阅读说明：本技术 一种基于地层信息的场地卓越周期的精简计算方法 (Simplified calculation method for site excellent period based on stratum information ) 是由 范留明 杨洋 凌光波 于 2019-09-24 设计创作，主要内容包括：本发明公开了一种基于地层信息的场地卓越周期的精简计算方法,应用卓越周期简便算法得到卓越周期的估计值,根据该值大小设定除场地地层信息以外的所有计算参数；把场地土视为地震波信号滤波器,计算脉冲波作用下的地面地震时程,并对其进行傅立叶变换得到振幅谱；通过判断振幅谱极大值与时间(或频率)的关系,获得高精度的卓越周期计算值。本发明一种基于地层信息的场地卓越周期的精简计算方法,计算过程简单、计算精度高。(The invention discloses a simplified calculation method of a site excellent period based on stratum information, which is characterized in that an estimated value of the excellent period is obtained by applying an excellent period simple algorithm, and all calculation parameters except the site stratum information are set according to the value; taking the field soil as a seismic wave signal filter, calculating a ground seismic time course under the action of pulse waves, and performing Fourier transform on the ground seismic time course to obtain an amplitude spectrum; by judging the relation between the maximum value of the amplitude spectrum and the time (or frequency), a high-precision excellent period calculation value is obtained. The simplified calculation method for the site excellent period based on the stratum information is simple in calculation process and high in calculation precision.)

1. A simplified calculation method for a site excellent period based on stratum information is characterized by comprising the following steps:

step 1, determining the number n of the site and the stratum density rho according to the investigation result of geotechnical engineering_iShear velocity v_iAnd the thickness h of the formation_i(ii) a Wherein, i is 1, 2.. said., n;

step 2, calculating a site excellent period estimated value t₀；

Step 3, calculating the seismic wave duration t_lAnd a time sampling interval Δ t;

step 4, calculating the sampling point number nt of the ground seismic wave holding time and the sampling point number nt of the seismic wave propagation time in the stratum i_iThe number nT of sampling points of the Fourier periodic spectrum of the ground seismic wave;

step 5, calculating the reflection coefficient R of the seismic waves at the boundary interface of the stratum i and the stratum i +1_i；

Step 6, calculating the time course u of the ground seismic wave₀ ^d；

Step 7, seismic wave time course u₀ ^dCarrying out attenuation treatment according to time;

step 8, performing Discrete Fourier Transform (DFT) on the seismic wave time interval u to obtain Fu (k);

step 9, judging whether the amplitude spectrum | Fu (k) | has a maximum value, if not, expanding nT by 20%, and returning to the step 8; if yes, determining the site excellent period T₀。

2. The method as claimed in claim 1, wherein in the step 2, the estimated value t of the period of excellence in the field is obtained₀The formula is as follows:

t₀＝4(h₁/v₁+h₂/v₂+……+h_n/v_n) (1)。

3. the method for performing reduced computation of site excellent period based on formation information as claimed in claim 2, wherein in the step 3, the seismic wave duration t_lThe formula is as follows:

t_l≥10t₀ (2)

the time sampling interval Δ t is calculated by the following equation (3):

Δt<0.02min(h₁/v₁，h₂/v₂，……，h_n/v_n) (3)。

4. the formation information-based site excellent period retrenchment meter of claim 3The calculation method is characterized in that in the step 4, the sampling point number nt of the ground seismic wave holding time and the sampling point number nt of the seismic wave propagation time in the stratum i_iThe sampling point number nT of the Fourier cycle spectrum of the ground seismic wave is calculated by the following formula:

nt＝Int(t_l/Δt) (4)

nt_i＝Int(h_i/v_i/Δt) (5)

nT＝Int(t₀/Δt) (6)

wherein Int is an integer function, i is 1, 2.

5. The method for performing a rehearsal calculation of a site excellent period based on formation information as claimed in claim 4, wherein in the step 5, the reflection coefficient R is_iThe formula is as follows:

R_i＝(ρ_i+1v_i+1-ρ_iv_i)/(ρ_i+1v_i+1+ρ_iv_i) Wherein, i is 1, 2, a. (7)

R_n1, wherein i ═ n; (8).

6. The method of claim 5, wherein in step 6, the seismic time interval u is a time interval of the seismic wave₀ ^dThe formula is as follows:

u₀ ^d(j)＝-u₁ ^p(j-nt₁)

u₁ ^d(j)＝(1+R₁)u₀ ^d(j-nt₁)-R₁u₂ ^p(j-nt₂)

u₁ ^p(j)＝R₁u₀ ^d(j-nt₁)+(1-R₁)u₂ ^p(j-nt₂)

u₂ ^d(j)＝(1+R₂)u₁ ^d(j-nt₂)-R₂u₃ ^p(j-nt₃)

u₂ ^p(j)＝R₂u₁ ^d(j-nt₂)+(1-R₂)u₃ ^p(j-nt₃)

......

u_i ^d(j)＝(1+R_i)u_i-1 ^d(j-nt_i)-R_iu_i+1 ^p(j-nt_i+1)

u_i ^p(j)＝R_iu_i-1 ^d(j-nt_i)+(1-R_i)u_i+1 ^p(j-nt_i+1)

......

u_n-1 ^d(j)＝(1+R_n-1)u_n-2 ^d(j-nt_n-1)-R_n-1u_n ^p(j-nt_n)

u_n-1 ^p(j)＝R_n-1u_n-2 ^d(j-nt_n-1)+(1-R_n-1)u_n ^p(j-nt_n)

u_n ^p(j)＝u_n ^d(j-nt_n)

wherein u is₀ ^dIs the ground seismic wave time course; u. of_i ^d、The seismic wave time courses of the lower interface and the upper interface of the formation i are respectively, wherein i is 1, 2. u. of₀ ^d、u_i ^d、Are time series, j denotes a time sample number, j 0, 1.

7. The method for simplifying calculation of excellence period of field based on formation information as claimed in claim 1, wherein in said step 7, the seismic wave is processed according to the following formulaJourney u₀ ^dCarrying out attenuation treatment according to time:

u(j)＝u₀ ^d(j)exp[-βjΔt] (9)

wherein the attenuation coefficient beta is-ln delta/t_l(ii) a Delta is a calculation precision value for controlling the attenuation coefficient and satisfies 0<δ<0.01；j＝0，1，......，nt-1。

8. The method for simplifying calculation of site excellent period based on formation information as claimed in claim 7, wherein in the step 8, the seismic time interval u is subjected to Discrete Fourier Transform (DFT) according to the following formula:

wherein i is an imaginary unit; k is 0, 1,.. cnt-1.

9. The method for simplifying calculation of site excellent period based on formation information as claimed in claim 8, wherein in the step 9, it is determined whether the amplitude spectrum | fu (k) | has a maximum value according to the following formula:

| Fu (k) | > | Fu (k-1) | and | Fu (k) | > | Fu (k +1) | (11)

|Fu(k)|>0.5max(|Fu(1)|，|Fu(2)|，......，|Fu(nT-1)|) (12)

If | Fu (k) | satisfies the above condition, the site excellent period is calculated by the following formula:

T₀＝0.5t₀+kΔt (13)。

Technical Field

The invention belongs to the technical field of geotechnical engineering investigation, and particularly relates to a simplified calculation method for a site excellent period based on stratum information.

Background

The excellent period refers to a harmonic component of seismic waves which have resonance action with the foundation soil layer. At present, methods for determining the excellent period of a field are roughly classified into two major types, namely a direct measurement method and a wave velocity method. In any method, calculation parameters except formation information need to be input, and even the calculation parameters need to be debugged, so that a proper calculation result can be obtained; and the calculation precision is not high, or the calculation process is complicated.

Disclosure of Invention

The invention aims to provide a simplified calculation method of a site excellent period based on stratum information, which is simple in calculation process and high in calculation precision.

The technical scheme adopted by the invention is that a simplified calculation method of the site excellent period based on stratum information is implemented according to the following steps:

step 1, determining the number n of the site and the stratum density rho according to the investigation result of geotechnical engineering_iShear velocity v_iAnd the thickness h of the formation_i(ii) a Wherein, i is 1, 2.. said., n;

step 2, calculating a site excellent period estimated value t₀；

Step 3, calculating the seismic wave duration t_lAnd a time sampling interval Δ t;

step 4, calculating the sampling point number nt of the ground seismic wave holding time and the sampling point number nt of the seismic wave propagation time in the stratum i_iThe number nT of sampling points of the Fourier periodic spectrum of the ground seismic wave;

step 5, calculating the reflection coefficient R of the seismic waves at the boundary interface of the stratum i and the stratum i +1_i；

Step 6, calculating the time course u of the ground seismic wave₀ ^d；

Step 7, seismic wave time course u₀ ^dCarrying out attenuation treatment according to time;

step 8, performing Discrete Fourier Transform (DFT) on the seismic wave time interval u to obtain Fu (k);

step 9, judging whether the amplitude spectrum | Fu (k) | has a maximum value, if not, expanding nT by 20%, and returning to the step 8; if yes, determining the site excellent period T₀。

The invention is also characterized in that:

in step 2, site excellent period estimated value t₀The formula is as follows:

t₀＝4(h₁/v₁+h₂/v₂+……+h_n/v_n) (1)。

in step 3, the seismic wave duration t_lThe formula is as follows:

t_l≥10t₀ (2)

the time sampling interval Δ t is calculated by the following equation (3):

Δt<0.02min(h₁/v₁，h₂/v₂，……，h_n/v_n) (3)。

in step 4, sampling point number nt of ground seismic wave holding time and sampling point number nt of seismic wave propagation time in stratum i_iThe sampling point number nT of the Fourier cycle spectrum of the ground seismic wave is calculated by the following formula:

nt＝Int(t_l/Δt) (4)

nt_i＝Int(h_i/v_i/Δt) (5)

nT＝Int(t₀/Δt) (6)

wherein Int is an integer function, i is 1, 2.

In step 5, the reflection coefficient R_iThe formula is as follows:

R_i＝(ρ_i+1v_i+1-ρ_iv_i)/(ρ_i+1v_i+1+ρ_iv_i) Wherein, i is 1, 2, a. (7)

R_n1, wherein i ═ n; (8).

In step 6, seismic wave time course u₀ ^dThe formula is as follows:

u₀ ^d(j)＝-u₁ ^p(j-nt₁)

u₁ ^d(j)＝(1+R₁)u₀ ^d(j-nt₁)-R₁u₂ ^p(j-nt₂)

u₁ ^p(j)＝R₁u₀ ^d(j-nt₁)+(1-R₁)u₂ ^p(j-nt₂)

u₂ ^d(j)＝(1+R₂)u₁ ^d(j-nt₂)-R₂u₃ ^p(j-nt₃)

u₂ ^p(j)＝R₂u₁ ^d(j-nt₂)+(1-R₂)u₃ ^p(j-nt₃)

......

u_i ^d(j)＝(1+R_i)u_i-1 ^d(j-nt_i)-R_iu_i+1 ^p(j-nt_i+1)

u_i ^p(j)＝R_iu_i-1 ^d(j-nt_i)+(1-R_i)u_i+1 ^p(j-nt_i+1)

......

u_n-1 ^d(j)＝(1+R_n-1)u_n-2 ^d(j-nt_n-1)-R_n-1u_n ^p(j-nt_n)

u_n-1 ^p(j)＝R_n-1u_n-2 ^d(j-nt_n-1)+(1-R_n-1)u_n ^p(j-nt_n)

u_n ^p(j)＝u_n ^d(j-nt_n)

wherein u is₀ ^dIs the ground seismic wave time course; u. of_i ^d、The seismic wave time courses of the lower interface and the upper interface of the formation i are respectively, wherein i is 1, 2. u. of₀ ^d、u_i ^d、Are time series, j denotes a time sample number, j 0, 1.

In step 7, the seismic wave time travel u is calculated according to the following formula₀ ^dCarrying out attenuation treatment according to time:

u(j)＝u₀ ^d(j)exp[-βjΔt] (9)

wherein the attenuation isCoefficient beta ═ ln delta/t_l(ii) a Delta is a calculation precision value for controlling the attenuation coefficient and satisfies 0<δ<0.01；j＝0，1，......，nt-1。

In step 8, performing Discrete Fourier Transform (DFT) on the seismic wave time interval u according to the following formula:

wherein i is an imaginary unit; k is 0, 1,.. cnt-1.

In step 9, whether the amplitude spectrum | fu (k) | has a maximum value is determined according to the following formula:

| Fu (k) | > | Fu (k-1) | and | Fu (k) | > | Fu (k +1) | (11)

|Fu(k)|>0.5max(|Fu(1)|，|Fu(2)|，......，|Fu(nT-1)|) (12)

If | Fu (k) | satisfies the above condition, the site excellent period is calculated by the following formula:

T₀＝0.5t₀+kΔt (13)。

the invention has the beneficial effects that:

the method adopts a simple algorithm with an excellent period to obtain an estimated value of the excellent period, and sets all calculation parameters except the field stratum information according to the value; taking the field soil as a seismic wave signal filter, calculating a ground seismic time course under the action of pulse waves, and performing Fourier transform on the ground seismic time course to obtain an amplitude spectrum; by judging the relation between the maximum value of the amplitude spectrum and the time (or frequency), a high-precision excellent period calculation value is obtained.

Drawings

FIG. 1 is a field stratum model in the method for simplifying calculation of excellent period of field based on stratum information;

FIG. 2 is a simplified calculation method of a distinguished period of a field based on stratum information, which is disclosed by embodiment 1, of an original ground earthquake time course;

FIG. 3 is a simplified calculation method of a distinguished period of a field based on stratum information, which is used for embodiment 1 of the invention, and the earthquake time course after attenuation processing is carried out;

FIG. 4 is a Fourier amplitude spectrum of seismic time course of embodiment 1 of the method for simplifying calculation of excellent period of field based on stratum information;

FIG. 5 is a simplified calculation method of excellent period of field based on stratum information, in accordance with embodiment 2, the time course of original ground earthquake;

FIG. 6 is a simplified calculation method of a site excellent period based on stratum information according to the invention, and the seismic time course after attenuation processing is performed in embodiment 2;

FIG. 7 is a Fourier amplitude spectrum of seismic time course of embodiment 2 of the method for simplifying calculation of excellent period of field based on formation information;

FIG. 8 is a simplified calculation method of excellent period of field based on stratum information in accordance with embodiment 3 of the present invention;

FIG. 9 is a simplified calculation method of a distinguished period of a field based on stratum information, which is shown in embodiment 3, and the seismic time course after attenuation processing;

FIG. 10 is a Fourier amplitude spectrum of seismic time course according to embodiment 3 of the method for simplifying calculation of excellent period of field based on formation information;

FIG. 11 is a simplified calculation method of excellent period of field based on stratum information, embodiment 4 of the invention is an original ground earthquake time course;

FIG. 12 is a simplified calculation method of a distinguished period of a field based on formation information, which is shown in FIG. 4, and the seismic time course after attenuation processing;

FIG. 13 is a Fourier amplitude spectrum of seismic time interval according to embodiment 4 of the method for simplifying calculation of excellent period of field based on formation information;

FIG. 14 is a simplified calculation method of excellent period of field based on stratum information, embodiment 5 of the invention is an original ground earthquake time course;

FIG. 15 is a simplified calculation method of a distinguished period of a field based on formation information, which is shown in FIG. 5, and shows a seismic time course after attenuation processing;

fig. 16 is a fourier amplitude spectrum of seismic time course of embodiment 5 of the method for simplifying calculation of the excellent period of the field based on the formation information.

Detailed Description

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

The invention relates to a simplified calculation method of a site excellent period based on stratum information, which is implemented according to the following steps:

step 1, determining the number n of the site and the stratum density rho according to the investigation result of geotechnical engineering_iShear velocity v_iAnd the thickness h of the formation_i(ii) a Wherein, i is 1, 2.

Step 2, calculating a site excellent period estimated value t₀；

Site excellent period estimation value t₀The formula is as follows:

t₀＝4(h₁/v₁+h₂/v₂+……+h_n/v_n) (1)。

step 3, calculating the seismic wave duration t_lAnd a time sampling interval Δ t;

seismic wave time t_lThe formula is as follows:

t_l≥10t₀ (2)

the time sampling interval Δ t is calculated by the following equation (3):

Δt<0.02min(h₁/v₁，h₂/v₂，……，h_n/v_n) (3)。

step 4, calculating the sampling point number nt of the ground seismic wave holding time and the sampling point number nt of the seismic wave propagation time in the stratum i_iThe number nT of sampling points of the Fourier periodic spectrum of the ground seismic wave;

sampling point number nt of ground seismic wave holding time and sampling point number nt of seismic wave propagation time in stratum i_iThe sampling point number nT of the Fourier cycle spectrum of the ground seismic wave is calculated by the following formula:

nt＝Int(t_l/Δt) (4)

nt_i＝Int(h_i/v_i/Δt) (5)

nT＝Int(t₀/Δt) (6)

wherein Int is an integer function, i is 1, 2.

Step 5, calculating the reflection coefficient R of the seismic waves at the boundary interface of the stratum i and the stratum i +1_i；

Reflection coefficient R_iThe formula is as follows:

R_i＝(ρ_i+1v_i+1-ρ_iv_i)/(ρ_i+1v_i+1+ρ_iv_i) Wherein, i is 1, 2, a. (7)

R_n1, wherein i ═ n; (8).

Step 6, calculating the time course u of the ground seismic wave₀ ^d；

Seismic time-path u₀ ^dThe formula is as follows:

u₀ ^d(j)＝-u₁ ^p(j-nt₁)

u₁ ^d(j)＝(1+R₁)u₀ ^d(j-nt₁)-R₁u₂ ^p(j-nt₂)

u₁ ^p(j)＝R₁u₀ ^d(j-nt₁)+(1-R₁)u₂ ^p(j-nt₂)

u₂ ^d(j)＝(1+R₂)u₁ ^d(j-nt₂)-R₂u₃ ^p(j-nt₃)

u₂ ^p(j)＝R₂u₁ ^d(j-nt₂)+(1-R₂)u₃ ^p(j-nt₃)

......

u_i ^d(j)＝(1+R_i)u_i-1 ^d(j-nt_i)-R_iu_i+1 ^p(j-nt_i+1)

u_i ^p(j)＝R_iu_i-1 ^d(j-nt_i)+(1-R_i)u_i+1 ^p(j-nt_i+1)

......

u_n-1 ^d(j)＝(1+R_n-1)u_n-2 ^d(j-nt_n-1)-R_n-1u_n ^p(j-nt_n)

u_n-1 ^p(j)＝R_n-1u_n-2 ^d(j-nt_n-1)+(1-R_n-1)u_n ^p(j-nt_n)

u_n ^p(j)＝u_n ^d(j-nt_n)

wherein u is₀ ^dIs the ground seismic wave time course; u. of_i ^d、The seismic wave time courses of the lower interface and the upper interface of the formation i are respectively, wherein i is 1, 2. u. of₀ ^d、u_i ^d、Are time series, j denotes a time sample number, j 0, 1.

Step 7, seismic wave time course u₀ ^dCarrying out attenuation treatment according to time;

the seismic wave time course u is processed according to the following formula₀ ^dCarrying out attenuation treatment according to time:

u(j)＝u₀ ^d(j)exp[-βjΔt] (9)

wherein the attenuation coefficient beta is-ln delta/t_l(ii) a Delta is a calculation precision value for controlling the attenuation coefficient and satisfies 0<δ<0.01；j＝0，1，......，nt-1。

Step 8, performing Discrete Fourier Transform (DFT) on the seismic wave time interval u to obtain Fu (k);

performing Discrete Fourier Transform (DFT) on the seismic wave time interval u according to the following formula:

wherein i is an imaginary unit; k is 0, 1,.. cnt-1.

Step 9, judging whether the amplitude spectrum | Fu (k) | has a maximum value, if not, expanding nT by 20%, and returning to the step 8; if yes, determining the site excellent period T₀；

Whether the amplitude spectrum | fu (k) | has a maximum value is judged according to the following formula:

| Fu (k) | > | Fu (k-1) | and | Fu (k) | > | Fu (k +1) | (11)

|Fu(k)|>0.5max(|Fu(1)|，|Fu(2)|，......，|Fu(nT-1)|) (12)

If | Fu (k) | satisfies the above condition, the site excellent period is calculated by the following formula:

T₀＝0.5t₀+kΔt (13)。