A method and system for analyzing seismic dynamic response of steep rock foundation pit

Abstract

The present invention discloses a method and system for analyzing the seismic dynamic response of a steep rock formation foundation pit, and the present invention relates to the technical field of foundation pit seismic dynamic response analysis. The method comprises the following steps: according to the test model seismic wave loading scheme, a shaking table similarity model test system is used to perform a horizontal and vertical bidirectional excitation test of the seismic load on the foundation pit model. By arranging sensors on the surface and inside of the foundation pit slope, the acceleration, pressure and displacement dynamic response parameters of the foundation pit slope during the whole process of seismic load excitation are obtained, the cumulative damage response law of the foundation pit slope under the continuous excitation of the seismic load is analyzed, and weights are assigned to the corresponding local damage indicators according to the coordinates of the location where the comprehensive monitoring unit is set, and the global damage index is obtained by weighted average calculation; based on the global damage index, the risk waveform input frequency under each amplitude series is determined, and the steep rock formation foundation pit to be analyzed is monitored in real time. If the real-time waveform input frequency is greater than the risk waveform input frequency, a safety indication is issued.

Description

Technical Field

[0001] The invention relates to the technical field of foundation pit earthquake dynamic response analysis, and in particular to a steep rock stratum foundation pit earthquake dynamic response analysis method and system. Background Art

[0002] The study of foundation pit earthquake dynamic response mainly refers to the response changes of velocity, acceleration, displacement, stress and strain caused by earthquake loads in the rock and soil mass around the foundation pit. At present, domestic and foreign scholars mainly use three methods to study the dynamic behavior of rock and soil mass under earthquake loads: theoretical analysis, numerical calculation and shaking table model test. The shaking table model test can reproduce the real environment of the foundation pit under the action of earthquake by applying earthquake waves to the model on the table for dynamic excitation. It plays an important role in studying the transmission process of earthquake waves in the stratum and their deformation and failure modes under earthquake. Due to its many advantages such as easy control and repeatability, the shaking table model test method has been favored by scientific researchers in many fields such as civil engineering, transportation engineering, water conservancy and hydropower engineering.

[0003] Domestic and foreign scholars have done a lot of research on the dynamic response and failure mode of rock foundation pits and slopes under earthquakes using shaking table model tests, and have achieved good research results. However, there is less attention paid to the dynamic response and instability mechanism of steep rock foundation pits. With the introduction of concepts such as underground hubs and three-dimensional transportation, some foundation pits have the characteristics of large scale, long cycle, and complex surrounding environment, which makes the construction of foundation pits more complex and the construction cycle longer, some even up to 3 to 5 years. If the foundation pit is in construction for a long time, it may be subjected to accidental loads such as earthquakes, which may cause damage or even collapse of surrounding buildings. Therefore, it is very meaningful to consider the dynamic response of the foundation pit under earthquake.

[0004] In the prior art, publication number CN116305480A discloses a method for analyzing the horizontal dynamic response of a single pile under the action of an earthquake S shear wave. The specific method includes: S1. Based on the characteristic parameters of the foundation soil, a soil dynamic equilibrium equation is created considering the influence of the foundation soil on the earthquake S shear wave; S2. In combination with the Euler beam and Pasternak foundation model, a dynamic equilibrium equation of the pile body unit is created; S3. The relationship between the pile body rotation angle, bending moment, shear force and the pile body horizontal displacement coefficient is determined and a corresponding coefficient equation group is created; S4. The dynamic equilibrium equation corresponding to the pile body displacement and internal force coefficient at the bottom of the pile is determined; S5. The dynamic equilibrium equation corresponding to the pile top displacement and the rotation coefficient is determined, thereby completing the analysis of the horizontal dynamic response process of the single pile under the action of the earthquake S shear wave. This scheme considers the horizontal vibration force analysis of pile foundation under the axial force of pile top and the propagation of seismic S shear wave in layered soil, which can provide theoretical guidance and reference for the seismic design of pile foundation engineering; however, the characteristic parameters of foundation soil in this scheme are usually uncertain, including the modulus and damping ratio of soil, and the complexity of geological layers is not considered, which will affect the accuracy of the analysis results. At the same time, when establishing the dynamic balance equation, it may be necessary to consider multiple forces and motion forms, and the equation may become complicated and difficult to solve, which also reduces the real-time performance and effectiveness of the system.

[0005] The above information disclosed in this Background section is only for enhancement of understanding of the background of the present disclosure and therefore it may contain information that does not constitute the prior art that is already known to one of ordinary skill in the art. Summary of the invention

[0006] The object of the present invention is to provide a method and system for analyzing the seismic dynamic response of a steeply inclined rock stratum foundation pit, so as to solve the problems raised in the above-mentioned background technology.

[0007] To achieve the above object, the present invention provides the following technical solutions:

[0008] A method for analyzing seismic dynamic response of a steep rock foundation pit, the specific steps comprising:

[0009] In view of the foundation pit parameters of the steep rock stratum foundation pit to be analyzed, a physical model of the steep rock stratum foundation pit is established, wherein the foundation pit parameters include the foundation pit depth, the foundation pit horizontal distance, the inclination angle of the rock mass slope structural surface, and the thickness of the rock mass slope structural surface;

[0010] According to the depth of the foundation pit, several comprehensive monitoring units are set at the bottom of the foundation pit model and the rock slope structure surface. The comprehensive monitoring unit is composed of acceleration sensors, pressure sensors and displacement sensors. The installation position of each comprehensive monitoring unit is a dynamic response monitoring point.

[0011] A physical model of a steep rock foundation pit with sensors installed is placed on a shaking table for a shaking table model test. The horizontal and vertical bidirectional excitation of the seismic load is used to simulate the earthquake scenario, where the excitation waveform is a natural seismic wave and a sine wave.

[0012] The applied amplitude levels of the excitation are set, and a number of subset data of waveform input frequencies and loading durations are set at each amplitude level. At each amplitude level, each amplitude simulation test is performed by changing the set subset data. Based on the increase of the input applied amplitude, the shaking table model test is performed step by step. When the structural surface of the model rock slope is destroyed in the test, the shaking table model test is terminated, and the dynamic response parameters of the comprehensive monitoring unit during the complete test process are recorded, and the dynamic response parameters include acceleration, pore water pressure and displacement;

[0013] At different times of the complete test, the corresponding local effective stress changes and strains are calculated according to the dynamic response parameters collected by the integrated monitoring units at different positions. Local damage indicators are calculated based on the local effective stress changes and strains. Weights are assigned to the corresponding local damage indicators according to the coordinates of the locations where the integrated monitoring units are set, and the global damage indicators are calculated by weighted average.

[0014] Filter out the moments when the global loss index is greater than the safety threshold as risk moments, record the amplitude level and waveform input frequency corresponding to each risk moment, and determine the risk waveform input frequency at each amplitude level. Monitor the steep rock foundation pit to be analyzed in real time to obtain the real-time amplitude level and real-time waveform input frequency. If the real-time waveform input frequency is greater than the risk waveform input frequency at the same amplitude level, a safety indication is issued.

[0015] Furthermore, according to the depth of the foundation pit, the logic for setting the sensor is as follows: the foundation pit depth is calibrated as H, the depth of the junction between the foundation pit and the soil layer is defined as 0, that is, H = 0, at the bottom of the foundation pit model with a depth of 0 and at a depth of and Multiple groups of sensors are set on each rock slope structure surface to form a four-layer layout, and multiple groups of sensors in each layer are equidistantly arranged;

[0016] The installation location of each integrated monitoring unit is a dynamic response monitoring point. The three sensors are bundled together to form an integrated monitoring unit to jointly collect the dynamic response parameters of the monitoring point.

[0017] Furthermore, horizontal and vertical bidirectional excitation of seismic loads are used to simulate earthquake scenarios, where the excitation waveforms are natural seismic waves and sine waves, and the applied amplitude series of the excitation is set to be natural seismic waves and sine waves of 0.1g, 0.2g, 0.3g to 0.7g, and the amplitude is input step by step from 0.1g to 0.7g. Under each amplitude level, a number of subset data of waveform input frequency and loading duration are set. Under each amplitude level, the input frequency of the sine wave is set to four levels of 10Hz, 15Hz, 20Hz and 25Hz, and the loading duration is set to 10s, 20s, 30s and 40s, respectively. 40s four levels, the test logic is to start the test from the excitation amplitude of 0.1g, under the fixed application of the excitation amplitude of 0.1g, select the sine wave with a frequency of 10Hz, and select the loading duration of 10s. After that, the excitation amplitude and the sine wave frequency remain unchanged, and the loading duration is increased to level two, that is, 20s. When the four levels of loading duration are all applied, the test is not over, and the input frequency of the sine wave is increased step by step. Similarly, after going through four levels of loading duration, when the four levels of sine wave input frequency are all applied, the test is not over, and the excitation amplitude is increased step by step.

[0018] Furthermore, at different times of the complete test, the corresponding local effective stress changes and strains are calculated according to the dynamic response parameters collected by the integrated monitoring units at different positions, wherein the formula for calculating the corresponding local effective stress changes is:

[0019] Δσ′ i (t) = Δσ i (t)-Δu i (t)

[0020] In the formula, Δσ′ i (t) is the local effective stress change of the ith dynamic response monitoring point at time t, Δσ i (t) is the total stress at the i-th dynamic response monitoring point at time t, Δu i (t) is the change in pore water pressure at the ith dynamic response monitoring point at time t, where i = 1, 2, …, P*4; P*4 is the number of all comprehensive monitoring units;

[0021] The total stress Δσ of the i-th dynamic response monitoring point at time t is i (t) is calculated from the acceleration based on the formula:

[0022] Δσ i (t) = ρ * α i (t)

[0023] Where ρ is the density of the rock mass, α i (t) represents the acceleration of the ith dynamic response monitoring point at time t;

[0024] The change of pore water pressure Δu at the i-th dynamic response monitoring point at time t i (t) The calculation is based on the formula:

[0025] Δu i (t) = u i (t)-u i (t-1)

[0026] In the formula, u i (t) represents the pore water pressure at the ith dynamic response monitoring point at time t, u i (t-1) represents the pore water pressure of the ith dynamic response monitoring point at time t-1;

[0027] The strain calculation is based on the formula:

[0028]

[0029] In the formula, ∈ i (t) is the strain of the ith dynamic response monitoring point at time t, H is the depth of the foundation pit, Δv i represents the displacement change of the ith dynamic response monitoring point at time t, where the displacement change expression formula is:

[0030] Δv i (t) = v i (t)-v i (t-1)

[0031] In the formula, v i (t) represents the displacement of the ith dynamic response monitoring point at time t, v i (t-1) represents the displacement of the i-th dynamic response monitoring point at time t-1.

[0032] Furthermore, the formula for calculating the local damage index based on the local effective stress change and strain is:

[0033]

[0034] Where D i (t) is the local damage index of the ith dynamic response monitoring point at time t, σ max,i represents the maximum effective stress allowed in the design at the i dynamic response monitoring point, ∈ max,i Represents the maximum allowable strain of the rock formation at the i dynamic response monitoring point.

[0035] Furthermore, according to the coordinates of the location where the integrated monitoring unit is set, weights are assigned to the corresponding local damage indicators. The logic for obtaining the global damage indicator by weighted average calculation is as follows: According to the installation location of the integrated monitoring unit, the initial position of each integrated monitoring unit, i.e., the dynamic response monitoring point, is recorded as (x i ,y i ,z i ), determine the center position of the foundation pit as (x c ,y c ,z c ), calculate the dynamic response monitoring point and the foundation pit center (x c ,y c ,z c ) i , calculate the distance R i The formula is:

[0036]

[0037] Based on the dynamic response monitoring point and the foundation pit center (x c ,y c ,z c ) i The formula for calculating the weight of the corresponding local damage index is:

[0038]

[0039] Where ω i represents the weight of the local damage index allocation of the ith dynamic response monitoring point;

[0040] The weights of the local damage indicators of all dynamic response monitoring points are normalized, and the formula for normalization is:

[0041]

[0042] In the formula, 4*P represents the number of dynamic response monitoring points;

[0043] According to the normalized weights of each local damage index, the global damage index is obtained by weighted average calculation. The formula for calculating the global damage index is:

[0044]

[0045] Where D total (t) represents the global damage index at time t.

[0046] Furthermore, the logic for calculating the risk waveform input frequency is as follows: calibrate the pre-set safety threshold as yz;

[0047] When Dtotal When (t)>yz, determine moment t as the risk moment; record the amplitude level and waveform input frequency corresponding to the risk moment, count the waveform input frequencies at the same amplitude level, and use their average as the risk waveform input frequency corresponding to the amplitude level.

[0048] The present invention also provides a steep rock stratum foundation pit seismic dynamic response analysis system, the steep rock stratum foundation pit seismic dynamic response analysis system is used to execute the steep rock stratum foundation pit seismic dynamic response analysis method, comprising:

[0049] A foundation pit model building module is used to analyze the foundation pit parameters of the steep rock stratum foundation pit to be analyzed and to build a physical model of the steep rock stratum foundation pit. The foundation pit parameters include the foundation pit depth, the foundation pit horizontal distance, the inclination angle of the rock slope structural surface, and the thickness of the rock slope structural surface.

[0050] The monitoring point setting module is used to set up several comprehensive monitoring units at the bottom of the foundation pit model and the rock slope structure surface according to the depth of the foundation pit. The comprehensive monitoring unit is composed of an acceleration sensor, a pressure sensor and a displacement sensor. The installation position of each comprehensive monitoring unit is a dynamic response monitoring point;

[0051] The excitation simulation application module is used to place a physical model of a steep rock foundation pit equipped with sensors on a shaking table to conduct a shaking table model test, and use horizontal and vertical bidirectional excitation of seismic loads to simulate earthquake scenarios, wherein the excitation waveforms are natural seismic waves and sine waves;

[0052] A dynamic response parameter monitoring module is used to set the applied amplitude level of the excitation, set a number of subset data of waveform input frequency and loading duration at each level of amplitude, perform each level of amplitude simulation test by changing the set subset data at each level of amplitude, perform shaking table model test step by step based on the increase of input applied amplitude, terminate the shaking table model test when the model rock slope structural surface is destroyed in the test, and record the dynamic response parameters of the comprehensive monitoring unit during the complete test process, wherein the dynamic response parameters include acceleration, pore water pressure and displacement;

[0053] The damage index analysis module is used to calculate the corresponding local effective stress changes and strains according to the dynamic response parameters collected by the integrated monitoring units at different positions at different times of the complete test, and obtain the local damage index based on the local effective stress changes and strains. The weight is assigned to the corresponding local damage index according to the coordinates of the location where the integrated monitoring unit is set, and the global damage index is obtained by weighted average calculation;

[0054] The foundation pit safety analysis module is used to screen out the moments when the global loss index is greater than the safety threshold as risk moments, record the amplitude level and waveform input frequency corresponding to each risk moment, so as to determine the risk waveform input frequency under each amplitude level, and monitor the steep rock stratum foundation pit to be analyzed in real time to obtain the real-time amplitude level and real-time waveform input frequency. If the real-time waveform input frequency is greater than the risk waveform input frequency under the same amplitude level, a safety indication is issued.

[0055] Compared with the prior art, the present invention has the following beneficial effects:

[0056] According to the seismic wave loading scheme of the test model, the foundation pit model was subjected to horizontal and vertical bidirectional excitation tests of seismic loads using a shaking table similar model test system. By placing sensors on the surface and inside the foundation pit slope, the dynamic response parameters of the foundation pit slope such as acceleration, pressure, and displacement during the whole process of seismic load excitation were obtained. The cumulative damage response law of the foundation pit slope under continuous seismic load excitation was discussed, and weights were assigned to the corresponding local damage indicators according to the coordinates of the location where the comprehensive monitoring unit was set, and the global damage index was obtained by weighted average calculation; based on the global damage index, the moment when the global loss index was greater than the safety threshold was selected as the risk moment, and the risk waveform input frequency under each amplitude level was determined. The steep rock stratum foundation pit to be analyzed was monitored in real time. If the real-time waveform input frequency was greater than the risk waveform input frequency under the same amplitude level, a safety indication was issued. This method is specifically designed for steep rock foundation pits. It takes into account the inclination characteristics and corresponding mechanical behavior of rock and soil. By setting acceleration, pore water pressure and displacement sensors, a comprehensive monitoring unit is formed to fully capture the dynamic response of the foundation pit. This multi-dimensional monitoring makes the assessment of the state of the foundation pit more comprehensive. By calculating the local effective stress change and strain, combined with the weighted average to obtain the global damage index, the overall safety and damage degree of the foundation pit can be more accurately judged. Finally, a dynamic assessment of the damage level of the foundation pit is carried out, which helps to take timely countermeasures. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is a schematic diagram of the overall method flow of the present invention;

[0058] Figure 2 It is a schematic diagram of the overall system structure of the present invention. DETAILED DESCRIPTION

[0059] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with specific embodiments.

[0060] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the present invention should be understood by people with ordinary skills in the field to which the present invention belongs. The words "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0061] Example:

[0062] See also Figure 1 , the present invention provides a technical solution:

[0063] A method for analyzing seismic dynamic response of a steep rock foundation pit, the specific steps comprising:

[0064] Step 1: Based on the foundation pit parameters of the steep rock stratum foundation pit to be analyzed, a physical model of the steep rock stratum foundation pit is established, wherein the foundation pit parameters include the foundation pit depth, the foundation pit horizontal distance, the inclination angle of the rock slope structural surface, and the thickness of the rock slope structural surface;

[0065] The characteristics of steeply inclined rock formations are taken into account, such as the depth of the foundation pit, horizontal distance, the inclination angle and thickness of the structural surface of the rock slope, so that the model can more realistically reflect the actual geological conditions. The depth of the foundation pit determines the propagation path and propagation mode of seismic waves in the soil. Deeper foundation pits may face more complex wave patterns because the speed and attenuation characteristics of seismic waves will be different when propagating in the soil at different depths;

[0066] The horizontal distance of the foundation pit determines the interaction between the foundation pit and adjacent structures (such as buildings, other foundation pits, etc.). Under earthquake action, adjacent structures may impose additional loads on the foundation pit, affecting its stability.

[0067] The inclination angle directly affects the stability of the slope. A steeper inclination angle may increase the risk of slope slip, especially after an earthquake, which may cause soil instability.

[0068] Thickness is directly related to the volume and mass of the slope. A thicker slope may provide better stability, but it may also generate greater inertial forces during an earthquake, thus affecting the response of the foundation pit.

[0069] A physical model of a foundation pit in a steep rock formation can be established. Parameters can be set according to the actual construction situation, or multiple groups of parameters can be set to determine the parameter group with the best stability.

[0070] Step 2: According to the depth of the foundation pit, several comprehensive monitoring units are set at the bottom of the foundation pit model and the rock slope structure surface. The comprehensive monitoring unit consists of an acceleration sensor, a pressure sensor and a displacement sensor. The installation position of each comprehensive monitoring unit is a dynamic response monitoring point;

[0071] According to the depth of the foundation pit, the logic for setting the sensor is as follows: the foundation pit depth is calibrated as H, the depth of the junction between the foundation pit and the soil layer is defined as 0, that is, H = 0, at the bottom of the foundation pit model with a depth of 0 and a depth of and Multiple groups of sensors are set on each rock slope structure surface to form a four-layer layout, and multiple groups of sensors in each layer are equidistantly arranged;

[0072] The installation location of each integrated monitoring unit is a dynamic response monitoring point. The three sensors are bundled together to form an integrated monitoring unit to jointly collect the dynamic response parameters of the monitoring point.

[0073] Multi-level data acquisition can fully capture the dynamic response of the foundation pit under earthquake action. This multi-level data acquisition helps to analyze the stress and deformation characteristics of the foundation pit at different depths.

[0074] Step 3: Place the physical model of the steep rock foundation pit with sensors on a shaking table for a shaking table model test, and use horizontal and vertical bidirectional excitation of seismic loads to simulate earthquake scenarios, where the excitation waveforms are natural seismic waves and sine waves;

[0075] By using natural seismic waves and sine waves, the impact of different types of earthquakes can be simulated more realistically. By using horizontal and vertical bidirectional excitation, the dynamic response of the foundation pit in different directions can be analyzed simultaneously, providing multi-dimensional data support.

[0076] Step 4: setting the applied amplitude level of the excitation, setting a number of subset data of waveform input frequency and loading duration at each level of amplitude, performing each level of amplitude simulation test by changing the set subset data at each level of amplitude, performing shaking table model tests step by step based on the increase of input applied amplitude, terminating the shaking table model test when the model rock slope structural surface is destroyed in the test, and recording the dynamic response parameters of the comprehensive monitoring unit during the complete test process, wherein the dynamic response parameters include acceleration, pore water pressure and displacement;

[0077] The horizontal and vertical bidirectional excitation of the seismic load is used to simulate the earthquake scenario, in which the excitation waveforms are natural seismic waves and sine waves. The applied amplitude series of the excitation is set to 0.1g, 0.2g, 0.3g to 0.7g of natural seismic waves and sine waves, and the amplitude is input step by step from 0.1g to 0.7g. At each level of amplitude, a number of subset data of waveform input frequency and loading duration are set. At each level of amplitude, the input frequency of the sine wave is set to 10Hz, 15Hz, 20Hz and 25Hz, and the loading duration is set to 10s, 20s, 30s and 40s, respectively. The test logic is to start the test from an excitation amplitude of 0.1g. Under the fixed application of the excitation amplitude of 0.1g, a sine wave with a frequency of 10Hz is selected, and the loading duration is selected as 10s. After that, the excitation amplitude and the sine wave frequency remain unchanged, and the loading duration is increased to level two, that is, 20s. When all four levels of loading duration are applied, the test is not over, and the input frequency of the sine wave is increased step by step. Similarly, after four levels of loading duration, when all four levels of sine wave input frequency are applied, the test is not over, and the excitation amplitude is increased step by step.

[0078] Step 5: At different times of the complete test, according to the dynamic response parameters collected by the integrated monitoring units at different positions, the corresponding local effective stress changes and strains are calculated, and the local damage index is calculated based on the local effective stress changes and strains. According to the coordinates of the location where the integrated monitoring unit is set, weights are assigned to the corresponding local damage indexes, and the global damage index is calculated by weighted average;

[0079] Effective stress refers to the actual stress in soil or rock. Effective stress is a key factor affecting the strength and deformation characteristics of soil and rock. Under loads such as earthquakes and construction, microcracks and pore changes will occur inside the soil or rock. These changes are usually closely related to changes in effective stress. When the effective stress decreases, the strength and bearing capacity of the material tend to weaken, resulting in damage.

[0080] The increase of strain is usually accompanied by the damage of rock mass. By monitoring the change of strain, the damage of rock mass can be obtained. The accumulation of strain may lead to fatigue and destruction of rock mass, so strain can be used as an indicator of local damage.

[0081] At different times of the complete test, the corresponding local effective stress changes and strains are calculated according to the dynamic response parameters collected by the integrated monitoring units at different positions. The formula for calculating the corresponding local effective stress changes is:

[0082] Δσ′ i (t) = Δσ i (t)-Δu i (t)

[0083] In the formula, Δσ′ i (t) is the local effective stress change of the ith dynamic response monitoring point at time t, Δσ i (t) is the total stress at the i-th dynamic response monitoring point at time t, Δu i (t) is the change in pore water pressure at the ith dynamic response monitoring point at time t, where i = 1, 2, …, P*4; P*4 is the number of all comprehensive monitoring units;

[0084] The total stress Δσ of the i-th dynamic response monitoring point at time t is i (t) is calculated from the acceleration based on the formula:

[0085] Δσ i (t) = ρ * α i (t)

[0086] Where ρ is the density of the rock mass, α i (t) represents the acceleration of the ith dynamic response monitoring point at time t;

[0087] The change of pore water pressure Δu at the i-th dynamic response monitoring point at time t i (t) The calculation is based on the formula:

[0088] Δu i (t) = u i (t)-u i (t-1)

[0089] In the formula, u i (t) represents the pore water pressure at the ith dynamic response monitoring point at time t, u i (t-1) represents the pore water pressure of the ith dynamic response monitoring point at time t-1;

[0090] The strain calculation is based on the formula:

[0091]

[0092] In the formula, ∈ i (t) is the strain of the ith dynamic response monitoring point at time t, H is the depth of the foundation pit, Δv i represents the displacement change of the ith dynamic response monitoring point at time t, where the displacement change expression formula is:

[0093] Δv i (t) = v i (t)-v i (t-1)

[0094] In the formula, v i(t) represents the displacement of the ith dynamic response monitoring point at time t, v i (t-1) represents the displacement of the i-th dynamic response monitoring point at time t-1.

[0095] The formula for calculating the local damage index based on the local effective stress change and strain is:

[0096]

[0097] Where D i (t) is the local damage index of the ith dynamic response monitoring point at time t, σ max,i represents the maximum effective stress allowed in the design at the i dynamic response monitoring point, ∈ max,i Represents the maximum allowable strain of the rock formation at the i dynamic response monitoring point.

[0098] Among them, the method for obtaining the maximum allowable effective stress is: according to the relevant design specifications and standards, there are usually recommended soil strength parameters that can be directly referenced. Before the foundation pit construction, a detailed engineering geological survey is carried out to obtain the geological data and physical and mechanical properties of the soil layer, and the maximum allowable effective stress is estimated through field tests (such as standard penetration tests, static penetration tests, etc.);

[0099] The maximum allowable strain of the rock formation is obtained by performing a uniaxial tensile test on the soil or rock to obtain the stress-strain curve of the material, thereby determining the maximum strain of the material; similarly, a compression test can also help determine the maximum strain, especially when considering the condition of the foundation pit soil. The methods for obtaining the maximum allowable effective stress and the maximum allowable strain of the rock formation are both relatively mature existing technologies and will not be elaborated here.

[0100] The coordinate system of the physical model of the foundation pit is established using three-dimensional rectangular coordinates, with the horizontal extension direction of the foundation pit as the x-axis, the width direction of the foundation pit as the y-axis, the depth direction of the foundation pit as the z-axis, the upward direction as the positive direction, and the vertex at the bottom of the upper left corner of the physical model of the foundation pit as the origin.

[0101] According to the coordinates of the location where the integrated monitoring unit is set, weights are assigned to the corresponding local damage indicators. The logic for obtaining the global damage indicator through weighted average calculation is as follows: According to the installation location of the integrated monitoring unit, the initial position of each integrated monitoring unit, i.e., the dynamic response monitoring point, is recorded as (x i ,y i ,z i ), determine the center position of the foundation pit as (x c ,y c ,z c ), calculate the dynamic response monitoring point and the foundation pit center (x c ,y c ,zc ) i , calculate the distance R i The formula is:

[0102]

[0103] Based on the dynamic response monitoring point and the foundation pit center (x c ,y c ,z c ) i The formula for calculating the weight of the corresponding local damage index is:

[0104]

[0105] Where ω i represents the weight of the local damage index allocation of the ith dynamic response monitoring point;

[0106] The weights of the local damage indicators of all dynamic response monitoring points are normalized, and the formula for normalization is:

[0107]

[0108] In the formula, 4*P represents the number of dynamic response monitoring points;

[0109] According to the normalized weights of each local damage index, the global damage index is obtained by weighted average calculation. The formula for calculating the global damage index is:

[0110]

[0111] Where D total (t) represents the global damage index at time t.

[0112] In this embodiment, the center position of the foundation pit model is selected as the reference point for allocating weights. In actual construction, the reference point can be selected according to the actual working conditions, and the position of important areas can be selected, such as the slope angle, the bottom of the foundation pit, etc.

[0113] Step 6: Filter out the moments when the global loss index is greater than the safety threshold as risk moments, record the amplitude level and waveform input frequency corresponding to each risk moment, and determine the risk waveform input frequency at each amplitude level. Monitor the steep rock foundation pit to be analyzed in real time to obtain the real-time amplitude level and real-time waveform input frequency. If the real-time waveform input frequency is greater than the risk waveform input frequency at the same amplitude level, a safety indication is issued.

[0114] The logic for calculating the risk waveform input frequency is as follows: calibrate the pre-set safety threshold to yz;

[0115] When D total When (t)>yz, determine moment t as the risk moment; record the amplitude level and waveform input frequency corresponding to the risk moment, count the waveform input frequencies at the same amplitude level, and use their average as the risk waveform input frequency corresponding to the amplitude level.

[0116] Among them, when D total When (t)≤yz, time t is judged to be a normal risk moment, that is, the current state of the foundation pit is relatively safe. The safety threshold yz is assessed by the expert group or set by the staff according to the actual situation.

[0117] See also Figure 2 The present invention also provides a steep rock stratum foundation pit seismic dynamic response analysis system, the steep rock stratum foundation pit seismic dynamic response analysis system is used to execute the steep rock stratum foundation pit seismic dynamic response analysis method, comprising:

[0118] A foundation pit model building module is used to analyze the foundation pit parameters of the steep rock stratum foundation pit to be analyzed and to build a physical model of the steep rock stratum foundation pit. The foundation pit parameters include the foundation pit depth, the foundation pit horizontal distance, the inclination angle of the rock slope structural surface, and the thickness of the rock slope structural surface.

[0119] The monitoring point setting module is used to set up several comprehensive monitoring units at the bottom of the foundation pit model and the rock slope structure surface according to the depth of the foundation pit. The comprehensive monitoring unit is composed of an acceleration sensor, a pressure sensor and a displacement sensor. The installation position of each comprehensive monitoring unit is a dynamic response monitoring point;

[0120] The excitation simulation application module is used to place a physical model of a steep rock foundation pit equipped with sensors on a shaking table to conduct a shaking table model test, and use horizontal and vertical bidirectional excitation of seismic loads to simulate earthquake scenarios, wherein the excitation waveforms are natural seismic waves and sine waves;

[0121] A dynamic response parameter monitoring module is used to set the applied amplitude level of the excitation, set a number of subset data of waveform input frequency and loading duration at each level of amplitude, perform each level of amplitude simulation test by changing the set subset data at each level of amplitude, perform shaking table model test step by step based on the increase of input applied amplitude, terminate the shaking table model test when the model rock slope structural surface is destroyed in the test, and record the dynamic response parameters of the comprehensive monitoring unit during the complete test process, wherein the dynamic response parameters include acceleration, pore water pressure and displacement;

[0122] The damage index analysis module is used to calculate the corresponding local effective stress changes and strains according to the dynamic response parameters collected by the integrated monitoring units at different positions at different times of the complete test, and obtain the local damage index based on the local effective stress changes and strains. The weight is assigned to the corresponding local damage index according to the coordinates of the location where the integrated monitoring unit is set, and the global damage index is obtained by weighted average calculation;

[0123] The foundation pit safety analysis module is used to screen out the moments when the global loss index is greater than the safety threshold as risk moments, record the amplitude level and waveform input frequency corresponding to each risk moment, so as to determine the risk waveform input frequency under each amplitude level, and monitor the steep rock stratum foundation pit to be analyzed in real time to obtain the real-time amplitude level and real-time waveform input frequency. If the real-time waveform input frequency is greater than the risk waveform input frequency under the same amplitude level, a safety indication is issued.

[0124] The above formulas are all dimensionless and numerical calculations. The formula is a formula for the most recent real situation obtained by collecting a large amount of data and performing software simulation. The preset parameters in the formula are set by technicians in this field according to actual conditions.

[0125] The above embodiments may be implemented in whole or in part by software, hardware, firmware or any other combination thereof. When implemented by software, the above embodiments may be implemented in whole or in part in the form of a computer program product. Those skilled in the art may appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein may be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed by hardware or software methods depends on the specific application and design constraints of the technical solution.

[0126] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, and may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0127] The above description is only a specific implementation manner of the present application, but the protection scope of the present application is not limited thereto. Any technician familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application.

Claims

1. A method for analyzing the seismic dynamic response of a steeply inclined rock foundation pit, characterized in that: The specific steps include: In view of the foundation pit parameters of the steep rock stratum foundation pit to be analyzed, a physical model of the steep rock stratum foundation pit is established, wherein the foundation pit parameters include the foundation pit depth, the foundation pit horizontal distance, the inclination angle of the rock mass slope structural surface, and the thickness of the rock mass slope structural surface; According to the depth of the foundation pit, several comprehensive monitoring units are set at the bottom of the foundation pit model and the rock slope structure surface. The comprehensive monitoring unit is composed of acceleration sensors, pressure sensors and displacement sensors. The installation position of each comprehensive monitoring unit is a dynamic response monitoring point. A physical model of a steep rock foundation pit with sensors installed is placed on a shaking table for a shaking table model test. The horizontal and vertical bidirectional excitation of the seismic load is used to simulate the earthquake scenario, where the excitation waveform is a natural seismic wave and a sine wave. The applied amplitude levels of the excitation are set, and a number of subset data of waveform input frequencies and loading durations are set at each amplitude level. At each amplitude level, each amplitude simulation test is performed by changing the set subset data. Based on the increase of the input applied amplitude, the shaking table model test is performed step by step. When the structural surface of the model rock slope is destroyed in the test, the shaking table model test is terminated, and the dynamic response parameters of the comprehensive monitoring unit during the complete test process are recorded, and the dynamic response parameters include acceleration, pore water pressure and displacement; At different times of the complete test, the corresponding local effective stress changes and strains are calculated according to the dynamic response parameters collected by the integrated monitoring units at different positions. Local damage indicators are calculated based on the local effective stress changes and strains. Weights are assigned to the corresponding local damage indicators according to the coordinates of the locations where the integrated monitoring units are set, and the global damage indicators are calculated by weighted average. The formula for calculating the corresponding local effective stress change is: Ds′ i (t)=Δσ i (t)-Δu i (t) In the formula, Δσ′ i (t) is the local effective stress change of the ith dynamic response monitoring point at time t, Δσ i (t) is the total stress at the i-th dynamic response monitoring point at time t, Δu i (t) is the change in pore water pressure at the ith dynamic response monitoring point at time t, where i = 1, 2, …, P*4; P*4 is the number of all comprehensive monitoring units; The total stress Δσ of the i-th dynamic response monitoring point at time t is i (t) is calculated from the acceleration based on the formula: Board i (t)=ρ*α i (t) Where ρ is the density of the rock mass, α i (t) represents the acceleration of the ith dynamic response monitoring point at time t; The change of pore water pressure Δu at the i-th dynamic response monitoring point at time t i (t) The calculation is based on the formula: Δu i (t)=u i (t)-u i (t-1) In the formula, u i (t) represents the pore water pressure at the ith dynamic response monitoring point at time t, u i (t-1) represents the pore water pressure of the ith dynamic response monitoring point at time t-1; The strain calculation is based on the formula: In the formula, ∈ i (t) is the strain of the ith dynamic response monitoring point at time t, H is the depth of the foundation pit, Δv i represents the displacement change of the ith dynamic response monitoring point at time t, where the displacement change expression formula is: Δv i (t)=v i (t)-v i (t-1) In the formula, v i (t) represents the displacement of the ith dynamic response monitoring point at time t, v i (t-1) represents the displacement of the i-th dynamic response monitoring point at time t-1; The formula for calculating the local damage index based on the local effective stress change and strain is: Where D i (t) is the local damage index of the ith dynamic response monitoring point at time t, σ max,i represents the maximum effective stress allowed in the design at the i dynamic response monitoring point, ∈ max,i represents the maximum allowable strain of the rock formation at the i dynamic response monitoring point; According to the coordinates of the location where the integrated monitoring unit is set, weights are assigned to the corresponding local damage indicators. The logic for obtaining the global damage indicator through weighted average calculation is as follows: According to the installation location of the integrated monitoring unit, the initial position of each integrated monitoring unit, i.e., the dynamic response monitoring point, is recorded as (x i ,y i ,z i ), determine the center position of the foundation pit as (x c ,y c ,z c ), calculate the dynamic response monitoring point and the foundation pit center (x c ,y c ,z c ) i , calculate the distance R i The formula is: Based on the dynamic response monitoring point and the foundation pit center (x c ,y c ,z c ) i The formula for calculating the weight of the corresponding local damage index is: Where ω i represents the weight of the local damage index allocation of the ith dynamic response monitoring point; The weights of the local damage indicators of all dynamic response monitoring points are normalized, and the formula for normalization is: In the formula, 4*P represents the number of dynamic response monitoring points; According to the normalized weights of each local damage index, the global damage index is obtained by weighted average calculation. The formula for calculating the global damage index is: Where D total (t) represents the global damage index at time t; Filter out the moments when the global loss index is greater than the safety threshold as risk moments, record the amplitude level and waveform input frequency corresponding to each risk moment, and determine the risk waveform input frequency at each amplitude level. Monitor the steep rock foundation pit to be analyzed in real time to obtain the real-time amplitude level and real-time waveform input frequency. If the real-time waveform input frequency is greater than the risk waveform input frequency at the same amplitude level, a safety indication is issued.

2. The method for analyzing seismic dynamic response of a steeply inclined rock foundation pit according to claim 1, characterized in that: The logic for setting sensors according to the depth of the foundation pit is as follows: the foundation pit depth is calibrated as H, and the depth of the interface between the foundation pit and the soil layer is defined as 0, that is, H = 0. and Multiple groups of sensors are set on each rock slope structure surface to form a four-layer layout, and multiple groups of sensors in each layer are equidistantly arranged; The installation location of each integrated monitoring unit is a dynamic response monitoring point. The three sensors are bundled together to form an integrated monitoring unit to jointly collect the dynamic response parameters of the monitoring point.

3. The method for analyzing seismic dynamic response of a steeply inclined rock foundation pit according to claim 1, characterized in that: The horizontal and vertical bidirectional excitation of the seismic load is used to simulate the earthquake scenario, in which the excitation waveforms are natural seismic waves and sine waves. The applied amplitude series of the excitation is set to 0.1g, 0.2g, 0.3g to 0.7g of natural seismic waves and sine waves, and the amplitude is input step by step from 0.1g to 0.7g. At each level of amplitude, a number of subset data of waveform input frequency and loading duration are set. At each level of amplitude, the input frequency of the sine wave is set to 10Hz, 15Hz, 20Hz and 25Hz, and the loading duration is set to 10s, 20s, 30s and 40s, respectively. The test logic is to start the test from an excitation amplitude of 0.1g. Under the fixed application of the excitation amplitude of 0.1g, a sine wave with a frequency of 10Hz is selected, and the loading duration is selected as 10s. After that, the excitation amplitude and the sine wave frequency remain unchanged, and the loading duration is increased to level two, that is, 20s. When all four levels of loading duration are applied, the test is not over, and the input frequency of the sine wave is increased step by step. Similarly, after four levels of loading duration, when all four levels of sine wave input frequency are applied, the test is not over, and the excitation amplitude is increased step by step.

4. The method for analyzing seismic dynamic response of a steeply inclined rock foundation pit according to claim 1, characterized in that: The logic for calculating the risk waveform input frequency is as follows: calibrate the pre-set safety threshold to yz; When D total When (t)>yz, determine moment t as the risk moment; record the amplitude level and waveform input frequency corresponding to the risk moment, count the waveform input frequencies at the same amplitude level, and use their average as the risk waveform input frequency corresponding to the amplitude level.

5. A seismic dynamic response analysis system for steep rock foundation pits, characterized by: The steep rock stratum foundation pit seismic dynamic response analysis system is used to execute the steep rock stratum foundation pit seismic dynamic response analysis method according to any one of claims 1 to 4, comprising: A foundation pit model building module is used to analyze the foundation pit parameters of the steep rock stratum foundation pit to be analyzed and to build a physical model of the steep rock stratum foundation pit. The foundation pit parameters include the foundation pit depth, the foundation pit horizontal distance, the inclination angle of the rock slope structural surface, and the thickness of the rock slope structural surface. The monitoring point setting module is used to set up several comprehensive monitoring units at the bottom of the foundation pit model and the rock slope structure surface according to the depth of the foundation pit. The comprehensive monitoring unit is composed of an acceleration sensor, a pressure sensor and a displacement sensor. The installation position of each comprehensive monitoring unit is a dynamic response monitoring point; The excitation simulation application module is used to place a physical model of a steep rock foundation pit equipped with sensors on a shaking table to conduct a shaking table model test, and use horizontal and vertical bidirectional excitation of seismic loads to simulate earthquake scenarios, wherein the excitation waveforms are natural seismic waves and sine waves; A dynamic response parameter monitoring module is used to set the applied amplitude level of the excitation, set a number of subset data of waveform input frequency and loading duration at each level of amplitude, perform each level of amplitude simulation test by changing the set subset data at each level of amplitude, perform shaking table model test step by step based on the increase of input applied amplitude, terminate the shaking table model test when the model rock slope structural surface is destroyed in the test, and record the dynamic response parameters of the comprehensive monitoring unit during the complete test process, wherein the dynamic response parameters include acceleration, pore water pressure and displacement; The damage index analysis module is used to calculate the corresponding local effective stress changes and strains according to the dynamic response parameters collected by the integrated monitoring units at different positions at different times of the complete test, and obtain the local damage index based on the local effective stress changes and strains. The weight is assigned to the corresponding local damage index according to the coordinates of the location where the integrated monitoring unit is set, and the global damage index is obtained by weighted average calculation; The foundation pit safety analysis module is used to screen out the moments when the global loss index is greater than the safety threshold as risk moments, record the amplitude level and waveform input frequency corresponding to each risk moment, so as to determine the risk waveform input frequency under each amplitude level, and monitor the steep rock stratum foundation pit to be analyzed in real time to obtain the real-time amplitude level and real-time waveform input frequency. If the real-time waveform input frequency is greater than the risk waveform input frequency under the same amplitude level, a safety indication is issued.

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