °C compared to Model 1. This is mainly due to the consideration of fatigue damage. The internal thermal conductivity coefficient of the bottom concrete will decrease, which is manifested macroscopically as a slower heat conduction rate from the inside of the bottom to the surface, and the surface temperature will not receive the timely replenishment of internal heat, resulting in a decrease. Afterwards, due to the heat dissipation effect of the bottom surface, the overall temperature of the bottom concrete decreases to near the ambient temperature with the decrease in temperature. During operation, due to the slow development of the elastic modulus of the bottom concrete and its high strength, the fatigue damage caused by changes in ambient temperature to the bottom concrete is relatively small. However, the temperature of the bottom concrete changes periodically with changes in ambient temperature during operation.

As shown in Figure 17 and Figure 18, in terms of internal temperature, considering the effect of fatigue damage, the peak temperature inside the bottom plate reaches 58.6 °C about 3 days after pouring, which has increased by about 3 °C compared to Model 1. This is mainly due to the decrease in thermal conductivity coefficient inside the bottom plate concrete after considering fatigue damage, which is manifested macroscopically as a slower heat conduction rate from the inside of the bottom plate to the surface, and the internal heat does not have time to diffuse to the surface, resulting in heat accumulation and increase. Afterwards, due to the heat dissipation effect of the top surface of the bottom plate, the temperature of the bottom plate gradually decreases. By February 2024, the internal temperature of the bottom plate has decreased to about 6 °C, and the temperature of the bottom plate concrete has also shown periodic changes with the ambient temperature during operation.

As shown in Figure 19 and Figure 20, in terms of temperature difference between the inside and outside, about 3 days after pouring, the maximum temperature difference between the inside and outside of the bottom plate reaches 30.5 °C, which has increased by about 3 °C compared to Model 1. Afterwards, as the bottom plate surface dissipates heat, the temperature difference between the inside and outside gradually decreases. By February 2024, the temperature difference between the inside and outside of the bottom plate has decreased to within 5 °C, and the temperature difference between the inside and outside of the concrete of the bottom plate has also shown periodic changes with the ambient temperature during operation.

In terms of maximum deformation, as shown in Figure 21 and Figure 22, there is not much difference between the displacement of the baseplate and the surface displacement with an increasing time. After pouring, the displacement of the baseplate in the direction of water flow first decreases with an increasing time and then increases to around 0.48 cm. The displacement in the direction of vertical water flow does not change significantly with the increase in time, with a maximum displacement of about 0.11 cm. The vertical displacement initially does not change significantly with the increase in time, but later, under the influence of the gravity of the upper pouring layer, the displacement gradually decreases to around −1.74 cm and remains basically unchanged. During the operation period, the maximum displacement inside the concrete of the baseplate is periodically affected by the ambient temperature.

After considering the effect of fatigue damage, the peak surface temperature of the baseplate decreases by about 1.0 °C, the peak internal temperature increases by about 3 °C, and the temperature difference between the inside and outside increases by about 3 °C. The overall maximum displacements of the baseplate in all directions relative to Model 1 vary by −0.16 cm to 0.07 cm. Due to the slow development and high strength of the elastic modulus of the bottom concrete during operation, the fatigue damage caused by changes in the ambient temperature to the bottom concrete is relatively small. However, the maximum displacement of the bottom concrete varies periodically with changes in the ambient temperature during operation.

As shown in Figure 23 and Figure 24, in terms of surface damage, due to the large temperature difference between the inside and outside (27 °C), the surface damage of the baseplate rapidly increases to around 0.28 within 3 days of pouring. During the operation period, due to the slow development of the elastic modulus of the baseplate concrete and its high strength, the fatigue damage caused by changes in the ambient temperature to the baseplate concrete is relatively small, and the growth of damage during the operation period is slow until it remains unchanged. In terms of internal damage, the internal damage of the baseplate also rapidly increases to around 0.23 within 3 days of pouring. During the same operation period, the internal damage of the baseplate grows slowly and remains unchanged, but the overall surface damage of the baseplate is slightly reduced. After considering the effect of fatigue damage, the early surface damage of the baseplate increases by about 0.15 relative to Model 1 (initial damage of 0.15), and the internal damage of the baseplate increases by about 0.10 (initial damage of 0.15). During operation, the growth of baseplate damage slows down and remains unchanged.

As shown in Figure 25 and Figure 26, in terms of surface stress, due to the large temperature difference between the inside and outside (28 °C), the surface of the baseplate exceeds the allowable tensile strength of the corresponding age concrete after 2 days of pouring (about 2 days of age), with a tensile stress of 1.53 MPa, and the risk of concrete cracking is extremely high. As the overall temperature of the baseplate decreases in the later stage, the temperature difference between the inside and outside decreases and the tensile stress on the surface of the baseplate gradually decreases. During operation, due to the slow development of the elastic modulus of the baseplate concrete and its high strength, the fatigue damage caused by changes in the ambient temperature to the concrete is relatively small, and the impact of damage on stress is also relatively small. During operation, the baseplate surface will experience stress fluctuations with a range of −1.4 MPa to −0.5 MPa due to seasonal changes.

In terms of internal stress, the early temperature hydration heat causes the internal compression of the baseplate, and as the temperature increases, the compressive stress gradually increases. After the internal temperature of the baseplate reaches its peak and enters the cooling period, the internal stress begins to gradually transform from compressive stress to tensile stress. During the wintering process, the maximum tensile stress reaches around 1.7 MPa (around February 2024), which is lower than the tensile strength. Similarly, due to seasonal changes during operation, stress fluctuations ranging from 1.2 MPa to 1.7 MPa will occur inside the baseplate.

Overall, considering the effect of fatigue damage, the temperature difference between the inside and outside of the baseplate increases, leading to stress growth. However, damage can also cause a decrease in the elastic modulus of the baseplate, resulting in a decrease in stress. Under the combined effect of the two, the specific manifestation is that the early surface tensile stress of the baseplate increases by about 0.1 MPa relative to Model 1 and the internal tensile stress of the baseplate decreases by about 1.0 MPa. During the overwintering period, the surface tensile stress increases by about 0.1 MPa while the internal tensile stress decreases by about 1.5 MPa. During the operation period, due to seasonal changes, stress fluctuations with amplitude ranges of −1.4 MPa to −0.5 MPa and 1.2 MPa to 1.7 MPa will occur on the surface and inside of the baseplate, respectively. The above fatigue damage will cause more microcracks in the baseplate structure, which is extremely detrimental to the safety of the baseplate structure during operation.

6.2.2. Peak Values of Various Parts

Table 4. Peak temperatures, maximum deformations, maximum damage, and stresses at the feature points of pump station.

Feature Location	Feature Point	Temperature Peak/°C	Maximum Displacement/cm			Maximum Damage	Maximum Principal Stress/MPa
			X	Y	Z
Baseplate	Surface	30.67	0.48	0.11	−1.74	0.29	1.53
	Internal	58.6				0.23	1.71
Inlet channel pier wall	Surface	29.79	0.25	0.06	−1.74	0.44	1.21
	Internal	55.57				0.23	2.63
Inlet channel baseplate	Surface	32.53	0.72	0.15	−1.41	0.44	0.8
	Internal	47.89				0.51	2.09
Outlet channel pier wall	Surface	32.51	0.38	0.16	−1.78	0.31	0.61
	Internal	47.81				0.45	1.41
Outlet channel baseplate	Surface	30.68	0.27	0.13	−1.4	0.81	1.12
	Internal	51.73				0.51	2.21
Mechanical and electrical layer pier wall	Surface	34.86	0.37	0.05	−0.79	0.31	1.09
	Internal	49.97				0.38	1.29

summarizes the maximum stresses, maximum displacements, and peak temperatures of feature points at different locations of the pump station. Based on the simulation results of the fatigue damage model considering the actual pouring layers of the pump station, the tensile stresses of the feature points of the pump station baseplate poured in May and the pier wall poured in September are relatively reduced. However, the early stress of the pier wall will still exceed the allowable tensile strength of the concrete, and even the tensile strength, and the risk of cracking is still high, mainly manifested as the easy occurrence of surface cracks in the early stage of the pier wall.

6.3. Key Control Structural Parameters, Warning Indicators, and Thresholds

Based on the multi-field coupling numerical simulation prediction and analysis results of thermo-mechanical fatigue damage in the entire process of pump station structure construction operation, the performance response parameters of the structure during operation, such as stress performance, deformation performance, and dynamic fatigue, have been obtained. Combined with the comparison of the results between the calculated values in Section 5.3 and the response characteristics of the solid structure (monitoring values), the following key control structural parameters for the long-term safe operation of the structure have been proposed (mainly the peak characteristic temperatures of key parts, the temperature difference between the inside and outside, the maximum deformation, the maximum damage, and the maximum tensile stress), together with the warning indicators (mainly the peak characteristic temperatures of key parts, the temperature difference between the inside and outside, the maximum deformation, and the maximum tensile stress) and the thresholds (mainly those corresponding to the peak characteristic temperatures of key parts, the temperature difference between the inside and outside, the maximum deformation, and the maximum tensile stress). As shown in

Table 5. Key control structure parameters, warning indicators, and thresholds for long-term safe operation of pump station structures.

Key Control Structural Parameters	Temperature Peak	Temperature Difference Between Inside and Outside	Maximum Displacement	Maximum Tensile Stress		Maximum Damage
Warning Indicators	Temperature peak	Temperature difference between inside and outside	Maximum displacement	Maximum tensile stress		/
Thresholds	≤55 °C	≤26 °C	≤1.7 cm	Early stage of construction	≤1.5 MPa	0.4
				Operation period	≤2.9 MPa

, the ultimate goal is to ensure the long-term safe and efficient operation of the structure.

This paper is based on the power exponent function damage constitutive model and has established a concrete thermo-mechanical-fatigue-damage model. It has focused on analyzing and exploring the mechanical behavior and damage evolution process in concrete structures under temperature changes from a three-dimensional perspective and analyzed the influences of damage on thermal diffusivity and the thermal conductivity coefficient. However, there has been a lack of research in simulating concrete crack propagation, and it is necessary to carry out relevant research in this area in the next step.

7. Conclusions

According to the actual construction pouring plan of the pump station concrete, and based on the above analysis results, it can be seen that the established thermo-mechanical-fatigue-damage model has calculated the results that are closer to the measured values and have higher prediction accuracy. The performance parameters of the pump station structure, such as stress performance, deformation performance, and dynamic fatigue damage, have been obtained for the construction operation period. The main conclusions are drawn as follows.

(1)

Fatigue damage can lead to a decrease in the internal thermal diffusivity of concrete, manifested macroscopically as a slower rate of heat conduction from the inside to the surface; insufficient time for internal heat to diffuse to the surface, resulting in heat accumulation and increase; and the insufficient timely replenishment of internal heat to reduce the surface temperature. That is, the peak surface temperature of the pump station structure decreases by about 1.0 °C, the peak internal temperature increases by about 3 °C, and the temperature difference between the inside and outside increases by about 3 °C.

(2)

After considering the effect of fatigue damage, the temperature of the pump station baseplate during the wintering period will still drop to around 5 °C and the tensile stress of the baseplate will rapidly increase with a decrease in the temperature. Although the temperature difference between the inside and outside is relatively high, the internal tensile stress of the baseplate during operation will decrease by about 1.5 MPa. The main reason is that the damage will cause a decrease in the elastic modulus of the concrete, resulting in a decrease in stress. However, the relative temperature difference between the inside and outside will lead to a greater increase in stress, which will be manifested as a decrease in the overall stress of the baseplate. Fatigue damage will cause more microcracks in the pump station structure, thereby reducing the strength of the pump station structure. This is extremely unfavorable for the safety of the pump station structure during operation.

(3)

This paper proposes warning indicators and thresholds for key parts of the pump station, including a temperature peak threshold of 55 °C, an internal and external temperature difference threshold of 26 °C, a maximum deformation threshold of 1.7 cm, a maximum damage threshold of 0.4, and thresholds corresponding to maximum tensile stress during early construction and operation periods of 1.5 MPa and 2.9 MPa, respectively, which can provide reference for similar projects.