Analytical method and system for earthquake-induced active earth pressure on bridge abutments

Abstract

The present invention discloses a method and system for analyzing the seismic active earth pressure of a bridge abutment. The method comprises the following steps: first, a calculation model for the horizontal acceleration distribution of the abutment can be established based on the three-segment design acceleration response spectrum specified in the current specification. Then, the characteristic angular frequency of the abutment to be analyzed can be obtained, and the characteristic angular frequency can be substituted into the calculation model for the horizontal acceleration distribution of the abutment, thereby calculating the various sinusoidal acceleration time-history component coefficients of the abutment at the characteristic angular frequency. Finally, all the sinusoidal acceleration time-history component coefficients and the various structural parameters of the abutment to be analyzed can be combined to calculate the seismic active earth pressure parameters of the abutment through the constructed analytical model for 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 specification are fully considered, the accuracy of the analytical results of the seismic active earth pressure of the abutment is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of computer-aided architectural design, and in particular to an analytical method and system for earthquake-induced active earth pressure on a bridge abutment. Background Art

[0002] Existing analytical calculation methods for active seismic earth pressure are all based on the Coulomb earth pressure model, and introduce concentrated or distributed forces representing seismic inertia forces into the equilibrium equations established by the Coulomb model. Among them, the pseudo-static method assumes that the backfill behind the platform is a rigid body with infinite shear modulus, does not consider the earthquake time history characteristics, and cannot deduce the distribution of the intensity of active seismic earth pressure along the back of the platform, which has significant defects. The horizontal layer analysis method still has limitations in considering the time history characteristics of seismic action and the propagation characteristics in the backfill. The pseudo-dynamic method uses a sine wave represented by the dominant frequency to approximate the frequency domain characteristics of seismic motion, but it still cannot fully reflect the complexity and diversity of seismic motion time history and propagation in engineering practice. Summary of the Invention

[0003] To address the shortcomings of existing technologies, this paper proposes a method and system for analyzing active earth pressure under bridge abutments. This method fully considers the frequency domain characteristics of the earthquake acceleration time history covered by the design response spectrum, thereby improving the accuracy of the analytical results. The specific technical solution is as follows:

[0004] In a first aspect, a method for analyzing active earth pressure on a bridge abutment caused by earthquakes is provided. In a first possible implementation of the first aspect, the method includes:

[0005] Establish a calculation model for the horizontal acceleration distribution of abutments based on the specified design acceleration response spectrum;

[0006] Obtaining the characteristic angular frequency of the abutment, and calculating the sinusoidal acceleration time history component coefficient corresponding to the abutment using the abutment horizontal acceleration distribution calculation model;

[0007] The various structural parameters of the abutment are obtained, and in combination with the sinusoidal acceleration time history component coefficient, the corresponding abutment seismic active earth pressure parameters are calculated through the constructed abutment seismic active earth pressure analytical model.

[0008] In combination with the first implementable manner of the first aspect, in a second implementable manner of the first aspect, establishing the calculation model for the horizontal acceleration distribution of the abutment includes:

[0009] According to the approximate conversion relationship between the response spectrum and the power spectrum density function based on random vibration theory, the design acceleration response spectrum is converted into a power spectrum density function;

[0010] A calculation model for the horizontal acceleration distribution of the abutment is constructed based on the power spectrum density function.

[0011] In combination with the second implementable manner of the first aspect, in a third implementable manner of the first aspect, constructing a calculation model for the horizontal acceleration distribution of an abutment based on the power spectral density function includes:

[0012] The power spectrum density function is simplified by using the trigonometric function superposition method to obtain the calculation model of the horizontal acceleration distribution of the abutment.

[0013] In combination with the first implementable manner of the first aspect, in a fourth implementable manner of the first aspect, constructing the bridge abutment seismic active earth pressure analytical model includes:

[0014] Construct the equilibrium equations of forces and moments based on the set analytical model;

[0015] Substituting the abutment horizontal acceleration distribution calculation model into the equilibrium equation group to solve the definite integral and series corresponding to the abutment earthquake active earth pressure analytical model;

[0016] An analytical model of the seismic active earth pressure on the abutment is established based on the solved definite integrals and series.

[0017] In combination with the first possible implementation of the first aspect, in a fifth possible implementation of the first aspect, the constructed analytical model of active seismic earth pressure on abutments includes:

[0018] Seismic active earth pressure resultant force model, seismic active earth pressure intensity distribution model and / or seismic active earth pressure action point height model.

[0019] In a second aspect, a system for analyzing active earth pressure on abutments under earthquake conditions is provided. In a first possible implementation of the second aspect, the system includes:

[0020] An acceleration distribution design module is configured to establish a calculation model for the horizontal acceleration distribution of the abutment based on a specified design acceleration response spectrum;

[0021] a component coefficient calculation module configured to obtain the characteristic angular frequency of the abutment and calculate the sinusoidal acceleration time history component coefficient corresponding to the abutment through the abutment horizontal acceleration distribution calculation model;

[0022] The pressure parameter analysis module is configured to obtain various structural parameters of the abutment, and calculate the corresponding abutment seismic active earth pressure parameters by combining the sinusoidal acceleration time history component coefficient and constructing an abutment seismic active earth pressure analysis model.

[0023] In combination with the first implementable manner of the second aspect, in a second implementable manner of the second aspect, the acceleration distribution design module includes:

[0024] a conversion unit configured to convert the design acceleration response spectrum into a power spectrum density function according to an approximate conversion relationship between the response spectrum and the power spectrum density function based on random vibration theory;

[0025] The construction unit is configured to construct a calculation model of the horizontal acceleration distribution of the abutment based on the power spectrum density function.

[0026] In combination with the second possible implementation of the second aspect, in a third possible implementation of the second aspect, the construction unit includes:

[0027] The simplification unit is configured to simplify the power spectrum density function by using a trigonometric function superposition method to obtain a calculation model of the horizontal acceleration distribution of the abutment.

[0028] In combination with the first implementable manner of the second aspect, in a fourth implementable manner of the second aspect, the pressure parameter parsing module includes:

[0029] an equation building unit configured to build a force and moment equilibrium equation system based on a set analysis model;

[0030] an equation solving unit configured to substitute the abutment horizontal acceleration distribution calculation model into the equilibrium equation group to solve the definite integral and series corresponding to the analytical model of the abutment seismic active earth pressure;

[0031] The model building unit is configured to establish the bridge abutment seismic active earth pressure analytical model according to the solved definite integral and sequence.

[0032] Beneficial Effects: The analytical method and system for determining seismic active earth pressure on abutments of the present invention establishes a calculation model for the horizontal acceleration distribution of abutments based on the design acceleration response spectrum specified in the specifications. Based on the characteristic angular frequency of the abutments, the corresponding sinusoidal acceleration time-history component coefficients can be calculated. Combined with the structural parameters of the abutments, the various seismic active earth pressure parameters of the abutments can be determined using the corresponding analytical model for seismic active earth pressure on the abutments. This fully considers the frequency domain characteristics of the seismic acceleration time history covered by the design response spectrum specified in the bridge seismic design specifications, thereby improving the accuracy of the analytical results for seismic active earth pressure on abutments. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] In order to more clearly illustrate the specific embodiments of the present invention, the following briefly introduces the drawings required for use in the specific embodiments. In all the drawings, each element or part is not necessarily drawn according to the actual scale.

[0034] Figure 1 A flow chart of an analytical method for earthquake active earth pressure on abutments provided in one embodiment of the present invention;

[0035] Figure 2 A system block diagram of an analytical system for earthquake-induced active earth pressure on abutments provided by one embodiment of the present invention;

[0036] Figure 3 An analysis model provided by an embodiment of the present invention;

[0037] Figure 4 The figure is a comparison chart 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;

[0038] Figure 5 The figure is a comparison chart 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;

[0039] Figure 6 The figure is a comparison chart of the analytical results of the pseudo-static method, pseudo-dynamic method and the analytical method of the present invention for working condition 3. DETAILED DESCRIPTION

[0040] The following embodiments of the technical solution of the present invention will be described in detail with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention and are therefore only examples and are not intended to limit the scope of protection of the present invention.

[0041] like Figure 1 The flowchart of the analytical method for the earthquake active earth pressure on abutments is shown. The analytical method includes:

[0042] Step 1: Establish a calculation model for the horizontal acceleration distribution of the abutment based on the specified design acceleration response spectrum;

[0043] Step 2: Obtain the characteristic angular frequency of the abutment, and calculate the sinusoidal acceleration time history component coefficient corresponding to the abutment through the abutment horizontal acceleration distribution calculation model;

[0044] Step 3: Obtain various structural parameters of the abutment, and calculate corresponding abutment seismic active earth pressure parameters by combining the sinusoidal acceleration time history component coefficients and constructing an analytical model of abutment seismic active earth pressure.

[0045] Specifically, a calculation model for the horizontal acceleration distribution of abutments can be established based on the three-segment design acceleration response spectrum specified in my country's current "Code for Seismic Design of Highway Bridges" (JTG / T 2231-01-2020). Next, the characteristic angular frequency of the abutment to be analyzed can be obtained and substituted into the calculation model for the horizontal acceleration distribution of the abutment to calculate the coefficients of the various sinusoidal acceleration time-history components of the abutment at this characteristic angular frequency. Finally, the parameters of the seismic active earth pressure on the abutment can be calculated using the constructed analytical model combining all the sinusoidal acceleration time-history coefficients and the structural parameters of the abutment to be analyzed. By fully considering the frequency domain characteristics of the seismic acceleration time history covered by the design response spectrum specified in the seismic design code for bridges, compared to traditional methods such as pseudo-static and pseudo-dynamic methods, the shear propagation of the seismic acceleration time history in the abutment backfill 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 for the seismic active earth pressure on the abutment.

[0046] In this embodiment, optionally, in step 1, establishing the calculation model of the horizontal acceleration distribution of the abutment includes:

[0047] According to the approximate conversion relationship between the response spectrum and the power spectrum density function based on random vibration theory, the design acceleration response spectrum is converted into a power spectrum density function;

[0048] A calculation model for the horizontal acceleration distribution of the abutment is constructed based on the power spectrum density function.

[0049] Specifically, the design acceleration response spectrum can first be converted into a power spectrum density function based on the approximate conversion relationship between the response spectrum and the power spectrum density function based on random vibration theory. The power spectrum density function is then simplified using the trigonometric function superposition method to establish a calculation model for the horizontal acceleration distribution of the abutment. This calculation model includes calculation models corresponding to different sinusoidal acceleration time-history component coefficients and a calculation model corresponding to the horizontal acceleration of the fill. The final calculation model for the horizontal acceleration distribution of the abutment is as follows:

[0050] ;

[0051] ;

[0052] ;

[0053] ;

[0054] ;

[0055] ;

[0056] ;

[0057] in, Represents the height from the abutment ,depth and fill shear wave velocity Related operators, Represents the moment of earthquake action, Represents a certain and The horizontal acceleration of the fill under represents the horizontal peak acceleration of the earthquake, represents the dimensionless characteristic angular frequency, which is calculated from the characteristic period, ~ They represent different sinusoidal acceleration time history component coefficients respectively.

[0058] In this embodiment, optionally, in step 3, constructing the bridge abutment seismic active earth pressure analytical model includes:

[0059] Construct the equilibrium equations of forces and moments based on the set analytical model;

[0060] Substituting the abutment horizontal acceleration distribution calculation model into the equilibrium equation group to solve the definite integral and series corresponding to the abutment earthquake active earth pressure analytical model;

[0061] An analytical model of the seismic active earth pressure on the abutment is established based on the solved definite integrals and series.

[0062] Specifically, first, the force and torque equilibrium equations can be constructed based on the set analysis model. The analysis model is as follows: Figure 3 shown. Figure 3 middle, represents the resultant active earth pressure from earthquake, represents the inertial force of earthquake action, represents the inertial force due to gravity, Represents the reaction force underneath the slip-cracked soil wedge, Represents the angle between the back of the retaining wall and the vertical direction, represents the slip angle, that is, the angle between the slip surface and the horizontal direction, represents the friction angle between the back of the retaining wall and the fill soil, Represents the internal friction angle of fill.

[0063] The calculation model corresponding to the horizontal acceleration of the fill and the calculation model corresponding to the coefficients of different sinusoidal acceleration time history components are substituted into the equilibrium equation group for solution to obtain the definite integrals and series required to construct the analytical model of the active earth pressure of the bridge abutment due to earthquakes, thereby constructing the corresponding analytical model of the active earth pressure of the bridge abutment due to earthquakes.

[0064] In this embodiment, the constructed bridge abutment seismic active earth pressure analytical model optionally includes:

[0065] Seismic active earth pressure resultant force model, seismic active earth pressure intensity distribution model and / or seismic active earth pressure action point height model.

[0066] Among them, the final earthquake active earth pressure resultant model is as follows:

[0067] ;

[0068] ;

[0069] in, Represents the fill weight, Represents the moment of interaction with earthquakes , abutment height and fill shear wave velocity Related operators, Representative A characteristic angular frequency.

[0070] When analyzing the resultant seismic active earth pressure on a bridge abutment, the sinusoidal acceleration time-history component coefficient can be calculated based on the characteristic angular frequency of the abutment to be analyzed through the calculation model of the horizontal acceleration distribution of the abutment. Then, combined with the structural parameters such as the fill weight of the abutment, the peak acceleration of the horizontal seismic motion, the height of the abutment, the time, and the slip angle, the resultant seismic active earth pressure on the abutment to be analyzed can be calculated through the above-mentioned resultant seismic active earth pressure model.

[0071] The final earthquake active earth pressure intensity distribution model is as follows:

[0072] .

[0073] in, is the acceleration due to gravity.

[0074] Based on the calculated sinusoidal acceleration time-history component coefficients, combined with structural parameters such as the angle between the retaining wall back and the vertical direction and the slip angle, the seismic active earth pressure intensity distribution of the abutment to be analyzed can be calculated using the above-mentioned seismic active earth pressure intensity distribution model.

[0075] The constructed earthquake active earth pressure action point height model is as follows:

[0076] ;

[0077] Based on the calculated sinusoidal acceleration time history component coefficients, combined with structural parameters such as the horizontal seismic peak acceleration and the abutment height, the height of the action point of the seismic active earth pressure resultant force of the abutment to be analyzed can be calculated using the above-mentioned seismic active earth pressure action point height model.

[0078] It should be understood that the existing standards do not include the height of the point of action of the resultant force of earthquake active earth pressure and the distribution of the intensity of earthquake active earth pressure.

[0079] In order to verify the analytical effect of the present invention, the pseudo-static method, pseudo-dynamic method and the analytical method of the present invention are used to analyze the active earth pressure of the bridge abutment under three working conditions. The comparison diagrams of the analytical results are shown as follows: Figure 4 、 Figure 5 、 Figure 6 shown. Figure 4-6 In the figure, 1#method (black solid line) represents the calculation results of the pseudo-static method, which is also the recommended method in the current Chinese standards; 2#method represents the calculation results of the pseudo-dynamic method; 3#method represents the method of the present invention.

[0080] pass Figure 4-6 As can be seen, the analytical method of the present invention provides more accurate results for the resultant seismic active earth pressure, with an average error reduction of 84% compared to the pseudo-static method and 54% compared to the pseudo-dynamic method. It also more accurately describes the nonlinear characteristics of the seismic active earth pressure intensity distribution. Therefore, the present invention offers greater accuracy than existing analytical methods.

[0081] like Figure 2 The system block diagram of the analytical system for earthquake active earth pressure on abutments shown in FIG. 1 includes:

[0082] An acceleration distribution design module is configured to establish a calculation model for the horizontal acceleration distribution of the abutment based on a specified design acceleration response spectrum;

[0083] a component coefficient calculation module configured to obtain the characteristic angular frequency of the abutment and calculate the sinusoidal acceleration time history component coefficient corresponding to the abutment through the abutment horizontal acceleration distribution calculation model;

[0084] The pressure parameter analysis module is configured to obtain various structural parameters of the abutment, and calculate the corresponding abutment seismic active earth pressure parameters by combining the sinusoidal acceleration time history component coefficient and constructing an abutment seismic active earth pressure analysis model.

[0085] Specifically, the analytical 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 for the abutment based on the three-segment design acceleration response spectrum in my country's current "Highway Bridge Seismic Design Code" (JTG / T2231-01-2020). 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 various sinusoidal acceleration time history component coefficients of the abutment at the characteristic angular frequency. The pressure parameter analysis module can combine all the sinusoidal acceleration time history component coefficients and the various structural parameters of the abutment to be analyzed, and calculate the seismic active earth pressure parameters of the abutment through the constructed abutment seismic active earth pressure analysis model. 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 results of the seismic active earth pressure of the abutment is improved.

[0086] In this embodiment, optionally, the acceleration distribution design module includes:

[0087] a conversion unit configured to convert the design acceleration response spectrum into a power spectrum density function according to an approximate conversion relationship between the response spectrum and the power spectrum density function based on random vibration theory;

[0088] The construction unit is configured to construct a calculation model of the horizontal acceleration distribution of the abutment based on the power spectrum density function.

[0089] Specifically, the acceleration distribution design module consists of a conversion unit and a construction unit. The conversion unit converts the design acceleration response spectrum into a power spectrum density function based on the approximate conversion relationship between the response spectrum and the power spectrum density function based on random vibration theory. The construction unit simplifies the power spectrum density function using trigonometric function superposition to establish a calculation model for the horizontal acceleration distribution of the abutment.

[0090] In this embodiment, optionally, the pressure parameter analysis module includes:

[0091] an equation building unit configured to build a force and moment equilibrium equation system based on a set analysis model;

[0092] an equation solving unit configured to substitute the abutment horizontal acceleration distribution calculation model into the equilibrium equation group to solve the definite integral and series corresponding to the analytical model of the abutment seismic active earth pressure;

[0093] The model building unit is configured to establish the bridge abutment seismic active earth pressure analytical model according to the solved definite integral and sequence.

[0094] 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 group of equilibrium equations of forces and moments based on the set analysis model. The equation solving unit can substitute the above-constructed abutment horizontal acceleration distribution calculation model into the said group of equilibrium equations to solve and obtain the definite integrals and series required to construct the abutment seismic active earth pressure analytical model. The model construction unit can construct the corresponding abutment seismic active earth pressure analytical model based on the solved definite integrals and series. The constructed seismic active earth pressure resultant model, seismic active earth pressure intensity distribution model and / or seismic active earth pressure action point height model are as described above.

[0095] By constructing the seismic active earth pressure resultant model, the seismic active earth pressure intensity distribution model and / or the seismic active earth pressure action point height model, the sinusoidal acceleration time component coefficient, as well as the abutment fill weight, horizontal seismic motion peak acceleration, abutment height, time, slip angle and other structural parameters can be calculated based on the abutment horizontal acceleration distribution calculation model, and the seismic active earth pressure resultant, seismic active earth pressure intensity distribution and action point height of the abutment to be analyzed can be calculated respectively.

[0096] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some or all of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the scope of the technical solutions of the embodiments of the present invention, and they should all be included in the scope of the claims and description of the present invention.

Claims

1. An analytical method for earthquake-induced active earth pressure on abutments, characterized in that: include: Establish a calculation model for the horizontal acceleration distribution of abutments based on the specified design acceleration response spectrum; Obtaining the characteristic angular frequency of the abutment, and calculating the sinusoidal acceleration time history component coefficient corresponding to the abutment using the abutment horizontal acceleration distribution calculation model; Obtaining various structural parameters of the abutment, and calculating corresponding abutment seismic active earth pressure parameters by using the constructed abutment seismic active earth pressure analytical model in combination with the sinusoidal acceleration time history component coefficient; Establishing the calculation model of the horizontal acceleration distribution of the abutment includes: According to the approximate conversion relationship between the response spectrum and the power spectrum density function based on random vibration theory, the design acceleration response spectrum is converted into the power spectrum density function; The power spectrum density function is simplified by using the trigonometric function superposition method, and a calculation model for the horizontal acceleration distribution of the abutment is established. Specifically: ； ； ； ； ； ； ； in, Represents the height from the abutment ,depth and fill shear wave velocity Related operators, Represents the moment of earthquake action, Represents a certain and The horizontal acceleration of the fill under represents the horizontal peak acceleration of the earthquake, represents the dimensionless characteristic angular frequency, which is calculated from the characteristic period, ~ They represent different sinusoidal acceleration time history component coefficients respectively.

2. The analytical method for determining active earth pressure on abutments due to earthquakes according to claim 1, characterized in that: Constructing the analytical model of the bridge abutment seismic active earth pressure includes: Construct the equilibrium equations of forces and moments based on the set analysis model; Substituting the abutment horizontal acceleration distribution calculation model into the equilibrium equation group to solve the definite integral and series corresponding to the abutment earthquake active earth pressure analytical model; An analytical model of the seismic active earth pressure on the abutment is established based on the solved definite integrals and series.

3. The analytical method for determining active earth pressure on abutments due to earthquakes according to claim 1, characterized in that: The analytical model of active earth pressure on abutments under earthquakes includes: Seismic active earth pressure resultant force model, seismic active earth pressure intensity distribution model and / or seismic active earth pressure action point height model.

4. An analytical system for active earth pressure on abutments due to earthquakes, characterized in that: include: An acceleration distribution design module is 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 sinusoidal acceleration time history component coefficient corresponding to the abutment through the abutment horizontal acceleration distribution calculation model; a pressure parameter analysis module configured to obtain various structural parameters of the abutment, and calculate corresponding abutment seismic active earth pressure parameters by using a constructed abutment seismic active earth pressure analysis model in combination with the sinusoidal acceleration time history component coefficient; Establishing the calculation model of the horizontal acceleration distribution of the abutment includes: According to the approximate conversion relationship between the response spectrum and the power spectrum density function based on random vibration theory, the design acceleration response spectrum is converted into the power spectrum density function; The power spectrum density function is simplified by using the trigonometric function superposition method, and a calculation model for the horizontal acceleration distribution of the abutment is established. Specifically: ； ； ； ； ； ； ； in, Represents the height from the abutment ,depth and fill shear wave velocity Related operators, Represents the moment of earthquake action, Represents a certain and The horizontal acceleration of the fill under represents the horizontal peak acceleration of the earthquake, represents the dimensionless characteristic angular frequency, which is calculated from the characteristic period, ~ They represent different sinusoidal acceleration time history component coefficients respectively.

5. The analytical system for bridge abutment seismic active earth pressure according to claim 4, characterized in that: The pressure parameter analysis module includes: an equation building unit configured to build a force and moment equilibrium equation system based on a set analysis model; an equation solving unit configured to substitute the abutment horizontal acceleration distribution calculation model into the equilibrium equation group to solve the definite integral and series corresponding to the analytical model of the abutment seismic active earth pressure; The model building unit is configured to establish the bridge abutment seismic active earth pressure analytical model according to the solved definite integral and sequence.

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