Method for determining incident seismic waves based on three-component seismic records

Abstract

The invention discloses a method for determining an incident seismic wave based on a three-component seismic record. The method specifically comprises the following steps: step 1, determining propagation velocities vP and vS of a seismic P wave and a seismic S wave on the ground surface of a site; 2, three-component seismic oscillation time histories ax, ay and az are selected; step 3, determining an incident angle alpha of the seismic P wave propagating to the ground and an azimuth angle theta of the projection of the incident direction on the horizontal plane; step 4, calculating an incident angle beta of the earthquake S wave propagating to the ground; 5, calculating a coefficient related to the seismic wave propagation direction; and step 6, according to the step 5, obtaining calculation expressions of the two components, namely the SV wave aSV and the SH wave aSH of the P wave aP and the S wave of the incident earthquake, so as to obtain time histories of the incident waves aP, aSV and aSH. The problem that oblique incidence seismic waves are inaccurately judged in current seismic response analysis is solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of earthquake engineering and disaster reduction and prevention in the water conservancy and civil construction engineering industry, and relates to a method for determining incident seismic waves based on three-component seismic records. Background Art

[0002] According to the relationship between the propagation direction and vibration direction of seismic waves, seismic waves emitted from the earthquake source can be divided into two types: P waves (longitudinal waves) and S waves (transverse waves). P waves vibrate along the propagation direction, S waves vibrate perpendicular to the propagation direction, and S waves can be further divided into two mutually perpendicular components: SV waves and SH waves. Among them, SV waves and P waves are located in a plane perpendicular to the ground, while SH waves are perpendicular to the plane. When these seismic waves propagate upward and reach the ground, they form seismic waves that are incident obliquely to the ground, referred to as incident seismic waves or incident waves. The incident seismic waves are reflected at the ground and cause ground vibrations of a certain duration, which are called seismic motions. The change process of seismic motions over time is usually expressed as x 、 y 、 z The three-component representation is called a seismic time history or seismic record. The incident wave and seismic motion can be acceleration, velocity or displacement, and the corresponding time history is the acceleration time history, velocity time history or displacement time history respectively.

[0003] When calculating the seismic response of an engineering site and its structures to obliquely incident seismic waves, it is necessary to input seismic P waves, SV waves, or SH waves propagating in a certain direction. These waves are collectively referred to as incident waves and are typically the applied loads in dynamic calculations. When inputting incident waves, the current common practice is to treat the horizontal component of the ground motion as an SV wave or SH wave, and the vertical component as a P wave. After making necessary adjustments, these components are used as the incident wave to calculate the seismic response. In reality, the incident wave and the ground motion it causes are two completely different concepts. Only in the case of vertical incidence is the incident wave exactly half the ground motion. Therefore, the above processing method is only an approximation for the case where the seismic wave is nearly vertically incident on the ground. If the propagation direction of the seismic wave is at a large angle to the vertical, such as an angle of incidence greater than 45°, the assumed approximate incidence condition no longer holds, and this simplified method of processing the incident wave is no longer applicable. Therefore, it is particularly necessary to find a method to reasonably determine the incident seismic wave. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for determining incident seismic waves based on three-component seismic records, which solves the problem of inaccurate judgment of oblique incident seismic waves in current seismic response analysis.

[0005] The technical solution adopted by the present invention is a method for determining incident seismic waves based on three-component seismic records, which specifically includes the following steps: Step 1: Determine the propagation speed of the surface earthquake P wave and earthquake S wave vP 、 v S ; Step 2: Select the three-component earthquake time history a x 、 a y 、 a z ; Step 3: Determine the incident angle of the earthquake P wave when it propagates to the ground α and the azimuth of the projection of the incident direction on the horizontal plane i ; Step 4: Calculate the incident angle of the earthquake S wave when it propagates to the ground β ; Step 5, calculating the coefficient related to the propagation direction of the seismic wave; Step 6: According to step 5, get the incident seismic P wave a P , two components of the S wave, the SV wave a SV and SH waves a SH The calculation expression of the incident wave is obtained a P 、 a SV and a SH schedule.

[0006] The present invention is also characterized in that: In step 3, the angle of incidence α The value range is: 0°< α <90°.

[0007] In step 3, the azimuth of the projection of the incident direction on the horizontal plane i The value range is: 0°< i <360°.

[0008] In step 4, the following formula (1) is used to calculate the earthquake S wave incident angle: β : (1).

[0009] In step 5, the coefficients related to the propagation direction of seismic waves include c P1 、 c P2 、 c P3 、 c SV1 、 c SV2 、 cSV3 、 c SH1 and c SH2 .

[0010] In step 5, c P1 、 c P2 、 c P3 、 c SV1 、 c SV2 、 c SV3 、 c SH1 and c SH2 The calculation formula is as follows: (2) (3) (4) (5) (6) (7) (8) (9).

[0011] In step 6, the incident seismic wave is calculated by the wave field superposition principle. a P 、 a SV and a SH , the specific formula is as follows: (10) (11) (12).

[0012] In step 6, the three-component ground motion at each time sampling point is a x 、 a y 、 a z Calculations are performed sequentially. After all sampling points are calculated, the incident seismic wave is formed. a P 、 a SV and aSH time series, i.e. the time history of incident seismic waves.

[0013] The beneficial effect of the present invention is that the mathematical expression of the incident seismic wave derived from the elastic wave propagation theory accurately reflects the relationship between the actual three-component seismic motion and the incident P wave, SV wave and SH wave, which not only avoids complicated mechanical deduction and a large amount of numerical calculation, but also frees the calculation accuracy of the incident wave from the limitation of the incident angle, and solves the problem of how to correctly obtain seismic P waves, SV waves and SH waves in the seismic response analysis of engineering sites and structures due to oblique incident seismic waves. It can provide reliable input waves for earthquake cracking analysis, engineering seismic design, earthquake damage prevention and control calculations, etc., and is particularly suitable for seismic design of major infrastructure that requires input of high-precision seismic waves. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 Schematic diagram of the vibration direction of seismic waves in space in the method for determining incident seismic waves based on three-component seismic records of the present invention; Figure 2 The present invention is a method for determining the incident seismic wave based on three-component seismic records; the incident direction of the seismic wave in a three-dimensional coordinate system; Figure 3 is a graph showing a time history of three-component seismic acceleration in Example 1 of the method for determining incident seismic waves based on three-component seismic records of the present invention; 4( a ) to 4 ( b ) are time history graphs of the acceleration of the incident seismic wave and its error in Example 1 of the method for determining the incident seismic wave based on three-component seismic records of the present invention; 5( a ) to 5 ( c ) are time history graphs of the ground motion and the acceleration of the incident wave in Example 2 of the method for determining the incident seismic wave based on three-component seismic records of the present invention; 6( a ) to 6 ( c ) are graphs showing the time history of three-component seismic acceleration in Example 3 of the method for determining incident seismic waves based on three-component seismic records of the present invention; 7( a ) to 7 ( c ) are time history graphs of acceleration of incident seismic waves in Example 3 of the method for determining incident seismic waves based on three-component seismic records of the present invention; 8( a ) to 8 ( c ) are three-component seismic velocity time history graphs of Example 4 of the method for determining incident seismic waves based on three-component seismic records of the present invention; 9( a ) to 9 ( c ) are time history graphs of the seismic incident wave velocity in Example 4 of the method for determining the incident seismic wave based on three-component seismic records of the present invention; FIG10( a ) to FIG10 ( c ) are graphs showing the time history of three-component seismic displacements in Example 5 of the method for determining incident seismic waves based on three-component seismic records according to the present invention; FIG11( a ) to FIG11 ( c ) are displacement time history curves of incident seismic waves in Example 5 of the method for determining incident seismic waves based on three-component seismic records of the present invention; FIG12( a ) to FIG12 ( c ) are displacement time history curves of incident seismic waves in Example 6 of the method for determining incident seismic waves based on three-component seismic records of the present invention. DETAILED DESCRIPTION

[0015] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0016] The method of determining incident seismic waves based on three-component seismic records of the present invention specifically includes the following steps: Step 1: Determine the seismic P-wave propagation velocity at the project site based on the site survey report, test report, or local experience. v P and earthquake S-wave propagation velocity v S If there are multiple strata on the site, the surface is the stratum closest to the ground.

[0017] Step 2: Select the three-component seismic time history suitable for site earthquake analysis based on the type and seismic intensity of the project site. a x 、 a y 、 a z Earthquake motion can be displacement, velocity or acceleration, and its time course can be obtained by artificial synthesis or by adjusting the actual earthquake wave. The vibration direction of the earthquake wave in space is as follows: Figure 1 shown.

[0018] Step 3: Determine the incident angle of the earthquake P wave when it propagates to the ground α (0°< α <90°, the azimuth of the projection of the incident direction on the horizontal plane (0°< i <360°). The incident direction of the seismic wave is as follows Figure 2 shown.

[0019] Step 4: Apply equation (1) to calculate the incident angle of the seismic S wave β , where formula (1) is derived from Snell's theorem: (1) Step 5: Use the following formulas (2) to (9) to calculate the coefficient c P1 、 c P2 、 c P3 、 cSV1 、 c SV2 、 c SV3 、 c SH1 and c SH2 These coefficients are only related to the propagation direction of seismic waves, so they are called seismic wave propagation direction coefficients. They reflect the relationship between the seismic waves incident on the ground and the three-component seismic motion.

[0020] (2) (3) (4) (5) (6) (7) (8) (9) Step 6: The seismic wave propagation direction coefficient obtained in step 5 c P1 、 c P2 、 c P3 、 c SV1 、 c SV2 、 c SV3 、 c SH1 and c SH2 , the incident P wave is calculated by the wave field superposition principle a P , incident SV wave a SV and the incident SH wave a SH Mathematical expressions (10) to (12): (10) (11) (12) Step 7: Calculate the incident wave at the ground according to expressions (10) to (12). It should be noted that since the earthquake motion is a time series of finite length, not a single value, the three-component earthquake motion at each time sampling point needs to be calculated. ax 、 a y 、 a z Calculate in sequence. After completing the calculation of the seismic motion of all sampling points according to this step, the incident P wave can be obtained. a P , incident SV wave a SV and the incident SH wave a SH schedule.

[0021] Example 1 Step 1: According to the geological survey report, the seismic wave velocity near the surface of a certain project site v p 、 v s They are equal to 670m / s and 330m / s respectively; Step 2: The site artificial earthquake acceleration time history obtained by theoretical calculation is as follows: Figure 3 As shown in the figure, the time sampling interval is 0.001s and the duration is 0.4s.

[0022] Step 3: Calculate the incident angle of the selected earthquake P wave at the ground according to the theoretical calculation α and the azimuth of the projection of the incident direction on the horizontal plane i ,Pick α = 15°, i = 210°.

[0023] Step 4: Calculate the incident angle of the earthquake S wave when it propagates to the ground according to formula (1): β :

[0024] Step 5: Set the angle parameter α = 15°, i = 210°, β = 7.3239 Substituting into equations (2) to (9), we can obtain:

[0025]

[0026]

[0027]

[0028]

[0029]

[0030]

[0031]

[0032] Step 6: Substitute the calculation results of step 5 into equations (10) to (12) to obtain the calculated incident wave a P 、 a SV and a SH The expression:

[0033]

[0034]

[0035] Writing the above formula in matrix form, we have

[0036] Step 7: convert the three-component earthquake time history a in step 2 into x 、a y 、a z Substituting the expression in the previous step, we can calculate the incident wave a as shown in Figure 4(a): P 、a SV and a SH The time course of the error (absolute value) between this result and the theoretical value is shown in Figure 4(b). (In scientific notation, E in Figure 4(b) represents multiplication by a power of 10, which is a concise way to write large and small numbers.) As can be seen from the figure, the error between the calculated values of SV waves, SH waves, and P waves and the theoretical values is very small, with the maximum error not exceeding 1.2×10 -4 m / s 2 , indicating that the above calculation method is correct.

[0037] Example 2 If the i Take 180°, keep other parameters unchanged, and follow the above steps to obtain the acceleration time history of the earthquake motion and the incident wave as shown in Figure 5 (a) and Figure 5 (b). Among them, Figure 5 (a) is the acceleration time history of the incident SV wave and the earthquake motion. x The acceleration time history of the component, Figure 5 (b) is the incident SH wave and the ground motion y The acceleration time history of the component, Figure 5 (c) is the incident P wave and the ground motion z As can be seen from the figure, the shapes of the incident SV wave, SH wave and P wave are respectively related to the earthquake components. a x 、 a y 、 az This indicates that when the earthquake wave is incident on the ground approximately vertically, the magnitude of the incident wave acceleration is approximately 1 / 2 of the ground acceleration caused by it.

[0038] Example 3 Formation parameters v p 、 v s 670m / s and 330m / s respectively; incident P wave α = 60°, i = 225°; the seismic acceleration time histories shown in Figures 6(a), 6(b), and 6(c) are selected, where Figures 6(a), 6(b), and 6(c) are the seismic acceleration time histories of x、y、z Component, time sampling interval 0.02s, duration 30s. According to the steps of Example 1, the acceleration time history of the incident wave is calculated as shown in Figure 7 (a), Figure 7 (b), and Figure 7 (c). Figures 7 (a), 7 (b), and 7 (c) are the acceleration time histories of the incident SV wave, SH wave, and P wave, respectively. It can be seen from the figure that the incident SV wave, SH wave, and P wave are related to the ground motion component. a x 、 a y 、 a z There are clear differences in shape. This indicates that the similarity in the time history between the incident wave and the ground motion only applies when the incident angle is small. As the incident angle increases, the difference between the two becomes increasingly significant. In this case, if the incident wave is still replaced by adjusting the ground motion, large calculation errors will occur.

[0039] Example 4 The seismic velocity time histories shown in Figures 8(a), 8(b), and 8(c) are used, where Figures 8(a), 8(b), and 8(c) are the seismic velocity time histories of the earthquake. x、y、z Component, other parameters are the same as those in Example 3. According to the steps of Example 1, the incident wave velocity history is calculated as shown in Figures 9 (a), 9 (b), and 9 (c). Figures 9 (a), 9 (b), and 9 (c) are the velocity history of the incident SV wave, SH wave, and P wave, respectively. It can be seen from the figure that, similar to the acceleration history, the velocity history of the incident SV wave, SH wave, and P wave is similar to the seismic velocity history component. a x 、 a y 、 a z There are also obvious differences in shape.

[0040] Example 5 The earthquake motion displacement time history shown in Figure 10 (a), Figure 10 (b), and Figure 10 (c) are selected, where Figure 10 (a), Figure 10 (b), and Figure 10 (c) are the earthquake motion displacement time history. x、y、z Component, other parameters are the same as those in Example 3. According to the steps of Example 1, the incident wave displacement time history is calculated as shown in Figures 11 (a), 11 (b), and 11 (c). Figures 11 (a), 11 (b), and 11 (c) are the displacement time history of the incident SV wave, SH wave, and P wave, respectively. It can be seen from the figure that, similar to the acceleration and velocity time history, the displacement time history of the incident SV wave, SH wave, and P wave is similar to the ground motion displacement time history component. a x 、 a y 、 a z There are also clear differences in shape, which are more pronounced due to the lower frequency of the displacement time history relative to the acceleration and velocity time history.

[0041] Example 6 The incident P wave parameters in Example 5 are adjusted to α = 15°, i = 180°, with other parameters unchanged, the incident wave displacement histories are calculated according to the steps of Example 1, as shown in Figures 12(a), 12(b), and 12(c). Figures 12(a), 12(b), and 12(c) represent the displacement histories of the incident SV wave, SH wave, and P wave, respectively. As can be seen from the figures, as the incident angle decreases, the incident wave displacement histories closely resemble the three-component ground motion displacement histories (Figures 10(a), 10(b), and 10(c)). Numerically, the latter is approximately twice the former, indicating that at small incident angles, the difference in shape between the two is not significant, and their numerical values are similarly exponential. The relationship between the ground motion and the incident wave displacement histories in this example is similar to the relationship between the ground motion and the incident wave acceleration histories in Example 2.

Claims

1. A method for determining incident seismic waves based on three-component seismic records, characterized in that: The specific steps include: Step 1: Determine the propagation speed of the surface earthquake P wave and earthquake S wave v P 、 v S ; Step 2: Select the three-component earthquake time history a x 、 a y 、 a z ; Step 3: Determine the incident angle of the earthquake P wave when it propagates to the ground α and the azimuth of the projection of the incident direction on the horizontal plane θ ; Step 4: Calculate the incident angle of the earthquake S wave when it propagates to the ground β ; Step 5, calculating the coefficient related to the propagation direction of the seismic wave; Step 6: According to step 5, get the incident seismic P wave a P , two components of the S wave and the SV wave a SV and SH waves a SH The calculation expression of the incident wave is obtained a P 、 a SV and a SH schedule.

2. The method for determining incident seismic waves based on three-component seismic records according to claim 1, characterized in that: In step 3, the incident angle α The value range is: 0°< α < 90°.

3. The method for determining incident seismic waves based on three-component seismic records according to claim 2, characterized in that: In step 3, the azimuth of the projection of the incident direction on the horizontal plane θ The value range is: 0°< θ < 360°.

4. The method for determining incident seismic waves based on three-component seismic records according to claim 3, characterized in that: In step 4, the following formula (1) is used to calculate the earthquake S wave incident angle: β : （1）。 5. The method for determining incident seismic waves based on three-component seismic records according to claim 4, characterized in that: In step 5, the coefficients related to the propagation direction of seismic waves include c P1 、 c P2 、 c P3 、 c SV1 、 c SV2 、 c SV3 、 c SH1 and c SH2 .

6. The method for determining incident seismic waves based on three-component seismic records according to claim 5, characterized in that: In the step 5, c P1 、 c P2 、 c P3 、 c SV1 、 c SV2 、 c SV3 、 c SH1 and c SH2 The calculation formula is as follows: （2） （3） （4） （5） （6） （7） （8） （9）。 7. The method for determining incident seismic waves based on three-component seismic records according to claim 6, characterized in that: In step 6, the incident seismic wave is calculated by the wave field superposition principle. a P 、 a SV and a SH , the specific formula is as follows: （10） （11） （12）。 8. The method for determining incident seismic waves based on three-component seismic records according to claim 7, characterized in that: In step 6, the three-component earthquake motion at each time sampling point is a x 、 a y 、 a z Calculations are performed sequentially. After all sampling points are calculated, the incident seismic wave is formed. a P 、 a SV and a SH time series, i.e. the time history of incident seismic waves.

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