Method for determining acceleration distribution of retaining wall

Abstract

The invention provides a retaining wall acceleration distribution determination method, system and device and a medium, and the method comprises the steps: determining a horizontal peak acceleration and a characteristic period according to a region where a retaining wall is located, and then constructing a design response spectrum according to the horizontal peak acceleration and the characteristic period; converting the design response spectrum into a power spectrum density, and then generating a random phase spectrum by using a Meisson rotation algorithm; and performing random time-history analysis based on the power spectrum density and the random phase spectrum to obtain the acceleration distribution of the retaining wall. The problem that in the prior art, due to the fact that near-fault retaining wall back filling acceleration distribution is predicted by means of numerical simulation based on finite elements or discrete elements, the actual engineering analysis efficiency is low is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of civil engineering, and in particular to a method, system, equipment and medium for determining acceleration distribution of a retaining wall. Background Art

[0002] Currently, the acceleration distribution of the backfill behind a near-fault retaining wall can only be predicted through numerical simulation based on finite element or discrete element methods. This is achieved by establishing a three-dimensional numerical simulation model of the retaining wall-fill system, dividing the grid / discrete particles based on the finite element method or discrete element method, applying near-fault seismic input and performing dynamic time-history analysis. After solving the system's dynamic response, the acceleration distribution of the fill area is extracted.

[0003] However, the numerical simulation method for calculating the acceleration distribution of the backfill of retaining walls near faults requires the establishment of a sophisticated three-dimensional numerical model. The modeling process is complex and computational efficiency is low. It is highly dependent on high-performance computing resources, making it difficult to promote and apply in actual projects and unable to meet the real-time analysis needs of seismic design of retaining walls near fault areas. Summary of the Invention

[0004] In response to the shortcomings of the existing technology, the present invention provides a method, system, equipment and medium for determining the acceleration distribution of a retaining wall, which solves the problem in the existing technology of relying on numerical simulation based on finite elements or discrete elements to predict the acceleration distribution of the backfill of a near-fault retaining wall, resulting in low efficiency in actual engineering analysis.

[0005] According to an embodiment of the present invention, a method for determining acceleration distribution of a retaining wall includes: Determine the horizontal peak acceleration and characteristic period according to the area where the retaining wall is located, and then construct the design response spectrum based on the horizontal peak acceleration and characteristic period; The design response spectrum is converted into power spectral density and then a random phase spectrum is generated using the Mersenne rotation algorithm; Random time history analysis is performed based on power spectrum density and random phase spectrum to obtain the acceleration distribution of the retaining wall.

[0006] Preferably, the power spectral density is as follows: in, To control the angular frequency, , is the equivalent damping ratio of the retaining wall-fill system, D is the duration of the earthquake motion, and r is the exceedance probability.

[0007] Preferably, the method for determining the earthquake duration is as follows: Artificially set the parameter value of r and then set multiple simulation durations; Fitting the first relationship curve of the power spectrum density versus the control angular frequency at each simulation duration; The simulation duration with the largest peak value in the first relationship curve is selected as the earthquake motion duration.

[0008] Preferably, the method for determining the exceedance probability is as follows: Artificially set the parameter value of D, and then set multiple simulation probability values; Fitting the second relationship curve of the power spectrum density changing with the control angular frequency at each simulation duration; The average power density of each second relationship curve is calculated, and the simulation probability value corresponding to the second relationship curve with the largest average density is selected as the exceedance probability.

[0009] Preferably, the method of generating a random phase spectrum using the Mersenne rotation algorithm includes: Create a prime number periodic sequence with a length of 2^19937-1, and then use the Mersenne Twister algorithm to extract values from the prime number periodic sequence to generate a pseudo-random number sequence; Normalize the pseudo-random number sequence to generate a normalized sequence with a value range in the interval [0,1); The normalized sequence is linearly mapped to the angular frequency domain of [0,2π) to obtain a random phase spectrum.

[0010] Preferably, the formula for the random time course analysis is as follows: Where a is the acceleration, is the sampling interval of the angular frequency domain, N is the number of sampling points, H is the height of the retaining wall, is the shear wave velocity of the retaining wall backfill, is the angular frequency of the i-th sampling point.

[0011] Preferably, the number of random numbers in the pseudo-random number sequence is the same as the number of sampling points.

[0012] On the other hand, according to an embodiment of the present invention, a system for determining the acceleration distribution of a retaining wall is further provided, wherein the system uses the above-mentioned method for determining the acceleration distribution of a retaining wall, and comprises: A positioning module, the positioning module is used to determine the area where the retaining wall is located, and the corresponding horizontal peak acceleration and characteristic period; a conversion module, wherein the calculation module is used to construct a design response spectrum according to the horizontal peak acceleration and the characteristic period, convert the design response spectrum into a power spectrum density, and generate a random phase spectrum using a Mersenne rotation algorithm; An analysis module is used to perform random time history analysis based on power spectrum density and random phase spectrum to obtain the acceleration distribution of the retaining wall.

[0013] On the other hand, according to an embodiment of the present invention, a computer is further provided, characterized in that it includes at least one processor and a memory, the memory stores a computer program, and the computer program is configured to be executed by the processor to implement the above-mentioned method for determining the acceleration distribution of a retaining wall.

[0014] On the other hand, according to an embodiment of the present invention, a storage medium is further provided, characterized in that: the storage medium is a computer-readable storage medium, a computer program is stored on the storage medium, and the computer program can be executed by one or more processors to implement the above-mentioned method for determining the acceleration distribution of a retaining wall.

[0015] Compared with the prior art, the present invention has the following beneficial effects: The present invention utilizes the approximate conversion relationship between the design response spectrum based on random vibration theory and the power spectrum density function to derive the corresponding power spectrum density. Then, combined with the random phase spectrum, with the help of the sinusoidal steady-state acceleration time history analysis of equidistant control in the frequency domain, the mathematical relationship for the acceleration distribution of the backfill of the retaining wall is derived, and finally the acceleration distribution of the backfill of the retaining wall near the fault is obtained. Through a relatively intuitive analytical calculation method, the acceleration distribution of the backfill of the retaining wall near the fault can be calculated and predicted using a compiler based on Excel or other numerical calculations, avoiding the use of the more time-consuming and labor-intensive finite element or discrete element numerical simulation, thereby improving the efficiency of engineering analysis and design. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 This is a flow chart of a method for determining acceleration distribution of a retaining wall according to an embodiment of the present invention.

[0017] Figure 2 This is a diagram showing changes in power spectrum density under different earthquake durations according to an embodiment of the present invention.

[0018] Figure 3 1 is a power spectrum density variation diagram under different exceedance probabilities according to an embodiment of the present invention.

[0019] Figure 4 1 is a comparison chart of the centrifuge vibration table test under different working conditions of the embodiment of the present invention and the results of the present invention. DETAILED DESCRIPTION

[0020] The technical solutions of the present invention are further described below with reference to the accompanying drawings and embodiments.

[0021] like Figure 1 As shown, an embodiment of the present invention proposes a method for determining the acceleration distribution of a retaining wall, including: Determine the horizontal peak acceleration and characteristic period according to the area where the retaining wall is located, and then construct the design response spectrum based on the horizontal peak acceleration and characteristic period; According to the area where the target retaining wall is located, the horizontal peak acceleration A corresponding to the target retaining wall is determined by checking the "China Earthquake Motion Parameter Zoning Map" (GB 18306-2015).

[0022] According to the type of site where the target retaining wall is located, the characteristic period Tg of the design response spectrum is determined based on the corresponding relationship in Table 1.

[0023] Table 1: Relationship between site type and characteristic period Venue Type Category Ⅰ0 venue Ⅰ Class 1 venue Class II sites Category III sites Category IV sites Characteristic cycle 0.75 0.75 0.85 1.05 1.05 The design response spectrum is constructed based on the horizontal peak acceleration A and the characteristic period Tg corresponding to different site types: Where T is the natural oscillation period.

[0024] The design response spectrum is converted into power spectral density and then a random phase spectrum is generated using the Mersenne rotation algorithm; According to the approximate relationship between the design response spectrum and the power spectrum density function, the design response spectrum is converted into the power spectrum density: in, To control the angular frequency, , is the equivalent damping ratio of the retaining wall-fill system. The values are taken as 0.05 for concrete structures, 0.03 for steel structures, and 0.10 for wooden structures.

[0025] D is the duration of earthquake motion. The present invention explores the influence law by controlling the variable method, artificially setting Tg to 0.4s, r to 50%, and sequentially setting multiple simulation durations: 20s, 30s, 40s, 50s, 60s, and 120s. Then, the power spectrum density is calculated as a function of angular frequency under different simulation durations, and these values are then fitted into a first relationship curve, such as Figure 2 As shown by Figure 2 It can be seen that as the duration D of the earthquake motion history becomes longer, the power spectrum density The lower the amplitude, the The impact of the overall trend can be ignored. From the perspective of structural seismic design safety, the higher the peak value, the stronger the seismic resistance. Therefore, defining D as small as possible is a safer consideration. In the process of structural dynamic analysis, the duration of natural wave acceleration history is usually longer, sometimes even exceeding 120s, while the duration of artificial seismic wave acceleration history fitting is usually not less than 30s. In summary, under the premise of meeting the minimum D value, the simulation duration with the largest peak value in the first relationship curve is selected as the seismic motion duration. In addition, from the perspective of structural seismic design safety and theoretical rigor, there may be some other unspecified impacts on the extreme values at both ends. Therefore, a conservative D=30s was selected.

[0026] r is the exceedance probability, to clarify r Similarly, the present invention explores the influence law through the control variable method, artificially setting Tg to 0.4s, D to 30s, r to 10%, 20%, 30%, 40%, 50%, and 60% in sequence, and then calculating the value of power spectrum density changing with angular frequency under different r values, and then fitting these values into the second relationship curve, such as Figure 3 As shown by Figure 3 It can be seen that as the exceedance probability r increases, the power spectrum density function The higher the amplitude, the higher the probability of exceedance. In the prior art, 0.15 is usually used, which is considered to be a highly accurate result. However, the design acceleration response spectrum is determined based on statistical averaging. Therefore, the average power density of each second relationship curve is calculated, and the simulation probability value corresponding to the second relationship curve with the largest average density is selected as the exceedance probability. In addition, considering the safety of structural seismic design and theoretical rigor, the extreme values at both ends may have some unspecified other effects. Therefore, the conservative value of r = 0.5 was selected.

[0027] Then, based on the Mersenne twister algorithm, a random phase spectrum is generated. First, a very large prime periodic sequence with a length of 2^19937-1 is created. Combining the bit mask operation and linear transformation of the state array, the Mersenne twister algorithm is used to extract values from the prime periodic sequence to generate a pseudo-random number sequence with high uniformity. The pseudo-random number sequence is then normalized to generate a normalized sequence with a uniform distribution in the interval [0,1). Finally, the generated normalized sequence is linearly mapped to the [0,2π) angular frequency domain to obtain a random phase spectrum. .

[0028] Random time history analysis is performed based on power spectrum density and random phase spectrum to obtain the acceleration distribution of the retaining wall.

[0029] The power spectral density above and random phase spectrum , substitute the horizontal random time history represented by the power spectral density function into the vertical distribution relationship of the retaining wall back to perform random time history analysis, and calculate the acceleration distribution a(z,t) of the back fill of the target retaining wall at depth z and time t.

[0030] in, The sampling interval of the angular frequency domain is 0.01π in the present invention, which is taken into account the efficiency of the numerical calculation process and meets the signal processing principle for Less than or equal to 2π / D; N is the number of sampling points, which is the bandwidth divided by the sampling interval get; is the angular frequency of the i-th sampling point; H is the height of the retaining wall, which is determined according to the actual project conditions; It is the shear wave velocity of the backfill of the retaining wall, and its value is determined according to the actual project conditions.

[0031] like Figure 4 As shown in the figure, under different working conditions, the calculation results of the present invention are compared and verified with the centrifuge vibration table test of the scaled model of the retaining wall. It can be seen from the figure that under the two working conditions, the curve changes of seismic waves 1 to 4 are very different. The curve of the method of the present invention is relatively stable and is less affected by external conditions. Therefore, it has higher accuracy and usually encompasses possible random results. Therefore, it also has the safety of seismic design.

[0032] On the other hand, an embodiment of the present invention further provides a retaining wall acceleration distribution determination system, characterized in that the system uses the above-mentioned retaining wall acceleration distribution determination method, including: A positioning module, the positioning module is used to determine the area where the retaining wall is located, and the corresponding horizontal peak acceleration and characteristic period; a conversion module, wherein the calculation module is used to construct a design response spectrum according to the horizontal peak acceleration and the characteristic period, convert the design response spectrum into a power spectrum density, and generate a random phase spectrum using a Mersenne rotation algorithm; An analysis module is used to perform random time history analysis based on power spectrum density and random phase spectrum to obtain the acceleration distribution of the retaining wall.

[0033] On the other hand, an embodiment of the present invention further provides a computer, characterized in that it includes at least one processor and a memory, the memory stores a computer program, and the computer program is configured to be executed by the processor to implement the above-mentioned method for determining the acceleration distribution of a retaining wall.

[0034] On the other hand, an embodiment of the present invention further provides a storage medium, characterized in that: the storage medium is a computer-readable storage medium, a computer program is stored on the storage medium, and the computer program can be executed by one or more processors to implement the above-mentioned method for determining the acceleration distribution of a retaining wall.

[0035] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A method for determining acceleration distribution of a retaining wall, characterized by: include: Determine the horizontal peak acceleration and characteristic period according to the area where the retaining wall is located, and then construct the design response spectrum based on the horizontal peak acceleration and characteristic period; The design response spectrum is converted into power spectral density and then a random phase spectrum is generated using the Mersenne rotation algorithm; Random time history analysis is performed based on power spectrum density and random phase spectrum to obtain the acceleration distribution of the retaining wall.

2. The method for determining the acceleration distribution of a retaining wall according to claim 1, wherein: The power spectral density is as follows: in, To control the angular frequency, , is the equivalent damping ratio of the retaining wall-fill system, D is the duration of the earthquake motion, and r is the exceedance probability.

3. The method for determining the acceleration distribution of a retaining wall according to claim 1, wherein: The method for determining the duration of earthquake motion is as follows: Artificially set the parameter value of r and then set multiple simulation durations; Fitting the first relationship curve of the power spectrum density versus the control angular frequency at each simulation duration; The simulation duration with the largest peak value in the first relationship curve is selected as the earthquake motion duration.

4. The method for determining the acceleration distribution of a retaining wall according to claim 1, wherein: The exceedance probability is determined as follows: Artificially set the parameter value of D, and then set multiple simulation probability values; Fitting the second relationship curve of the power spectrum density changing with the control angular frequency at each simulation duration; The average power density of each second relationship curve is calculated, and the simulation probability value corresponding to the second relationship curve with the largest average density is selected as the exceedance probability.

5. The method for determining the acceleration distribution of a retaining wall according to claim 1, wherein: Methods for generating random phase spectra using the Mersenne twister algorithm include: Create a prime number periodic sequence with a length of 2^19937-1, and then use the Mersenne Twister algorithm to extract values from the prime number periodic sequence to generate a pseudo-random number sequence; Normalize the pseudo-random number sequence to generate a normalized sequence with a value range in the interval [0,1); The normalized sequence is linearly mapped to the angular frequency domain of [0,2π) to obtain a random phase spectrum.

6. The method for determining acceleration distribution of a retaining wall according to claim 1, wherein: The formula for the random time history analysis is as follows: Where a is the acceleration, is the sampling interval of the angular frequency domain, N is the number of sampling points, H is the height of the retaining wall, is the shear wave velocity of the retaining wall backfill, is the angular frequency of the i-th sampling point.

7. The method for determining the acceleration distribution of a retaining wall according to claim 6, wherein: The number of random numbers in the pseudo-random number sequence is the same as the number of sampling points.

8. A retaining wall acceleration distribution determination system, characterized by: The system uses a retaining wall acceleration distribution determination method according to any one of claims 1 to 7, comprising: A positioning module, the positioning module is used to determine the area where the retaining wall is located, and the corresponding horizontal peak acceleration and characteristic period; a conversion module, wherein the calculation module is used to construct a design response spectrum according to the horizontal peak acceleration and the characteristic period, convert the design response spectrum into a power spectrum density, and generate a random phase spectrum using a Mersenne rotation algorithm; An analysis module is used to perform random time history analysis based on power spectrum density and random phase spectrum to obtain the acceleration distribution of the retaining wall.

9. A computer, characterized in that: The system comprises at least one processor and a memory, wherein the memory stores a computer program, and the computer program is configured to be executed by the processor to implement the method for determining the acceleration distribution of a retaining wall according to any one of claims 1 to 7.

10. A storage medium, characterized in that: The storage medium is a computer-readable storage medium, on which a computer program is stored. The computer program can be executed by one or more processors to implement a method for determining the acceleration distribution of a retaining wall as described in any one of claims 1 to 7.

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