Method and system for analyzing active earth pressure of bridge abutment earthquake

Abstract

The invention discloses a method and a system for analyzing active earth pressure of an abutment earthquake. Comprising the steps that firstly, a bridge abutment horizontal acceleration distribution calculation model can be established based on a three-section type design acceleration response spectrum specified in an existing specification; then, the characteristic angular frequency of a bridge abutment to be analyzed can be obtained, the characteristic angular frequency is substituted into the bridge abutment horizontal acceleration distribution calculation model, and therefore various sine acceleration time-history component coefficients of the bridge abutment under the characteristic angular frequency are obtained through calculation; and finally, in combination with all sine acceleration time-history component coefficients and various structural parameters of the to-be-analyzed bridge abutment, calculating to obtain earthquake active soil pressure parameters of the bridge abutment through the constructed bridge abutment earthquake active soil pressure analysis model. The frequency domain characteristics of the seismic acceleration time history covered by the design response spectrum specified in the bridge aseismic design specification are fully considered, so that the accuracy of the analysis result of the bridge abutment seismic active earth pressure is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of computer-aided architectural design, and particularly relates to an analytical method and system for the seismic active earth pressure of abutments. Background Art

[0002] Existing analytical calculation methods for seismic active earth pressure are all based on the Coulomb earth pressure model, and a concentrated force or distributed force representing seismic inertial force is introduced based on the equilibrium equation established by the Coulomb model. Among them, the pseudo-static method assumes that the backfill of the abutment is a rigid body with infinite shear modulus, does not consider the time-history characteristics of earthquakes, and cannot deduce the distribution of seismic active earth pressure intensity along the back of the abutment, with defects that cannot be ignored. The horizontal layer analysis method still has limitations in considering the time-history characteristics of seismic motion and its propagation characteristics in the fill. The pseudo-dynamic method approximates the frequency-domain characteristics of seismic motion by using a sine wave represented by the dominant frequency, but it is still difficult to fully reflect the complexity and diversity of seismic motion time-history and propagation in engineering practice. Summary of the Invention

[0003] Aiming at the deficiencies of the existing technology, the present invention proposes an analytical method and system for the seismic active earth pressure of abutments, which fully considers the frequency-domain characteristics of the seismic acceleration time-history covered by the design response spectrum and improves the accuracy of the analytical results. The specific technical solutions are as follows: In the first aspect, an analytical method for the seismic active earth pressure of an abutment is provided. In the first feasible implementation manner of the first aspect, it includes: Establishing a calculation model for the horizontal acceleration distribution of the abutment based on a specified design acceleration response spectrum; Obtaining the characteristic angular frequency of the abutment, and calculating the sine acceleration time-history component coefficient corresponding to the abutment through the calculation model for the horizontal acceleration distribution of the abutment; Obtaining the structural parameters of the abutment, and combining with the sine acceleration time-history component coefficient, calculating the corresponding seismic active earth pressure parameters of the abutment through the established analytical model for the seismic active earth pressure of the abutment.

[0004] Combined with the first feasible implementation manner of the first aspect, in the second feasible implementation manner of the first aspect, establishing the calculation model for the horizontal acceleration distribution of the abutment includes: Converting the design acceleration response spectrum into a power spectral density function according to the approximate conversion relationship between the response spectrum and the power spectral density function based on random vibration theory; Constructing a calculation model for the horizontal acceleration distribution of the abutment based on the power spectral density function.

[0005] Combined with the second feasible implementation manner of the first aspect, in the third feasible implementation manner of the first aspect, constructing the calculation model for the horizontal acceleration distribution of the abutment based on the power spectral density function includes: The power spectral density function is simplified by using the trigonometric function superposition method to obtain the calculation model of the horizontal acceleration distribution of the abutment.

[0006] Combined with the first implementation manner of the first aspect, in the fourth implementation manner of the first aspect, constructing the analytical model of the seismic active earth pressure of the abutment includes: Based on the set analysis model, establish the equilibrium equations of force and moment; Substitute the calculation model of the horizontal acceleration distribution of the abutment into the equilibrium equations to solve the definite integral and sequence corresponding to the analytical model of the seismic active earth pressure of the abutment; Establish the analytical model of the seismic active earth pressure of the abutment according to the obtained definite integral and sequence.

[0007] Combined with the first implementation manner of the first aspect, in the fifth implementation manner of the first aspect, the constructed analytical model of the seismic active earth pressure of the abutment includes: The resultant force model of the seismic active earth pressure, the intensity distribution model of the seismic active earth pressure, and / or the height model of the acting point of the seismic active earth pressure.

[0008] In the second aspect, an analytical system for the seismic active earth pressure of the abutment is provided. In the first implementation manner of the second aspect, it includes: The acceleration distribution design module is configured to establish a calculation model of the horizontal acceleration distribution of the abutment based on the specified design acceleration response spectrum; The component coefficient calculation module is configured to obtain the characteristic angular frequency of the abutment and calculate the sine acceleration time history component coefficient corresponding to the abutment through the calculation model of the horizontal acceleration distribution of the abutment; The pressure parameter analysis module is configured to obtain the structural parameters of the abutment and calculate the corresponding seismic active earth pressure parameters of the abutment by combining the sine acceleration time history component coefficient through the constructed analytical model of the seismic active earth pressure of the abutment.

[0009] Combined with the first implementation manner of the second aspect, in the second implementation manner of the second aspect, the acceleration distribution design module includes: The conversion unit is configured to convert the design acceleration response spectrum into a power spectral density function according to the approximate conversion relationship between the response spectrum and the power spectral density function based on the random vibration theory; The construction unit is configured to establish a calculation model of the horizontal acceleration distribution of the abutment based on the power spectral density function.

[0010] Combined with the second implementation manner of the second aspect, in the third implementation manner of the second aspect, the construction unit includes: A simplification unit, configured to simplify the power spectral density function by using a trigonometric function superposition method to obtain the calculation model of the horizontal acceleration distribution of the abutment.

[0011] Combined with the first implementation manner of the second aspect, in the fourth implementation manner of the second aspect, the pressure parameter analysis module includes: An equation construction unit, configured to construct a balance equation set of force and moment based on a set analysis model; An equation solving unit, configured to substitute the calculation model of the horizontal acceleration distribution of the abutment into the balance equation set to solve the definite integral and sequence corresponding to the analytical model of the seismic active earth pressure of the abutment; A model construction unit, configured to establish the analytical model of the seismic active earth pressure of the abutment according to the solved definite integral and sequence.

[0012] Beneficial effects: By using the analytical method and system for the seismic active earth pressure of the abutment of the present invention, by establishing a calculation model of the horizontal acceleration distribution of the abutment based on the design acceleration response spectrum specified in the code, according to the characteristic angular frequency of the abutment, the sine acceleration time history component coefficient corresponding to the abutment can be calculated, and then combined with the structural parameters of the abutment, through the corresponding analytical model of the seismic active earth pressure of the abutment, various seismic active earth pressure parameters of the abutment can be determined. In this way, the frequency domain characteristics of the seismic acceleration time history covered by the design response spectrum specified in the bridge seismic design code are fully considered, thereby improving the accuracy of the analytical results of the seismic active earth pressure of the abutment. Description of the Drawings

[0013] In order to more clearly illustrate the specific implementation manners of the present invention, the drawings required for the specific implementation manners will be briefly introduced below. In all the drawings, the components or parts do not necessarily draw according to the actual ratio.

[0014] Figure 1 It is a flowchart of the analytical method for the seismic active earth pressure of the abutment provided by an embodiment of the present invention; Figure 2 It is a system block diagram of the analytical system for the seismic active earth pressure of the abutment provided by an embodiment of the present invention; Figure 3 It is an analysis model provided by an embodiment of the present invention; Figure 4 It is a comparison diagram of the analytical results of the pseudo-static method, the pseudo-dynamic method and the analytical method of the present invention for working condition 1; Figure 5 It is a comparison diagram of the analytical results of the pseudo-static method, the pseudo-dynamic method and the analytical method of the present invention for working condition 2; Figure 6 It is a comparison diagram of the analytical results of the pseudo-static method, the pseudo-dynamic method and the analytical method of the present invention for working condition 3. Specific embodiments

[0015] The embodiments of the technical solution of the present invention will be described in detail below with reference to the accompanying drawings. The following embodiments are only used to illustrate the technical solution of the present invention more clearly, so they are only examples and cannot be used to limit the protection scope of the present invention.

[0016] As Figure 1 shown in the flowchart of the analytical method for the seismic active earth pressure of the abutment, the analytical method includes: Step 1: Establish a calculation model for the horizontal acceleration distribution of the abutment based on the specified design acceleration response spectrum; Step 2: Obtain the characteristic angular frequency of the abutment, and calculate the sine acceleration time history component coefficient corresponding to the abutment through the calculation model of the horizontal acceleration distribution of the abutment; Step 3: Obtain the structural parameters of the abutment, and combine the sine acceleration time history component coefficient, and calculate the corresponding seismic active earth pressure parameters of the abutment through the established analytical model of the seismic active earth pressure of the abutment.

[0017] Specifically, first, based on the three-segment design acceleration response spectrum in the current "Code for Seismic Design of Highway Bridges" (JTG / T 2231-01-2020) in China, a calculation model for the horizontal acceleration distribution of the abutment can be established. Then, the characteristic angular frequency of the abutment to be analyzed can be obtained, and this characteristic angular frequency can be substituted into the calculation model of the horizontal acceleration distribution of the abutment, so as to calculate the sine acceleration time history component coefficients of the abutment at this characteristic angular frequency. Finally, by combining all the sine acceleration time history component coefficients and the structural parameters of the abutment to be analyzed, the seismic active earth pressure parameters of the abutment can be calculated through the established analytical model of the seismic active earth pressure of the abutment. Since the frequency domain characteristics of the seismic acceleration time history covered by the design response spectrum specified in the bridge seismic design code are fully considered, compared with traditional methods such as the pseudo-static method and the pseudo-dynamic method, the shear propagation of the seismic acceleration time history in the backfill of the abutment is considered, and multiple characteristic periods are used to characterize the frequency domain characteristics of the ground motion, thereby improving the accuracy of the analytical results of the seismic active earth pressure of the abutment.

[0018] In this embodiment, optionally, in step 1, establishing the calculation model for the horizontal acceleration distribution of the abutment includes: According to the approximate conversion relationship between the response spectrum and the power spectral density function based on the random vibration theory, convert the design acceleration response spectrum into a power spectral density function; Based on the power spectral density function, establish a calculation model for the horizontal acceleration distribution of the abutment.

[0019] Specifically, first, the design acceleration response spectrum can be converted into a power spectral density function according to the approximate conversion relationship between the response spectrum based on the random vibration theory and the power spectral density function. Then, the power spectral density function is simplified by using the trigonometric function superposition method, so as to establish a calculation model for the horizontal acceleration distribution of the abutment. The calculation model for the horizontal acceleration distribution of the abutment includes calculation models corresponding to different sine acceleration time history component coefficients and a calculation model corresponding to the horizontal acceleration of the fill soil. The finally established calculation model for the horizontal acceleration distribution of the abutment is as follows: ; ; ; ; ; ; ; Among them, represents an operator related to the abutment height , depth and the shear wave velocity of the fill soil , represents the moment of the seismic action, represents the horizontal acceleration of the fill soil under certain and , represents the peak horizontal ground acceleration, represents the dimensionless characteristic angular frequency, which is calculated from the characteristic period, ~ respectively represent different sine acceleration time history component coefficients.

[0020] In this embodiment, optionally, in step 3, constructing the analytical model of the seismic active earth pressure of the abutment includes: Constructing a balance equation set of forces and moments based on the set analysis model; Substituting the calculation model of the horizontal acceleration distribution of the abutment into the balance equation set to solve the definite integral and sequence corresponding to the analytical model of the seismic active earth pressure of the abutment; Establishing the analytical model of the seismic active earth pressure of the abutment according to the solved definite integral and sequence.

[0021] Specifically, first, a balance equation set of forces and moments can be constructed based on the set analysis model, and the analysis model is as Figure 3 shown. Figure 3 In it, represents the resultant force of the seismic active earth pressure, The inertial force representing the seismic action The inertial force representing the gravity action The reaction force below the sliding soil wedge The angle between the retaining wall back and the vertical direction The sliding angle, i.e., the angle between the sliding surface and the horizontal direction The friction angle between the retaining wall back and the fill The internal friction angle of the fill

[0022] Substitute the calculation models corresponding to the horizontal acceleration of the above fill and the calculation models corresponding to the coefficient of different sine acceleration time history components into the equilibrium equations to solve, and obtain the definite integral and series required to construct the analytical model of the seismic active earth pressure of the abutment, and thus the corresponding analytical model of the seismic active earth pressure of the abutment can be constructed.

[0023] In this embodiment, optionally, the constructed analytical model of the seismic active earth pressure of the abutment includes: The seismic active earth pressure resultant force model, the seismic active earth pressure intensity distribution model, and / or the seismic active earth pressure acting point height model.

[0024] Among them, the finally constructed seismic active earth pressure resultant force model is specifically: ; ; Among them, Represents the fill unit weight Represents the operator related to the moment of the seismic action , the abutment height and the shear wave velocity of the fill Related operator Represents the th characteristic angular frequency.

[0025] When analyzing the seismic active earth pressure resultant force of the abutment, the coefficient of the sine acceleration time history component can be calculated through the horizontal acceleration distribution calculation model of the abutment according to the characteristic angular frequency of the abutment to be analyzed, and then combined with the structural parameters such as the fill unit weight, the peak horizontal ground acceleration, the abutment height, the time, and the sliding angle of the abutment, the seismic active earth pressure resultant force of the abutment to be analyzed can be calculated through the above seismic active earth pressure resultant force model.

[0026] The finally constructed seismic active earth pressure intensity distribution model is specifically: .

[0027] Among them, Is the acceleration due to gravity.

[0028] According to the calculated sine acceleration time - history component coefficients, combined with structural parameters such as the angle between the retaining wall back and the vertical direction, the slip - crack angle, etc., through the above - mentioned seismic active earth pressure intensity distribution model, the seismic active earth pressure intensity distribution of the abutment to be analyzed can be calculated.

[0029] The established model for the height of the action point of the seismic active earth pressure is specifically as follows: ; According to the calculated sine acceleration time - history component coefficients, combined with structural parameters such as the peak horizontal ground acceleration and the abutment height, through the above - mentioned model for the height of the action point of the seismic active earth pressure, the height of the action point of the resultant force of the seismic active earth pressure of the abutment to be analyzed can be calculated.

[0030] It should be understood that in the existing specifications, there is no height of the action point of the resultant force of the seismic active earth pressure and the seismic active earth pressure intensity distribution.

[0031] To verify the analysis effect of the present invention, the pseudo - static method, the pseudo - dynamic method, and the analysis method of the present invention are respectively used to analyze the seismic active earth pressure of the abutment under 3 working conditions, and the comparison diagrams of the analysis results obtained are respectively as Figure 4 、 Figure 5 、 Figure 6 shown. Figures 4-6 In the figure, 1#method (black solid line) represents the calculation result of the pseudo - static method, which is also the recommended method in the current specifications of our country; 2#method represents the calculation result of the pseudo - dynamic method; 3#method represents the method of the present invention.

[0032] Through Figures 4-6 It can be seen that the analysis method of the present invention has higher accuracy for the analysis result of the resultant force of the seismic active earth pressure. Compared with the pseudo - static method, the average error is reduced by 84%, and compared with the pseudo - dynamic method, the average error is reduced by 54%. The description of the non - linear characteristics of the seismic active earth pressure intensity distribution is more accurate. Therefore, the present invention has higher accuracy than the existing analysis methods.

[0033] As Figure 2 shown in the system block diagram of the analysis system of the seismic active earth pressure of the abutment, this analysis system includes: An acceleration distribution design module configured to establish a calculation model for the horizontal acceleration distribution of the abutment based on a specified design acceleration response spectrum; A component coefficient calculation module configured to obtain the characteristic angular frequency of the abutment and calculate the sine acceleration time - history component coefficients corresponding to the abutment through the calculation model for the horizontal acceleration distribution of the abutment; The pressure parameter analysis module is configured to obtain various structural parameters of the abutment, and combine with the sine acceleration time-history component coefficient, and calculate the corresponding seismic active earth pressure parameters of the abutment through the established seismic active earth pressure analysis model of the abutment.

[0034] Specifically, the analysis system includes an acceleration distribution design module, a component coefficient calculation module, and a pressure parameter analysis module. Among them, the acceleration distribution design module can establish a horizontal acceleration distribution calculation model of the abutment based on the three-segment design acceleration response spectrum in the current "Code for Seismic Design of Highway Bridges" (JTG / T 2231-01-2020) in China. The component coefficient calculation module can obtain the characteristic angular frequency of the abutment to be analyzed, and substitute the characteristic angular frequency into the horizontal acceleration distribution calculation model of the abutment, so as to calculate the sine acceleration time-history component coefficients of the abutment at this characteristic angular frequency. The pressure parameter analysis module can combine all the sine acceleration time-history component coefficients and various structural parameters of the abutment to be analyzed, and calculate the seismic active earth pressure parameters of the abutment through the established seismic active earth pressure analysis model of the abutment. Since the frequency-domain characteristics of the seismic acceleration time history covered by the design response spectrum specified in the bridge seismic design code are fully considered, the accuracy of the analysis result of the seismic active earth pressure of the abutment is improved. In this embodiment, optionally, the acceleration distribution design module includes: A conversion unit configured to convert the design acceleration response spectrum into a power spectral density function according to the approximate conversion relationship between the response spectrum and the power spectral density function based on the random vibration theory; A construction unit configured to construct a horizontal acceleration distribution calculation model of the abutment based on the power spectral density function.

[0035] Specifically, the acceleration distribution design module includes a conversion unit and a construction unit. The conversion unit can convert the design acceleration response spectrum into a power spectral density function according to the approximate conversion relationship between the response spectrum and the power spectral density function based on the random vibration theory. The construction unit can simplify the power spectral density function by using the trigonometric function superposition method to establish a horizontal acceleration distribution calculation model of the abutment.

[0036] In this embodiment, optionally, the pressure parameter analysis module includes: An equation construction unit configured to construct a balance equation set of force and moment based on a set analysis model; An equation solving unit configured to substitute the horizontal acceleration distribution calculation model of the abutment into the balance equation set to solve the definite integral and sequence corresponding to the seismic active earth pressure analysis model of the abutment; A model construction unit configured to establish the seismic active earth pressure analysis model of the abutment according to the solved definite integral and sequence.

[0037] Specifically, the pressure parameter analysis module includes an equation construction unit, an equation solving unit, and a model construction unit. Among them, the equation construction unit can construct a balance equation set of force and moment based on a set analysis model. The equation solving unit can substitute the above-mentioned calculated model of the horizontal acceleration distribution of the abutment into the balance equation set for solution to obtain the definite integral and sequence required for constructing the analytical model of the seismic active earth pressure of the abutment. The model construction unit can construct the corresponding analytical model of the seismic active earth pressure of the abutment according to the obtained definite integral and sequence. The constructed resultant force model of the seismic active earth pressure, the intensity distribution model of the seismic active earth pressure, and / or the height model of the acting point of the seismic active earth pressure are as described above.

[0038] Through the constructed resultant force model of the seismic active earth pressure, the intensity distribution model of the seismic active earth pressure, and / or the height model of the acting point of the seismic active earth pressure, the coefficient of the sine acceleration time history component calculated by the calculated model of the horizontal acceleration distribution of the abutment, as well as structural parameters such as the fill weight of the abutment, the peak horizontal ground acceleration, the height of the abutment, time, and the slip angle, can be used to calculate the resultant force of the seismic active earth pressure, the intensity distribution of the seismic active earth pressure, and the height of the acting point of the resultant force of the seismic active earth pressure of the abutment to be analyzed, respectively.

[0039] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the claims and the description of the present invention.

Claims

1. An analytical method for the active earth pressure of abutments during earthquakes, characterized in that Including: Establishing a calculation model for the horizontal acceleration distribution of the abutment based on the specified design acceleration response spectrum; Obtaining the characteristic angular frequency of the abutment, and calculating the sine acceleration time history component coefficient corresponding to the abutment through the horizontal acceleration distribution calculation model of the abutment; Obtaining various structural parameters of the abutment, and combining with the sine acceleration time history component coefficient, calculating the corresponding seismic active earth pressure parameters of the abutment through the established analytical model of seismic active earth pressure of the abutment.

2. The analytical method for the active earth pressure of abutment under earthquake according to claim 1, wherein Establishing the horizontal acceleration distribution calculation model of the abutment includes: Converting the design acceleration response spectrum into a power spectral density function according to the approximate conversion relationship between the response spectrum and the power spectral density function based on the random vibration theory; Constructing a horizontal acceleration distribution calculation model of the abutment based on the power spectral density function.

3. The analytical method for the active earth pressure of abutment under earthquake according to claim 2, wherein Constructing a horizontal acceleration distribution calculation model of the abutment based on the power spectral density function includes: Simplifying the power spectral density function by using the trigonometric function superposition method to obtain the horizontal acceleration distribution calculation model of the abutment.

4. The analytical method for the active earth pressure of abutment under earthquake according to claim 1, characterized in that, Constructing the analytical model of seismic active earth pressure of the abutment includes: Constructing a balance equation set of force and moment based on the set analysis model; Substituting the horizontal acceleration distribution calculation model of the abutment into the balance equation set to solve the definite integral and sequence corresponding to the analytical model of seismic active earth pressure of the abutment; Establishing the analytical model of seismic active earth pressure of the abutment according to the solved definite integral and sequence.

5. The analytical method for the active earth pressure of abutment under earthquake according to claim 1, characterized in that, The established analytical model of seismic active earth pressure of the abutment includes: The seismic active earth pressure resultant force model, the seismic active earth pressure intensity distribution model and / or the seismic active earth pressure action point height model.

6. An analytical system for the active earth pressure of abutments during earthquakes, characterized in that, Including: An acceleration distribution design module configured to establish a calculation model for the horizontal acceleration distribution of the abutment based on the specified design acceleration response spectrum; A component coefficient calculation module configured to obtain the characteristic angular frequency of the abutment, and calculate the sine acceleration time history component coefficient corresponding to the abutment through the horizontal acceleration distribution calculation model of the abutment; A pressure parameter analysis module configured to obtain various structural parameters of the abutment, and combine with the sine acceleration time history component coefficient, calculate the corresponding seismic active earth pressure parameters of the abutment through the established analytical model of seismic active earth pressure of the abutment.

7. The analytical system for the active earth pressure of abutment under earthquake according to claim 6, characterized in that The acceleration distribution design module includes: A conversion unit configured to convert the design acceleration response spectrum into a power spectral density function according to the approximate conversion relationship between the response spectrum and the power spectral density function based on the random vibration theory; A construction unit configured to construct a horizontal acceleration distribution calculation model of the abutment based on the power spectral density function.

8. The analytical system for the active earth pressure of abutments during earthquakes according to claim 7, characterized in that, The construction unit includes: A simplification unit configured to simplify the power spectral density function by using the trigonometric function superposition method to obtain the horizontal acceleration distribution calculation model of the abutment.

9. The analytical system for the active earth pressure of abutments during earthquakes according to claim 6, wherein The pressure parameter analysis module includes: An equation construction unit configured to construct a balance equation set of force and moment based on the set analysis model; An equation solving unit configured to substitute the horizontal acceleration distribution calculation model of the abutment into the balance equation set to solve the definite integral and sequence corresponding to the analytical model of seismic active earth pressure of the abutment; A model construction unit, configured to establish the analytical model of the seismic active earth pressure of the abutment according to the definite integral and the sequence obtained by solving.

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