A method for quantitatively evaluating dam-foundation dynamic interaction effect

Abstract

A kind of dam-foundation dynamic interaction effect quantitative evaluation method belongs to the field of water conservancy engineering seismic safety analysis. The steps are as follows: first, the finite element analysis model of foundation free field and dam-foundation coupling is established respectively, and the dynamic time history analysis is carried out to obtain the seismic response results; second, the dynamic response data of each characteristic point of the two models is obtained, the free field influence factor components of all characteristic points are calculated, and the single-index free field influence factor is obtained; if multiple dynamic response evaluation indexes need to be selected for comprehensive evaluation in actual engineering analysis, multiple dynamic response evaluation indexes are selected to calculate the comprehensive free field influence factor; finally, the single-index free field influence factor or the comprehensive free field influence factor is compared with the threshold value, and the significant degree of dam-foundation dynamic interaction effect is quantitatively determined. The present application is simple in modeling, high in calculation efficiency, and can provide direct and quantitative decision basis for the selection of seismic input method in high earth-rock dam seismic analysis.

Description

Technical Field

[0001] This invention belongs to the field of seismic safety analysis of water conservancy projects, and relates to a quantitative evaluation method for the dynamic interaction effect between the dam body and the foundation, specifically a quantitative evaluation method for the dynamic interaction effect between the dam body and the foundation of high earth-rock dams. Background Technology

[0002] With the continuous expansion of the global construction scale of high earth-rock dams (dam height greater than 200m) and the continuous improvement of their seismic fortification standards, the dynamic interaction between the dam body and the foundation has become a key factor affecting the seismic response of dams. Accurate assessment of this effect is crucial for ensuring the seismic safety of major water conservancy projects. However, in current engineering practice, a unified and quantitative technical standard has not yet been formed for the selection of seismic motion input methods.

[0003] Currently, the mainstream seismic motion input methods in the seismic analysis of high earth-rock dams fall into two categories: one is the vibration input method based on the rigid foundation assumption. This method is simple to model and computationally efficient, and is widely used in preliminary engineering design and rapid scheme comparison. For example, Tian Guichuan et al. (2015) used this method to calculate the key response indicators of the dam body in their paper "Seismic Response and Stability Analysis of Earth-Rock Dams Based on Dynamic Finite Element Method," providing a preliminary seismic design basis for the project. However, this method directly applies the seismic motion to the bottom of the truncated dam foundation, failing to simulate the propagation, reflection, and energy radiation (i.e., radiation damping) of seismic waves in the actual infinite domain foundation, essentially ignoring the dynamic coupling of the dam body-foundation system. For large-scale high earth-rock dams with significant material nonlinearity, this simplification may lead to significant deviations in the calculation results, causing distortion in the seismic capacity assessment, thereby triggering safety hazards or resulting in overly conservative design and economic losses.

[0004] The second type of method is the wave input method, which considers the dynamic interaction effect between the dam body and the foundation. This type of method can reasonably simulate the propagation characteristics and radiation damping effect of seismic waves in the foundation. For example, Chinese invention patent (application number: 201710217997.X) introduces artificial boundaries to simulate infinite-domain foundation conditions, providing a more accurate boundary description for structural dynamic response analysis. However, such methods generally suffer from complex modeling and high computational costs, making them difficult to widely apply in engineering feasibility studies, preliminary design, or the selection of numerous alternatives. Therefore, in engineering practice, there is an urgent need for a method that can quickly and quantitatively assess the strength of the dynamic interaction effect between the dam body and the foundation, so as to scientifically guide whether it is necessary to use the more refined but computationally expensive wave input method in seismic analysis, thereby achieving a balance between technical rationality and economy while ensuring engineering safety.

[0005] In summary, while the advantages and disadvantages of the two types of seismic motion input methods mentioned above are widely recognized in both academic research and engineering practice, there is still a lack of objective and quantitative decision-making basis for how to scientifically select the appropriate method under specific engineering conditions. Engineers often rely on experience to make judgments, making it difficult to achieve the optimal balance between safety and economy. Therefore, engineering practice urgently needs a method that can quickly and quantitatively determine the strength of the dynamic interaction effect between the dam body and the foundation, providing a clear scientific basis for whether to use the wave input method in seismic analysis, thereby optimizing the technical approach and improving the economic efficiency of the project while ensuring its seismic safety. Summary of the Invention

[0006] This invention addresses the lack of a simple and quantifiable method for evaluating the dynamic interaction effects between the dam body and the foundation in existing technologies. It proposes a quantitative evaluation method for the dynamic interaction effects between the dam body and the foundation. This method achieves quantitative analysis of the dam body's seismic response through numerical simulation and constructs an evaluation index system with the "free field influence factor" as its core, thereby comprehensively and quantitatively evaluating the intensity of the dynamic interaction between the dam body and the foundation. This invention can efficiently and accurately assess the importance of dynamic interaction, thus providing a direct quantitative basis for decision-making regarding whether a more precise wave input method should be adopted in engineering projects.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] A quantitative evaluation method for the dynamic interaction effect between the dam body and the foundation includes the following steps:

[0009] The first step is to establish a free-field finite element analysis model of the foundation and a coupled finite element analysis model of the dam body and foundation based on the engineering data of the target earth-rock dam.

[0010] During the construction of the finite element analysis model of the dam-foundation coupling, it is required that the foundation intercept range of the dam-foundation coupling system be no less than 1.5 times the dam height in both the depth and horizontal directions outside the dam area.

[0011] The second step involves selecting constitutive models for the dam body and foundation, and employing a seismic input method that considers the dynamic interaction between the dam body and foundation. Dynamic time history analyses are then performed on the foundation free-field finite element analysis model and the dam body-foundation coupled finite element analysis model established in the first step, respectively, to obtain the seismic response results of the foundation free-field finite element analysis model and the dam body-foundation coupled finite element analysis model.

[0012] The third step is to identify the interface and characteristic points of the dam foundation and obtain dynamic response data.

[0013] The physical boundary region where the dam body and foundation are in direct contact and share forces is defined as the dam-foundation interface, and the finite element mesh nodes arranged on the dam-foundation interface are defined as feature points. Each finite element mesh node has unique spatial coordinates. Based on this, the dynamic response data of the following two feature points are extracted: first, the feature points at the dam-foundation interface in the coupled dam-foundation finite element analysis model; second, the feature points at corresponding locations in the foundation free-field finite element analysis model with the same spatial coordinates as the nodes in the coupled dam-foundation finite element analysis model. Thus, the dynamic response data of each corresponding feature point in both models are obtained.

[0014] Fourth, based on the dynamic response data of the characteristic points of the dam-foundation coupling finite element analysis model and the characteristic points of the foundation free field finite element analysis model in the third step, the free field influence factor component F of characteristic point i and dynamic response evaluation index k is calculated using the following formula. i,k :

[0015] (1)

[0016] Where i represents the index of the feature point; Let i be the dynamic response value of feature point i in the finite element analysis model of dam-foundation coupling. denoted as the dynamic response value of feature point i in the finite element analysis model of the foundation free field; k is any one of the dynamic response evaluation indicators among acceleration, velocity, displacement, stress, strain, excess pore water pressure, and excess pore water pressure ratio.

[0017] Fifth, based on the method in step four, calculate the free field influence factor components of all characteristic points on the dam foundation interface, and then use formula (2) to calculate the single index free field influence factor corresponding to the dynamic response evaluation index k. :

[0018] (2)

[0019] in, The length, area, or volume represented by feature point i is determined based on the mesh length, area, or volume of the finite element analysis model; n represents the number of feature points at the dam foundation interface.

[0020] The above is the calculation method for the free field influence factor corresponding to a single dynamic response evaluation index. If multiple dynamic response evaluation indexes need to be selected for comprehensive evaluation in actual engineering analysis, then proceed to step six.

[0021] Step 6: When selecting m dynamic response evaluation indicators simultaneously, calculate the single-index free-field influence factor corresponding to dynamic response evaluation indicator k according to steps 4 and 5 respectively. kThere are m factors in total. Either formula (3) or formula (4) can be chosen to calculate the comprehensive free field influence factor. ;

[0022] (3)

[0023] (4)

[0024] Where m represents the number of selected dynamic response evaluation indicators; F 加速度 The single-index free-field influence factor representing acceleration; F 速度 The single-index free-field influence factor representing velocity; F 应力 The single-index free-field influence factor representing stress.

[0025] Step 7: Calculate the single-index free-field influence factor. Or a comprehensive free field influence factor The significance of the dam-foundation dynamic interaction effect is quantitatively determined by comparing it with a preset threshold. The preset threshold includes at least a first threshold α and a second threshold β, where α < β. The first threshold α is recommended to be 3% to 7%, and the second threshold β is recommended to be 10% to 15%. The specific comparison rules are as follows:

[0026] (1) If If the dynamic interaction between the dam and the foundation is weak, then the traditional vibration input method should be used for seismic analysis.

[0027] (2) If If the dam-foundation interaction effect is deemed to be moderate, the fluctuation input method should be adopted for projects with a seismic intensity exceeding VII.

[0028] (3) If If the dam-foundation interaction effect is strong, then the wave input method that can take into account the dynamic interaction between the dam body and the foundation should be used for seismic analysis.

[0029] Furthermore, the method described is applicable to both two-dimensional and three-dimensional analysis.

[0030] Furthermore, dynamic time history analysis is applicable to various constitutive models such as equivalent linear analysis and elastoplastic analysis.

[0031] Furthermore, the method described is applicable to earth-rock dams on bedrock and earth-rock dams on overburden foundations, and its basic principles can also be extended to the quantitative assessment of the dynamic interaction effects between gravity dams, nuclear islands, high-rise buildings, and other structures and foundations.

[0032] The beneficial effects of this invention are as follows:

[0033] (1) This invention proposes the core quantitative indicator of "free field influence factor" to achieve a direct and quantitative evaluation of the strength of the dynamic interaction effect between high earth-rock dam and foundation.

[0034] (2) The method of the present invention is highly versatile and can be applied not only to earth-rock dams on rocky foundations, but also to various buildings such as earth-rock dams, gravity dams, nuclear islands, and high-rise buildings on overburden foundations.

[0035] (3) By setting a clear discrimination threshold, the method of the present invention can provide a direct basis for the selection of seismic motion input method for seismic analysis of important structures such as earth-rock dams, thereby improving the accuracy of seismic analysis and evaluation of the project. Attached Figure Description

[0036] Figure 1 This is a flowchart of the quantitative evaluation method of the present invention;

[0037] Figure 2 The free-field foundation finite element model established in the case of this invention;

[0038] Figure 3 The finite element model of the dam-foundation coupled system established in the case of this invention;

[0039] Figure 4 This is a schematic diagram of the distribution of feature points on the dam foundation interface in this invention. Detailed Implementation

[0040] The present invention will be further described below with reference to specific embodiments.

[0041] This embodiment provides a quantitative evaluation method for the dynamic interaction effect between the dam body and foundation of a high earth-rock dam. The specific implementation process includes the following steps:

[0042] The first step, based on the engineering data of the target earth-rock dam, confirms that the dam's height L1 = H, where H is 200m, the dam crest width is 14m, and the upstream and downstream slope ratios are both 1:2. Based on this, a free-field finite element analysis model of the foundation and a finite element analysis model of the dam-foundation coupling are established. The foundation intercept range of the dam-foundation coupling system extends beyond the dam's location to a depth and a horizontal distance equal to twice the dam's height, respectively, and is designated as L2 = 2H and L3 = 2H.

[0043] In the second step, the Duncan-Chang EB model was used for the dam fill material in the static analysis, and an equivalent linear model was used for the dam body in the seismic response analysis. The linear elastic model was used for the foundation in both static and dynamic calculations. Using a seismic motion input method that considers the dynamic interaction between the dam body and the foundation, dynamic time-history analyses were performed on the foundation free-field finite element analysis model and the dam body-foundation coupled finite element analysis model established in the first step, respectively, to obtain the seismic response results of the foundation free-field finite element analysis model and the dam body-foundation coupled finite element analysis model.

[0044] The third step is to identify the interface and characteristic points of the dam foundation and obtain dynamic response data.

[0045] The physical boundary region where the dam body and foundation are in direct contact and share forces is defined as the dam-foundation interface, and the finite element mesh nodes arranged on the dam-foundation interface are defined as feature points. Each finite element mesh node has unique spatial coordinates. Dynamic response data are extracted from two types of feature points: first, the feature points at the dam-foundation interface in the coupled dam-foundation finite element analysis model; and second, the feature points at corresponding locations in the foundation free-field finite element analysis model with the same spatial coordinates as the nodes in the coupled dam-foundation finite element analysis model. Thus, dynamic response data for each corresponding feature point in both models are obtained.

[0046] Fourth, based on the dynamic response data of the characteristic points of the dam-foundation coupling finite element analysis model and the characteristic points of the foundation free field finite element analysis model in the third step, the free field influence factor components F of characteristic point i, maximum horizontal acceleration, and maximum horizontal velocity are calculated using the following formula. i,最大水平加速度 F i,最大水平加速度 :

[0047] (1)

[0048] in, Let i be the dynamic response value of feature point i in the finite element analysis model of dam-foundation coupling. denoted as the dynamic response value of feature point i in the finite element analysis model of the foundation free field; k is any one of the dynamic response evaluation indicators among acceleration, velocity, displacement, stress, strain, excess pore water pressure, and excess pore water pressure ratio.

[0049] Fifth, following the method described in step four, calculate the free-field influence factor components of all characteristic points on the dam foundation interface, and then use the following formula to calculate the single-index free-field influence factor F of acceleration and velocity. 最大水平加速度 F 最大水平速度 :

[0050] (2)

[0051] in, The length, area, or volume represented by feature point i is determined based on the mesh length, area, or volume of the finite element analysis model; n represents the number of feature points at the dam foundation interface.

[0052] The calculation result is: F 最大水平加速度 =30.1%, F 最大水平速度 =26.9%.

[0053] Step 6: Calculate the comprehensive free field influence factor using formula (3). ;

[0054] (3)

[0055] Where m represents the number of selected dynamic response evaluation indicators; F 最大水平加速度 The single-index free-field influence factor representing the maximum horizontal acceleration; F 最大水平速度 A single-index free-field influence factor representing the maximum horizontal velocity;

[0056] The calculation result is: =28.5%.

[0057] Step 7: Calculate the comprehensive free-field influence factor. The comparison is made with preset thresholds, which include at least a first threshold α and a second threshold β, where α < β; the first threshold α is recommended to be 3% to 7%, and the second threshold β is recommended to be 10% to 15%; the specific evaluation rules are as follows:

[0058] (1) If If the dynamic interaction between the dam and the foundation is weak, then the traditional vibration input method should be used for seismic analysis.

[0059] (2) If If the dam-foundation interaction effect is deemed to be moderate, the fluctuation input method should be adopted for projects with a seismic intensity exceeding VII.

[0060] (3) If If the dam-foundation interaction effect is strong, then the wave input method that can take into account the dynamic interaction between the dam body and the foundation should be used for seismic analysis.

[0061] The calculation results of this embodiment =28.5% was compared with the threshold, and it was determined that the dynamic interaction between the dam body and the foundation of the 200m high earth-rock dam was a "strong effect". Therefore, a wave input method that can take into account the dynamic interaction between the dam body and the foundation must be used for seismic analysis.

[0062] The evaluation results of this case study indicate that the presence of the dam increases the average seismic response of the dam foundation by approximately 28.5%, and the interaction effect cannot be ignored. In subsequent in-depth seismic safety analysis and detailed design, it is recommended to adopt a wave input method that can reasonably account for the damping effect of seismic wave radiation to ensure the accuracy of seismic response prediction and the reliability of engineering assessment, and to avoid errors that may arise from using a simplified rigid foundation input method.

[0063] The above-described embodiments are merely examples of implementation methods of the present invention, but should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements are all within the scope of protection of the present invention.

Claims

1. A quantitative evaluation method for the dynamic interaction effect between dam body and foundation, characterized in that, The quantitative evaluation method includes the following steps: The first step is to establish a free-field finite element analysis model of the foundation and a coupled finite element analysis model of the dam body and foundation based on the engineering data of the target earth-rock dam. The second step is to select constitutive models for the dam body and foundation, and use the seismic input method that considers the dynamic interaction between the dam body and the foundation to perform dynamic time history analysis on the foundation free field finite element analysis model and the dam body-foundation coupled finite element analysis model established in the first step, and obtain the seismic response results of the foundation free field finite element analysis model and the dam body-foundation coupled finite element analysis model. The third step is to identify the interface and characteristic points of the dam foundation and obtain dynamic response data. The physical boundary region where the dam body and foundation are in direct contact and share forces is defined as the dam-foundation interface. Finite element mesh nodes arranged on the dam-foundation interface are defined as feature points, and each finite element mesh node has unique spatial coordinates. Dynamic response data are extracted from the following two feature points: first, the feature points at the dam-foundation interface in the coupled dam-foundation finite element analysis model; second, the feature points at corresponding locations in the foundation free-field finite element analysis model whose spatial coordinates are identical to those of the nodes in the coupled dam-foundation finite element analysis model. Thus, dynamic response data for each corresponding feature point in both models is obtained. The fourth step involves calculating the free-field influence factor F of characteristic point i and dynamic response evaluation index k based on the dynamic response data obtained in the third step. i,k ; The fifth step is to calculate the free-field influence factor components of all characteristic points on the dam foundation interface, and to calculate the single-index free-field influence factor corresponding to the dynamic response evaluation index k. ; The above is the calculation method for the free field influence factor corresponding to a single dynamic response evaluation index. If multiple dynamic response evaluation indexes need to be selected for comprehensive evaluation in actual engineering analysis, then proceed to step six. Step 6: When selecting m dynamic response evaluation indicators simultaneously, calculate the single-index free-field influence factor corresponding to dynamic response evaluation indicator k according to steps 4 and 5 respectively. k There are m elements in total. Calculate the comprehensive free field influence factor. ; Step 7: Calculate the single-index free-field influence factor. Or a comprehensive free field influence factor The results are compared with a preset threshold for evaluation and analysis.

2. The quantitative evaluation method for the dynamic interaction effect between the dam body and the foundation according to claim 1, characterized in that, In the first step, during the construction of the finite element analysis model of the dam-foundation coupling, it is required that the foundation intercept range of the dam-foundation coupling system be no less than 1.5 times the dam height in both the depth and horizontal directions outside the area where the dam is located.

3. The quantitative evaluation method for the dynamic interaction effect between the dam body and the foundation according to claim 1, characterized in that, The dynamic time history analysis in the second step is applicable to constitutive models for equivalent linear analysis and elastoplastic analysis.

4. The method for quantitatively evaluating the dynamic interaction effect between the dam body and the foundation according to claim 1, characterized in that, In the fourth step, the free field influence factor component F of characteristic point i and dynamic response evaluation index k is calculated using formula (1). i,k ; (1) in, Let i be the dynamic response value of feature point i in the finite element analysis model of dam-foundation coupling. denoted as the dynamic response value of feature point i in the finite element analysis model of the foundation free field; k is any one of the dynamic response evaluation indicators among acceleration, velocity, displacement, stress, strain, excess pore water pressure, and excess pore water pressure ratio.

5. The quantitative evaluation method for the dynamic interaction effect between the dam body and the foundation according to claim 1, characterized in that, In the fifth step, the single-index free field influence factor corresponding to the dynamic response evaluation index k is calculated using formula (2). : (2) in, The length, area, or volume represented by feature point i is determined based on the mesh length, area, or volume of the finite element analysis model; n represents the number of feature points at the dam foundation interface.

6. The quantitative evaluation method for the dynamic interaction effect between the dam body and the foundation according to claim 1, characterized in that, In the sixth step, either formula (3) or formula (4) can be selected to calculate the comprehensive free field influence factor. ; (3) (4) Where m represents the number of selected dynamic response evaluation indicators; F 加速度 The single-index free-field influence factor representing acceleration; F 速度 The single-index free-field influence factor representing velocity; F 应力 The single-index free-field influence factor representing stress.

7. The quantitative evaluation method for the dynamic interaction effect between the dam body and the foundation according to claim 1, characterized in that, In the seventh step, the preset thresholds include a first threshold α and a second threshold β, where α < β; the comparison rule is: (1) If If the dam-foundation dynamic interaction effect is weak, then the traditional vibration input method should be used for seismic analysis. (2) If If the dam-foundation interaction effect is deemed to be moderate, the fluctuation input method should be adopted for projects with a seismic intensity exceeding VII. (3) If If the dam-foundation interaction effect is strong, then the wave input method that can consider the dynamic interaction between the dam body and the foundation should be used for seismic analysis.

8. The quantitative evaluation method for the dynamic interaction effect between the dam body and the foundation according to claim 7, characterized in that, In the seventh step, the first threshold α is set to 3%~7%, and the second threshold β is set to 10%~15%.

9. The quantitative evaluation method for the dynamic interaction effect between the dam body and the foundation according to claim 1, characterized in that, The quantitative evaluation method described herein is applicable to both two-dimensional and three-dimensional analysis.

10. The method for quantitatively evaluating the dynamic interaction effect between the dam body and the foundation according to claim 1, characterized in that, The quantitative evaluation method described herein is applicable to earth-rock dams on bedrock and earth-rock dams on overburden foundations, and can be extended to the quantitative evaluation of the dynamic interaction effects of gravity dams, nuclear islands, and high-rise buildings and foundations.

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