A design spectrum amplitude calculation method for near-earthquake fault region

Abstract

The application provides a design criterion spectrum amplitude calculation method for a near-earth fault region. According to the site type of a target structure engineering address, the characteristic period T g of the design criterion spectrum is matched; according to the site type of the target structure engineering address, the first attenuation index γ1 of the design criterion spectrum is matched; then, according to the first attenuation index γ1, the second attenuation index γ2 of the design criterion spectrum is matched in combination with the site type of the target structure engineering address; then, according to the characteristic period T g , the first attenuation index γ 1 and the second attenuation index γ 2 of the design criterion spectrum, the design criterion spectrum formula for the near-earth fault region is designed, and the criterion spectrum amplitude is calculated. The application eliminates the conservative deviation caused by the inconsistency of the actual descending trend, can more accurately reflect the real spectrum characteristics of the near-fault ground motion, especially the long-period pulse characteristics, and provides more reasonable design basis for the seismic design of bridge, building and other engineering structures in the near-fault region. The criterion spectrum of the application and the existing specification spectrum under each group of site categories are calculated.

Description

Technical Field

[0001] This invention relates to the field of seismic design technology for civil engineering structures, and specifically to a method for calculating the spectral amplitude of design standards for near-earthquake fault zones. Background Technology

[0002] Near-fault ground motions generally refer to ground motions within a fault distance of less than 20 km. Due to the influence of rupture directionality, hanging wall effect, slip-thrust effect, and significant long-period components, their time-frequency domain characteristics differ significantly from those of far-field ground motions, resulting in a stronger destructive force on engineering structures. Acceleration design response spectrum is a crucial basis for seismic design of structures. Domestic and international research shows that the long-period response spectrum of near-fault pulse-type ground motions is significantly higher than that of conventional ground motions. Therefore, using design response spectra obtained from mid- and far-field records for near-fault structural design is inherently unsafe.

[0003] Regarding the current standards, the European standard Euro Code 8 only requires that the response spectrum in the near-fault zone should not be lower than the conventional spectrum, but does not give a clear correction factor; the California bridge seismic design code in the United States adjusts the long period segment through an amplification factor; my country's "Code for Seismic Design of Buildings" stipulates that the spectral acceleration within 5 km of the fault distance should be multiplied by an amplification factor of 1.5, and 5 to 10 km should be multiplied by a factor of not less than 1.25; while my country's bridge seismic design codes only suggest avoiding faults and do not make clear requirements for the correction of the design spectrum. The existing correction methods are mostly based on peak amplification and fail to systematically consider the comprehensive variation law of near-fault ground motion in terms of amplification factor, characteristic period and attenuation index, so (1) the existing standards mainly determine the values ​​of characteristic period and attenuation index of near-fault ground motion standard spectrum based on mid- and far-field records, which fails to fully reflect the spectral characteristics of near-fault ground motion in the long period frequency band.

[0004] (2) Existing standards or related studies have made relatively rough provisions on the spectral amplitude of the long period segment of the standard spectrum, which makes it difficult to accurately depict the prominent characteristics of the long period component of near-fault ground motion.

[0005] (3) The existing standard spectrum does not distinguish between different site categories in enough detail. The difference in spectral parameters between site categories is only reflected in the characteristic period.

[0006] Therefore, to address the above issues, a method for calculating the spectral amplitude of design standards for near-seismic fault zones is needed. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this invention proposes a method for calculating the spectral amplitude of design specifications for near-seismic fault regions. This method solves the technical problem that existing correction methods are mostly based on peak amplification and fail to systematically consider the comprehensive variation of near-fault ground motion in terms of amplification coefficient, characteristic period, and attenuation index.

[0008] The technical solution adopted in this invention includes: Based on the site type of the target structural engineering site, the characteristic period T of the design standard spectrum is matched. g ; Based on the site type of the target structural engineering site, match the first attenuation index γ1 of the design standard spectrum; Then, based on the first attenuation index γ1 and the site type of the target structural engineering site, the second attenuation index γ2 of the standard spectrum is matched. Furthermore, for areas near earthquake faults, based on the characteristic period T g The standard spectrum formula is designed using the first attenuation index γ1 and the second attenuation index γ2, and the standard spectrum amplitude is calculated.

[0009] Furthermore, the site types of the target structural engineering sites include five categories: Category I0 sites, Category I1 sites, Category II sites, Category III sites, and Category IV sites. If the site type is Class I0, then T g Take 0.70s; if the site type is Class I1, then T g Take 0.75s; if the site type is Class II, then T g Take 0.85s; if the site type is Class III, then T g Take 1.05s; if the site type is Class IV, then T g Take 1.10s.

[0010] Furthermore, the first attenuation index γ1 of the design standard spectrum is matched according to the site type of the target structural engineering address; if the engineering site is a Class I0 site or a Class I1 site, then γ1 is 1.00. If the project site is a Class II site, then γ1 is taken as 1.05s; If the engineering site is a Class III or Class IV site, then γ1 is taken as 1.10s.

[0011] Furthermore, the step of matching the second attenuation index γ2 of the standard spectrum based on the first attenuation index γ1 and the site type of the target structural engineering address includes: For Class I0 and Class I1 sports fields, the second attenuation index γ2 is calculated as follows:

[0012] The calculation formulas for Class II, Class III, and Class IV venues are as follows: .

[0013] Furthermore, the aforementioned design standard spectrum formula, for calculating the standard spectrum amplitude, includes: When the characteristic period t of the near-earthquake fault region is between 0s and 0.1s, the expression for calculating the standard spectral amplitude β(t) is as follows: β(t) = 1.0 + 10·(β max -1.0)·t; When the characteristic period t of the near-seismic fault region is between 0.1s and 0.8T g The expression for calculating the standard spectral amplitude β(t) is as follows: β(t)=β max (Platform segment constant) When the characteristic period t of the near-seismic fault region is 0.8T g -1.5T g The expression for calculating the standard spectral amplitude β(t) is as follows:

[0014] When the characteristic period t of the near-seismic fault region is 1.5T g -5.0T g The expression for calculating the standard spectral amplitude β(t) is as follows: β(t)=(T g / t) γ1 ·β max ; When the characteristic period t of the near-seismic fault region is 5.0T g -10s, the standard spectral amplitude β(t) is calculated as follows: β(t) = 5.0 γ1-γ2 ·(T g / t) γ2 ·β max .

[0015] Furthermore, the present invention provides a computer storage medium storing a computer program that can run on a processor. When the processor executes the computer program, it implements the method for calculating the design standard spectral amplitude for near-seismic fault regions as described above.

[0016] Furthermore, the present invention provides an electronic device including a memory and a processor, the processor being configured to execute program instructions stored in the memory to implement the method described in any one of the above.

[0017] Furthermore, the present invention provides a computer program product, including a computer program that, when executed by a processor, implements the method described in any one of the above-described methods.

[0018] As can be seen from the above technical solution, the beneficial technical effects of the present invention are as follows: 1. It eliminates the conservative bias caused by discrepancies between the actual downward trend and the actual seismic motion, and can more accurately reflect the true spectral characteristics of near-fault ground motion, especially the long-period pulse characteristics, providing a more reasonable design basis for the seismic design of bridges, buildings and other engineering structures in near-fault areas. The standard spectrum of this invention and the spectrum of existing standards were calculated for each group of site categories. Attached Figure Description

[0019] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn to scale.

[0020] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a structural diagram of the storage medium of the present invention; Figure 3 This is a comparison chart of the standard spectrum of the present invention and the standard spectrum for Class I0 sites of the present invention; Figure 4 This is a comparison chart of the standard spectrum of this invention and the standard spectrum for Class I1 sites. Figure 5 This is a comparison chart of the standard spectrum of this invention and the standard spectrum for Class II sites of this invention; Figure 6 This is a comparison chart of the standard spectrum of the present invention and the standard spectrum for Class III sites of the present invention; Figure 7 This is a comparison chart of the standard spectrum of the present invention and the standard spectrum for Class IV sites of the present invention; Figure 8 This is a diagram illustrating an embodiment of the standard spectrum for Class II sites of the present invention. Detailed Implementation

[0021] The embodiments of the technical solution of the present invention will now be described in detail with reference to the accompanying drawings. These embodiments are merely illustrative of the technical solution of the present invention and are therefore intended to limit the scope of protection of the present invention.

[0022] It should be noted that, unless otherwise stated, the technical or scientific terms used in this application should have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0023] Example 1 like Figure 1 As shown, this embodiment provides a method for calculating the design standard spectral amplitude in near-seismic fault zones; the working principle of the embodiment is explained in detail below: The technical solution adopted in this invention includes: Based on the site type of the target structural engineering site, the characteristic period T of the design standard spectrum is matched. g ; Based on the site type of the target structural engineering site, match the first attenuation index γ1 of the design standard spectrum; Then, based on the first attenuation index γ1 and the site type of the target structural engineering site, the second attenuation index γ2 of the standard spectrum is matched. Furthermore, for areas near earthquake faults, based on the characteristic period T g The standard spectrum formula is designed using the first attenuation index γ1 and the second attenuation index γ2, and the standard spectrum amplitude is calculated.

[0024] In this embodiment, the site type of the target structural engineering address includes five categories, namely, Class I0 site, Class I1 site, Class II site, Class III site and Class IV site; If the site type is Class I0, then T g Take 0.70s; if the site type is Class I1, then T g Take 0.75s; if the site type is Class II, then T g Take 0.85s; if the site type is Class III, then T g Take 1.05s; if the site type is Class IV, then T g Take 1.10s, as shown in Table 1; Table 1. Characteristic period T in the corrected quasi-spectrum g Value (seconds)

[0025] In this embodiment, the first attenuation index γ1 of the design standard spectrum is matched according to the site type of the target structural engineering address; if the engineering site is a Class I0 site or a Class I1 site, then γ1 is 1.00. If the project site is a Class II site, then γ1 is taken as 1.05s; If the engineering site is a Class III or Class IV site, then γ1 is taken as 1.10s, as shown in Table 2; Table 2. Values ​​of the first attenuation index γ1 in the corrected quasi-spectrum.

[0026] In this embodiment, the step of matching the second attenuation index γ2 of the standard spectrum based on the first attenuation index γ1 and the site type of the target structural engineering address includes: For Class I0 and Class I1 sports fields, the second attenuation index γ2 is calculated as follows:

[0027] The calculation formulas for Class II, Class III, and Class IV venues are as follows: .

[0028] In this embodiment, the design standard spectrum formula for calculating the standard spectrum amplitude includes: When the characteristic period t of the near-earthquake fault region is between 0s and 0.1s, the expression for calculating the standard spectral amplitude β(t) is as follows: β(t) = 1.0 + 10·(β max -1.0)·t; When the characteristic period t of the near-seismic fault region is between 0.1s and 0.8T g The expression for calculating the standard spectral amplitude β(t) is as follows: β(t)=β max Where, β max This is a platform segment constant, which is 2.5.

[0029] When the characteristic period t of the near-seismic fault region is 0.8T g -1.5T g The expression for calculating the standard spectral amplitude β(t) is as follows:

[0030] When the characteristic period t of the near-seismic fault region is 1.5T g -5.0T g The expression for calculating the standard spectral amplitude β(t) is as follows: β(t)=(T g / t) γ1 ·β max ; When the characteristic period t of the near-seismic fault region is 5.0T g -10s, the standard spectral amplitude β(t) is calculated as follows: β(t) = 5.0 γ1-γ2 ·(T g / t) γ2 ·β max .

[0031] In this embodiment, the β max T g The value of γ1 is obtained through the following steps. Specifically, for the 2190 groups of horizontal near-fault ground motion records obtained through screening, they are first grouped according to 5 site categories. Within each group, the standard acceleration response spectrum of each record is calculated based on the Duhamel integral, as shown in the following expression:

[0032] In the formula, ω is the frequency, τ is the time, T is the time length of the ground motion acceleration time history, ξ is the damping ratio, a(τ) is the ground motion acceleration time history, and S(ω) is the solution of the acceleration response spectrum.

[0033] Based on this, using the four-segment standard spectral model as the objective function, the expression is as follows:

[0034] To address the segmented structure of the four-segment standard spectral model, piecewise least squares method is used to obtain initial estimates of each characteristic parameter. Fitting is then performed segmentally based on the physical meaning of each parameter and its corresponding period interval: the amplification factor β for the plateau segment... max Based on 0.1s to 0.8T g The average response spectrum amplitude of the interval is determined by fitting, and the expression is as follows:

[0035] Characteristic period T g The inflection point of the spectral values ​​transitioning from a constant plateau to power-law decay is obtained by locating the spectral values. The first decay exponent γ1 and the second decay exponent γ2 correspond to 1.5Tg to 5.0T, respectively. g 5.0T g The decay intervals of ~10s were linearized using a logarithmic transformation and then solved using the least squares method. The initial parameters obtained through piecewise fitting effectively narrowed the search range for subsequent optimization, improving overall calibration efficiency and result stability. In this embodiment, based on the initial parameters, a hybrid optimization framework constructed using differential evolution and particle swarm optimization is employed for global calibration, overcoming the limitations of interval connection bias and uneven fitting accuracy across the entire period inherent in piecewise least squares fitting. The optimization aims to minimize the sum of squared residuals between the fitted standard spectrum and the corresponding site-average standard response spectrum within the 0-10s period, with a period sampling step of 0.01s, covering all commonly used design period ranges for engineering structures. The optimization process uses the initial parameters obtained from piecewise least squares as the population center, and generates an initial population by setting search boundaries for each parameter within reasonable engineering intervals. In each iteration, the particle swarm optimization algorithm is first used to update individual positions and velocities, and to update local and global optimal solutions, leveraging its rapid convergence advantage in local optimization. Then, differential evolution is performed on the updated population, employing mutation, crossover, and greedy selection operations to generate a new generation of population with better fitness, relying on its strong global search capability to avoid the algorithm getting trapped in local optima.

[0036] The iteration terminates when the preset maximum number of iterations is reached, or when the change in the global optimal fitness over multiple consecutive generations falls below the convergence threshold. The final output is β for each set of site conditions. max Tg The global optimal calibration values ​​of γ1 and γ2 are shown in Table 4.

[0037] Table 4. Characteristic parameter calibration results

[0038] In this embodiment, the present invention targets 0.8 T during the fitting process. g ~1.5 T g Linear interpolation transition correction is introduced into the interval. First, control points are determined at both ends of the interval: the left endpoint corresponds to a period of 0.8T. g The spectral amplitude is taken as the peak value β of the plateau segment. max The period corresponding to the right endpoint is 1.5T. g The spectral amplitude is taken as the calculated value (1 / 1.5) of the first power function decay segment within that period. γ1 ·β max For any period t within the interval, the corresponding spectral amplitude is calculated using a two-point linear interpolation formula, as shown below: This step eliminates the characteristic period T of the traditional standard spectrum. g The direct transition to power-function decay in the vicinity causes abrupt amplitude changes and a conservative spectral value. Specifically, in this embodiment, a linear transition is used to smoothly connect the plateau segment and the first power-function decay segment, correcting the problem of the traditional spectral type at T. g The deviation at the inflection point makes the spectrum shape more closely match the actual attenuation law of near-fault ground motion, further improving the full-cycle fitting accuracy. The above calibration method ultimately provides the characteristic parameter values ​​for each site category.

[0039] In this embodiment, as Figures 3-7 This invention, based on a strong earthquake database, selects a large number of near-fault horizontal ground motion records according to established criteria for fault distance, moment magnitude, and peak ground acceleration. The large sample size and strong representativeness provide ample data support for the statistical calibration of standard spectral parameters. Furthermore, a calibration strategy combining least-squares piecewise fitting with differential evolution and particle swarm optimization algorithms is employed. Linear interpolation correction is introduced in the plateau segment to eliminate conservative bias caused by discrepancies with the actual downward trend, thus more accurately reflecting the true spectral characteristics of near-fault ground motions, especially long-period pulse characteristics. This provides a more reasonable design basis for the seismic design of bridges, buildings, and other engineering structures in near-fault areas. The root mean square error (RMSE) of the standard spectrum of this invention, existing standard spectra, and literature-corrected spectra relative to the actual average standard ground motion spectrum was calculated and compared for each site category. The comparison results are shown in Table 3.

[0040] Table 3 Comparison of Actual Ground Motion Mean Standard Spectrum and Design Spectrum for Each Site Category

[0041] In this embodiment, Table 3 shows that the RMSE of the actual near-fault earthquake record response spectrum obtained by the present invention is 20.2% lower than that of the design standard spectrum in the "Code for Seismic Design of Highway Bridges" (JTG / T 2231-01-2020); and 6.5% lower than that in reference [1]. This verifies that the standard spectrum obtained by the present invention has higher fitting accuracy and better engineering applicability in the near-fault region.

[0042] Example 2 In this embodiment, as Figure 2 The present invention provides a computer storage medium storing a computer program that can run on a processor. When the processor executes the computer program, it implements the method for calculating the design standard spectral amplitude for near-seismic fault regions as described above.

[0043] Example 3 In this embodiment, as Figure 8 Taking Class II sites as an example, based on Tables 1 and 2 and the expressions in Example 1, it can be seen that:

[0044]

[0045]

[0046] For a period t ranging from 0 s to 0.1 s, the design standard spectral amplitude β(t) is a straight line between 1.0 and the standard spectral plateau height of 2.5, as shown in the following formula.

[0047]

[0048] For a period t ranging from 0.1 s to 0.68 s, the standard spectral amplitude β(t) is designed to be 2.5 times the standard spectral plateau height, as shown in the following formula.

[0049]

[0050] For a period t ranging from 0.68 s to 1.275 s, the design standard spectral amplitude β(t) is a linear interpolation of the platform height and the starting position of the first descending segment of the exponent, as shown in the following formula.

[0051]

[0052] For a period t ranging from 1.275 s to 4.25 s, the standard spectral amplitude β(t) is designed as the first descending segment of the exponential curve, as shown in the following formula.

[0053]

[0054] For periods t ranging from 4.25 s to 10.0 s, the standard spectral amplitude β(t) is designed as the second decreasing segment of the exponential curve, as shown in the following formula.

[0055] .

[0056] Example 2 In this embodiment, the present invention provides an electronic device including a memory and a processor, wherein the processor is configured to execute program instructions stored in the memory to implement the method described in any one of the above embodiments.

[0057] In a specific implementation scenario, electronic devices may include, but are not limited to, microcomputers and servers. In addition, electronic devices may also include carrier devices such as laptops and tablets, without limitation.

[0058] Example 3 In this embodiment, the present invention provides a computer program product, including a computer program that, when executed by a processor, implements the method described in any one of the above descriptions. Specifically, the computer program product may be a software or program product containing a computer program, capable of running on a computing device or stored on any available medium.

[0059] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to 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 specification of the present invention.

Claims

1. A method for calculating the spectral amplitude of design standards in near-seismic fault zones, characterized in that, include: Based on the site type of the target structural engineering site, the characteristic period T of the design standard spectrum is matched. g ; Based on the site type of the target structural engineering site, match the first attenuation index γ1 of the design standard spectrum; Then, based on the first attenuation index γ1 and the site type of the target structural engineering site, the second attenuation index γ2 of the standard spectrum is matched. Furthermore, for areas near earthquake faults, based on the characteristic period T g The standard spectrum formula is designed using the first attenuation index γ1 and the second attenuation index γ2, and the standard spectrum amplitude is calculated.

2. The method for calculating the spectral amplitude of design standards in near-seismic fault zones according to claim 1, characterized in that, The site types of the target structural engineering sites include five categories: Category I0, Category I1, Category II, Category III, and Category IV. If the site type is Class I0, then T g Take 0.70s; If the site type is Class I1, then T g Take 0.75s; if the site type is Class II, then T g Take 0.85s; if the site type is Class III, then T g Take 1.05s; if the site type is Class IV, then T g Take 1.10s.

3. The method for calculating the spectral amplitude of design standards in near-seismic fault zones according to claim 1, characterized in that, The first attenuation index γ1 of the design standard spectrum is matched according to the site type of the target structural engineering site; if the engineering site is a Class I0 site or a Class I1 site, then γ1 is 1.

00. If the project site is a Class II site, then γ1 is taken as 1.05s; If the engineering site is a Class III or Class IV site, then γ1 is taken as 1.10s.

4. The method for calculating the spectral amplitude of design standards in near-seismic fault zones according to claim 1, characterized in that, The second attenuation index γ2 of the standard spectrum is matched based on the first attenuation index γ1 and the site type of the target structural engineering site. include: For Class I0 and Class I1 sports fields, the second attenuation index γ2 is calculated as follows: The calculation formulas for Class II, Class III, and Class IV sports fields are as follows: 。 5. The method for calculating the spectral amplitude of design standards in near-seismic fault zones according to claim 1, characterized in that, The aforementioned design standard spectrum formula, for calculating the standard spectrum amplitude, includes: When the characteristic period t of the near-earthquake fault region is between 0s and 0.1s, the expression for calculating the standard spectral amplitude β(t) is as follows: β(t)=1.0+10·(β max -1.0)·t; When the characteristic period t of the near-seismic fault region is between 0.1s and 0.8T g The expression for calculating the standard spectral amplitude β(t) is as follows: β(t)=β max (Platform segment constant) When the characteristic period t of the near-seismic fault region is 0.8T g -1.5T g The expression for calculating the standard spectral amplitude β(t) is as follows: When the characteristic period t of the near-seismic fault region is 1.5T g -5.0T g The expression for calculating the standard spectral amplitude β(t) is as follows: β(t)=(T g / t) γ1 ·b max ; When the characteristic period t of the near-seismic fault region is 5.0T g -10s, the standard spectral amplitude β(t) is calculated as follows: β(t)=5.0 γ1-γ2 ·(T g / t) γ2 ·b max 。 6. A computer storage medium storing a computer program executable on a processor, characterized in that, When the processor executes the computer program, it implements the method for calculating the design standard spectral amplitude of near-seismic fault regions as described in any one of claims 1-5.

7. An electronic device, characterized in that, It includes a memory and a processor, the processor being configured to execute program instructions stored in the memory to implement the method of any one of claims 1-5.

8. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1-5.

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