A nonlinear static analysis method for the impact of blasting vibration on surrounding buildings based on on-site vibration velocity measurements

Abstract

The present invention discloses a nonlinear static analysis method for the impact of blasting vibration on surrounding buildings based on on-site vibration velocity measurement, belonging to the technical field of engineering blasting. The safety assessment method comprises the following steps: Step 1: On-site detection and data acquisition to obtain the vibration velocity of the target structure and the blasting seismic wave velocity vibration curve at the target structure; Step 2: Calculate the inelastic pseudo-absolute acceleration-relative displacement S of the structure. A，e ‑S D，e The curve is the target structure's demand curve. Step 3: Build a multi-degree-of-freedom structural model and perform a static pushover analysis to obtain the structure's load-displacement response V-D curve, which is then transformed to obtain the capacity curve of the equivalent SDOF structure. Step 4: Move the target structure's demand and capacity curves to the same coordinate system. The intersection of the demand and capacity curves reflects the local damage of the structure. This method not only determines whether the structure will fail globally but also analyzes the extent and location of local damage.

Description

Technical Field

[0001] The invention belongs to the technical field of engineering blasting, and in particular relates to a nonlinear static analysis method of the influence of blasting vibration on surrounding buildings based on on-site measurement of vibration velocity. Background Art

[0002] Currently, research on the impact of blasting vibration on surrounding buildings is incomplete. The main regulation, the "Safety Code for Blasting" (GB6722-2010), uses only particle velocity and dominant frequency as criteria for safety assessment, while also considering factors such as building importance and quality. However, considering blasting operations, which often involve both high- and low-frequency components, a single dominant frequency corresponding to the maximum amplitude frequency is inappropriate and incomplete. Furthermore, this regulation, which only uses ground velocity to assess the impact of blasting vibration on surrounding buildings, ignores the details of the force structure and the combination of different modes, and may be overly conservative. The "Code for Seismic Design of Buildings" (GB50011-2010 (2016 edition), which serves as another basis for assessment, relies on traditional seismic loads. Many coefficients, such as the seismic influence coefficient and earthquake rarity, are derived from seismic analysis, making it difficult to determine the values ​​for blasting-induced seismic waves.

[0003] Traditional analysis methods assume that a structure's low-order modal responses are more pronounced. Low-frequency fluctuations make the structure's overall response more pronounced, especially the first mode. However, earthquake waves typically contain higher-frequency components and sharper waveforms, resulting in more pronounced high-order modal responses. High-frequency fluctuations can cause significant high-order modal vibrations in localized areas of the structure. This has led to many buildings experiencing localized damage due to high-order modes. Traditional calculation methods and related specifications focus only on overall structural damage and ignore localized damage, which in turn leads to the neglect of high-order modes.

[0004] Existing methods for calculating the impact of blasting on ground structures rely primarily on dynamic time-history analysis. This method requires a large amount of computing power and suffers from significant computational redundancy, making it unsuitable for preliminary blasting designs or when multiple structures require calculation. Furthermore, dynamic time-history analysis places extremely high demands on the precision and accuracy of models and theoretical assumptions, leading to significant errors when accurate data is unavailable. Summary of the Invention

[0005] The purpose of this invention is to establish a systematic and relatively simple safety evaluation method for buildings under blasting vibration. The analysis process can not only determine whether the structure will be damaged as a whole, but also analyze the local damage situation and location.

[0006] The present invention provides a nonlinear static analysis method for the impact of blasting vibration on surrounding buildings based on on-site vibration velocity measurement. The safety assessment method includes the following steps:

[0007] Step 1: On-site detection and data collection to obtain the vibration velocity of the target structure and the blasting seismic wave velocity vibration curve at the target structure;

[0008] Step 2: Calculate the structural inelastic pseudo-absolute acceleration-relative displacement S A，e -S D，e curve, i.e., the demand curve of the target structure;

[0009] Step 3: Establish a multi-degree-of-freedom structural model and perform static pushover analysis on it to obtain the load-displacement response relationship VD curve of the structure, and deform it to obtain the capacity curve of the equivalent SDOF structure;

[0010] Step 4: The demand curve and capacity curve of the target structure are moved to the same coordinate system. The intersection of the demand curve and the capacity curve reflects the local damage of the structure.

[0011] Furthermore, in step 2, the inelastic pseudo-absolute acceleration-relative displacement S A，e -S D，e The curve is determined as follows:

[0012] The specific process of step 2 includes:

[0013] Step 201: Establish a single degree of freedom system, and apply the blasting seismic wave to the single degree of freedom system based on the vibration velocity obtained in step 1 and the blasting seismic wave velocity vibration curve;

[0014] Step 202: Use numerical methods to solve formula (1) to obtain the pseudo-absolute acceleration of the structure with given stiffness k and mass m and time S A，e -t curve, similarly, we can get the relative displacement and time S D，e -t curve;

[0015]

[0016] In the above formula, represents the absolute acceleration, represents the absolute velocity, y represents the absolute displacement, Represents the measured ground velocity function, x g (t) represents the ground displacement function, c represents the ground-to-ground damping;

[0017] Step 203: Maintaining the mass m of the single-degree-of-freedom system, by changing the stiffness k of the single-degree-of-freedom system, obtain the pseudo-absolute acceleration and time S of the single-degree-of-freedom system with different natural frequencies. A，e -t curve, similarly, we can get the relative displacement and time S D，e -t curve;

[0018] Step 204: Take each SA，e -t curve S A，e The maximum value is obtained, and the pseudo-absolute acceleration and period of the single degree of freedom system S A，e -T curve; similarly, the relative displacement and period of the single degree of freedom system S D，e -The curve between T;

[0019] Step 205: Pseudo-absolute acceleration response spectrum S A，e -T curve and relative displacement response spectrum S D，e -T curve is converted to obtain the inelastic pseudo-absolute acceleration-relative displacement S A，e -S D，e curve.

[0020] Furthermore, in step 204, the structure is simulated as a single degree of freedom system S with absolute acceleration and period A，e The expression of the curve between -T is as follows:

[0021]

[0022] In the above formula, ξ represents the critical damping of the structure, For flexible systems with ξ<0.05,

[0023] Then ω represents the natural frequency of the single-degree-of-freedom system, and τ is the Duhamel integration variable.

[0024] Furthermore, the single degree of freedom system S of the relative displacement and period of the structure in step 204 D，e The curve between -T is expressed as follows:

[0025]

[0026] Furthermore, the specific process of step 205 is as follows:

[0027] The specific process of step 205 is:

[0028] (1) For the elastic SDOF system, it can be seen from the differential relationship that S A，e =ω d 2 S D，e , S V，e =ω d S D，e , we can get:

[0029]

[0030] For elastic SDOF systems with the same structural stiffness and mass, T is the same, and the corresponding elastic S can be obtained. A，e -S D，e relation;

[0031] (2) For an inelastic SDOF system with a bilinear force-deformation relationship, the inelastic acceleration spectrum S A，i and inelastic displacement spectrum S D，i Determined as:

[0032]

[0033] In the above formula, μ is the ductility coefficient of the ratio of maximum displacement to yield displacement, R μ is the ductility reduction factor, and the ductility reduction factor R is expressed using a bilinear spectrum. μ :

[0034] When T c <T

[0035] R μ =μ, when T c >T

[0036] In the above formula, Tc is the characteristic period of blasting earthquake motion, which is defined as the transition period from the constant acceleration section to the constant velocity section of the response spectrum, that is, the transition period from the short-period range to the medium-term range. c >T, R μ =μ, in the medium and long period range S D，i =S D，e , that is, the displacement of the inelastic system is equal to the displacement of the corresponding elastic system in the same period. Based on the above relationship, the inelastic pseudo-absolute acceleration-relative displacement S can be obtained A，e -S D，e curve.

[0037] Furthermore, the process of determining the capability curve of the structure in step 3 includes:

[0038] Step 301: Establish a multi-degree-of-freedom structural model;

[0039] Step 302: Determine the characteristics of the multi-degree-of-freedom structural model: determine the structural stiffness and calculate the natural frequency ω based on the mechanical model and stiffness characteristics of the structure i , vibration shape Participation coefficient Γ i And the equivalent mass m corresponding to each vibration mode j ;

[0040] Step 303: Apply displacement loads to the multi-degree-of-freedom structural model to perform nonlinear displacement analysis. During each iteration, the load shape for each iteration is calculated based on the structural characteristics determined in step 302. The load magnitude is increased by continuously increasing the load coefficient λ. As the load increases, components in weak locations of the structure yield, and the stiffness of the yielded components is corrected.

[0041] Step 304: After the correction, repeat steps 302 and 303, and continuously increase the load until the lateral displacement of the structure reaches the predetermined target displacement or too many plastic hinges appear in the structure to form a mechanism. By recording the total internal force and total deformation, the load-displacement response relationship VD curve is obtained;

[0042] Step 305: Convert the VD curve of the structural MDOF system into the S curve of the structural SDOF system. a -D* graph, that is, the capacity curve of the structure is obtained.

[0043] Furthermore, the specific process of step 303 includes:

[0044] Step 3031: Determine the displacement load vector Size

[0045] Displacement load vector at any time during the analysis By directly scaling the applied force vector with the load factor λ and the standard displacement load vector The product of gets:

[0046]

[0047] The load factor λ is automatically increased by load control or response control increment strategy. A series of loads can be obtained for λ. The response of the structure is obtained through model calculation, thus obtaining the load-response relationship curve.

[0048] Step 3032: Determine the displacement load vector shape;

[0049] Step 3033: Add the displacement load vector. The displacement load is added by incremental update, that is, the balanced displacement load in the previous iteration process is added. The load vector of the given iteration step t is obtained by adding the newly derived displacement load vector increment The new load factor is the current load factor increment Δλ t Scaling vector with current modality and the nominal load vector The product between P0 represents the defined standard load vector, λ n Indicates the load factor, F j represents the equivalent inertia force of the jth layer of the structure;

[0050] Step 3034: Analyze and calculate that as the lateral load increases, the components in the weak parts of the structure reach yield. The stiffness of the yielded components is corrected and the next round of iteration begins.

[0051] Furthermore, in step 3032, the displacement load vector The shape of the normalized modal scale vector Determine, calculated at the beginning of each load increment, the normalized modal scale vector The solution is to directly solve the scale vector and perform mode combination:

[0052] Δ j =φ ij Γ i S d

[0053] When considering local damage, since the high-order modes have similar modal frequencies or frequency coupling, the CQC rule is used to combine the modes, and for the j-th layer of the structure, the following is obtained:

[0054]

[0055] Furthermore, the displacement load vector in step 3032 The shape of the normalized modal scale vector Determine, calculated at the beginning of each load increment, the normalized modal scale vector The solution is to use the superposition of inter-layer displacements and determine the modal δ by using the eigenvalue vector ij The inter-story displacement of the structure is combined under each vibration mode using the CQC rule. For the j-th layer, the displacement of the modal combination of each layer below the layer is summed to obtain the displacement mode Δ of the i-th layer. j :

[0056]

[0057] Δ j After normalization, we get:

[0058]

[0059] Furthermore, the specific process of step 305 includes:

[0060] Since the MDOF system can be decoupled by the participation coefficient Γ, the differential equation of motion based on the orthogonality is transformed into the basic form of the solution:

[0061]

[0062] Define m* as the equivalent mass of the system, which is When the earthquake load is regarded as an inertial force, the external force on the structure is only the elastic restoring force of the structure.

[0063] Simplifying, we get:

[0064]

[0065] The equivalent displacement is D * =D i / Γ, the equivalent force is F * =V / Γ, the total base shear force of the structure is

[0066]

[0067] The transformations of displacement and force are both constants Γ. Therefore, the force-displacement relationship defined by the VD diagram of the MDOF system also applies to the F*-D* diagram of the equivalent SDOF system. This is visualized by dividing both the force and displacement by Γ and by changing the scales of the two axes of the force-displacement diagram. The initial stiffness of the equivalent SDOF system remains the same as that defined by the base shear-top displacement diagram of the MDOF system.

[0068] When a solution is required based on a bilinear system, the elastic period of the ideal bilinear system T can be determined as:

[0069]

[0070] D y * and F y * Represent the yield displacement and force of the system respectively, since The equivalent force can be expressed by acceleration, that is, by F * =m * S a , S a The VD diagram of the MDOF system is converted into the S diagram of the SDOF system. a -D* graph.

[0071] Compared with the prior art, the present invention has the following advantages:

[0072] 1. The method and process for establishing a blasting response requirement spectrum based on field-measured blasting seismic wave velocities is primarily due to the ease of obtaining on-site measured velocities, eliminating the need for other data measurements and reducing engineering workload. Furthermore, ground velocity more directly reflects the energy transmitted by seismic waves, which is more closely related to the kinetic energy and stresses a structure may experience. A higher velocity indicates greater kinetic energy carried by the seismic wave, and potentially greater structural damage.

[0073] 2. The present invention adopts a load application method that controls the load based on force during the analysis process and continuously updates the dynamic response, and combines the modes through CQC rules to make the results closer to the actual situation.

[0074] 3. Compared with the procedure discrimination method, the present invention can more accurately reflect the damage situation and process, local damage situation and structural response, facilitate subsequent blasting optimization and structural reinforcement, and can be more easily implemented and significantly save computing power compared to dynamic time-history analysis.

[0075] 4. The present invention can be implemented through a graphical method, which is more convenient and intuitive.

[0076] 5. In the present invention, the capacity spectrum and demand spectrum are calculated separately and have no direct correlation. The calculation of demand spectrum does not limit the specific structure, and the calculation of capacity spectrum does not specify the specific blasting seismic wave input. The calculation process is only related to S a The maximum absolute acceleration is not directly related to the explosion situation, so it can be used as a coefficient to establish different structures for different S a capacity curve, so it is possible to establish a database of capacity spectrum and demand spectrum for a certain blasting type and existing structure respectively, which can be achieved directly through graphics without numerical simulation.

[0077] 6. The seismic waves generated by the explosion are mainly composed of medium and low frequency components. For this type of frequency fluctuation, the change in ground velocity can better reflect the actual impact of the wave, while acceleration is usually used to capture high-frequency components, and its response to medium and low frequencies is not as obvious as velocity.

[0078] 7. The ground velocity waveform is usually smoother and more representative than the acceleration waveform, and can more clearly reflect the propagation characteristics of the blasting seismic wave.

[0079] 8. Acceleration signals often contain more high-frequency noise, which can interfere with the signal's authenticity and make it more difficult to determine the impact of the blast. In contrast, ground velocity signals are less affected by noise, making it easier to obtain stable and meaningful measurements. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 It is a schematic diagram of the vibration curve of blasting seismic wave velocity;

[0081] Figure 2 It is the formation of earthquake response spectrum;

[0082] Figure 3 It is a typical blasting response spectrum curve.

[0083] Figure 4 It is a typical smooth elastic acceleration spectrum and the corresponding elastic displacement spectrum.

[0084] Figure 5 is the elastic response spectrum S A，e -S D，e Schematic diagram of .

[0085] Figure 6is the inelastic quasi-absolute acceleration-relative displacement S A，e -S D，e Schematic diagram of the curve.

[0086] Figure 7 It is a graph showing the relationship between the equivalent stiffness and displacement and velocity of a single degree of freedom system.

[0087] Figure 8 It is a schematic diagram of the VD curve of the corresponding relationship between load and displacement obtained by structural deformation; among them, Base shear is the base shear force, Top displacement is the roof displacement, and incremental lateral load is the increased lateral load.

[0088] Figure 9 It is the capability curve of the SDOF system.

[0089] Figure 10 It is a schematic diagram that combines the structural demand curve and the capacity curve in the same coordinate system. DETAILED DESCRIPTION

[0090] The preferred embodiments of the present invention are described in detail below with reference to the accompanying drawings so that the advantages and features of the present invention can be more easily understood by those skilled in the art, thereby making a clearer and more precise definition of the protection scope of the present invention.

[0091] This embodiment specifically provides a nonlinear static analysis method for the impact of blasting vibration on surrounding buildings based on on-site measurement of vibration velocity. Figure 1-10 As shown, it is introduced in detail from the following aspects.

[0092] 1. On-site testing and data collection

[0093] Blasting excavation was carried out in the test section, and velocity detection was performed on the in-track blasting vibration test to obtain velocity time history curves, maximum velocity amplitude and main frequency at different blast center distances. The Sadovsky formula was used to perform regression analysis on the velocity peak data of the tunnel surface particles to obtain the vibration velocity attenuation formula for the blasting.

[0094] The formula is as follows:

[0095] V=K(Q 1 / 3 / R) α

[0096] Where: V is the peak vibration velocity of the particle, cm / s;

[0097] The maximum section of Q is the charge amount, kg;

[0098] R is the distance from the explosion source to the measuring point, m;

[0099] K and α are the coefficient and attenuation index related to site conditions, respectively.

[0100] By taking the logarithm of both sides of the formula, it can be converted into a linear equation:

[0101] lnV=lnK+αln(Q 1 / 3 / R)

[0102] The least square method is used for calculation and combined with practical engineering application to obtain the linear vibration velocity attenuation curve.

[0103] Based on the results of this formula, the vibration velocity of the structure to be analyzed can be determined. Combined with the measured blasting velocity time history curve, the blasting seismic wave velocity vibration curve at the structure to be analyzed can be obtained. (Of course, if the time history curve cannot be measured, a typical blasting seismic wave velocity vibration curve can also be used.) At the same time, the blasting seismic wave spectrum analysis is performed on the monitoring data to determine the frequency band that contributes most to the blasting vibration energy, and the dominant frequency characteristics of the horizontal ground vibration are compared and analyzed.

[0104] 2. Establish the seismic response spectrum of the single degree of freedom system

[0105] (1) Theoretical derivation

[0106] Assume that there is an elastic single degree of freedom system (elastic SDOF) with mass m, damping c between it and the ground, and stiffness k. For the elastic single degree of freedom system, it is subjected to a given blasting seismic wave (the ground velocity function is measured as From the integral relationship, the ground displacement function is x g (t), the acceleration function is ) action. Then the absolute displacement of the elastic single degree of freedom system is y, and the absolute velocity is The absolute acceleration is The relative displacement with respect to the ground is y′=yx g (t), the relative speed is The relative acceleration is

[0107] For the elastic SDOF system, the elastic restoring force is S=ky′=k(yx g (t)), assuming the damping system is a viscous damping model, the damping force on the system is

[0108] Based on Newton's second law, the system equilibrium equation is:

[0109]

[0110] The differential equation of motion of the elastic SDOF system can be expressed as

[0111]

[0112] The integral relationship based on velocity and displacement can be rewritten as:

[0113]

[0114] It can be simplified

[0115]

[0116] Written in the form of a homogeneous linear differential equation

[0117]

[0118] The critical damping of the structure is ξ=c / 2mω0, and the fundamental frequency is Based on the Duhamel integration method, the steady-state solution of the relative motion function of the mass of the elastic SDOF system can be expressed as

[0119]

[0120] According to the integral relationship, we can get

[0121]

[0122] in For the structure with ξ<0.05, ω0 is considered to be approximate. For the flexible system with ξ<0.05, Therefore ω0 ≈ ω d ,based on It can be expressed as the absolute velocity and acceleration function obtained by differentiating the displacement function:

[0123]

[0124] Assume that the elastic relative displacement response spectrum is S D，e =|yx g (t)| max , elastic pseudo-velocity response spectrum Elastic pseudo-absolute acceleration response spectrum Based on the differential relationship, we know that S A，e =ω d 2 S D，e , S V，e =ω d S D，e .

[0125] For elastic single degree of freedom systems, the inertial force is regarded as an equivalent force reflecting the impact of blasting on the structural system and used to verify the structure. The inertial force of blasting that the structure experiences during the blasting process is

[0126]

[0127] Opposite the flexible structure, Can be ignored The elastic restoring force of the structure is equal to the inertial force:

[0128] F(t)=ky′(t)=mω 2 y′(t) (7)

[0129] y′(t)=F(t) / k=F(t)δ (8)

[0130] Here, δ = 1 / k, the flexibility coefficient of the elastic SDOF. The left side of the equal sign represents the relative displacement of the system per unit degree of freedom during the blast, while the right side represents the relative displacement of the single degree of freedom system caused by the instantaneous inertial force. Therefore, it can be assumed that the relative displacement of the structure caused by a blast at a given instant is due to the instantaneous inertial force. This is why the inertial force can be understood as an equivalent load that reflects the effects of the blast.

[0131] For flexible systems with ξ<0.05, Therefore ω0 ≈ ω d Therefore, ω is used to represent the natural frequency of the system, and integrating equations 5 and 6, we can get

[0132]

[0133] For the maximum horizontal earthquake action F e，max =mS A，e , S A，e It can be expressed as

[0134]

[0135] Same S D，e It can be expressed as

[0136]

[0137] (2) Establish the pseudo-absolute acceleration spectrum response curve and relative displacement response spectrum curve of elastic explosion

[0138] The blasting seismic wave velocity vibration curve is obtained by detecting the data in the first step. Figure 1 For example.

[0139] Based on the theory in (1), we can directly solve the assumed single-degree-of-freedom motion equation (Eq. 1) by actually using numerical methods (such as the central difference method and the Newmark method) to obtain the pseudo-absolute acceleration and time S of the structure with given stiffness k and mass m. A，e -t curve.

[0140] Now keep the mass of single degree of freedom, and by changing the stiffness of the structure, we can get the pseudo-absolute acceleration and time S under the single degree of freedom system with different natural frequencies. A，e -t curve between Figure 2 shown.

[0141] Take each S A，e -t curve S A，e The maximum value is obtained, and the pseudo-absolute acceleration and time S under the single degree of freedom system with different natural frequencies are obtained. A，e -t, which is the curve of the pseudo-absolute acceleration response spectrum of the elastic explosion. Using a similar method, the elastic relative displacement response spectrum S D，e -T curve. Smooth S can be obtained by bilinearization. A，e -T and S D，e -T curve.

[0142] For each explosion, the corresponding quasi-absolute acceleration S can be obtained A -T curve, through the data collection and calculation of the same blasting mode and blasting design, the S under this blasting mode can be obtained. A -T database. By smoothing these curves and considering different factors (blasting amount, blasting center distance, blasting method, formation conditions, formation velocity, damping coefficient, etc.), we can get a blasting empirical response spectrum curve based on certain variation coefficients. Through this curve, we can directly get the blasting response spectrum curve based on blasting amount, blasting center distance, blasting method, formation conditions or other coefficients without acceleration measurement (or only ground velocity measurement) and numerical calculation, such as Figure 3 shown.

[0143] 3. Obtain quasi-absolute acceleration-relative displacement S A，e -S D，e Curve (demand curve)

[0144] For the elastic SDOF system, we know from the differential relationship that S A，e =ω d 2 S D，e , S V，e =ω d S D，e , we can get:

[0145]

[0146] Where S A，e and S D，eare the values ​​in the elastic acceleration spectrum and displacement spectrum, respectively, corresponding to the corresponding period T and fixed viscous damping ratio. When we assume that the damping is 5%, the peak pseudo-ground acceleration is normalized by the gravity acceleration g, and the typical smooth elastic acceleration spectrum and the corresponding elastic displacement spectrum are as follows: Figure 4 shown.

[0147] For elastic SDOF systems with the same structural stiffness and mass, T is the same, and the corresponding elastic S can be obtained. A，e -S D，e Therefore, the two elastic response spectra can be expressed as S A，e -S D，e Format drawing, such as Figure 5 shown.

[0148] For an inelastic SDOF system with a bilinear force-deformation relationship, the inelastic acceleration spectrum (S A，i ) and inelastic displacement spectrum (S D，i ) can be determined as:

[0149]

[0150] Where μ is the ductility coefficient of the ratio of maximum displacement to yield displacement, R μ is the ductility reduction factor, i.e. the hysteresis energy dissipation of the ductile structure. Now we use the bilinear spectrum to express the ductility reduction factor R μ :

[0151] When T c <T

[0152] R μ =μ, when T c >T

[0153] Where Tc is the characteristic period of blasting earthquake motion. It is defined as the transition period from the constant acceleration section (short period range) to the constant velocity section (medium period range) of the response spectrum. c >T, R μ =μ, we can see that in the medium and long period range, we can find the equal displacement law S D，i =S D，e , that is, the displacement of the inelastic system is equal to the displacement of the corresponding elastic system in the same period. Based on the above relationship, the inelastic pseudo-absolute acceleration-relative displacement S can be obtained A，e -S D，e Curves such as Figure 6 shown.

[0154] 4. Static pushover analysis

[0155] Pushover analysis is performed by subjecting the structure to a gravity load and a monotonically increasing lateral force pattern. The lateral force represents the inertial force that the simulated structure will experience when subjected to ground shaking. Under the increasing load, the elastic and inelastic behavior of the individual components increases, and the various structural elements yield sequentially. As a result, the structure experiences a loss of stiffness with each event. Pushover analysis allows the determination of nonlinear force-displacement relationships for multi-degree-of-freedom systems. Lateral loads can represent the extent of base shear caused by seismic loads. Their configuration may be proportional to the distribution of mass along the building height, mode shapes, or other practical means. In principle, any force and displacement can be selected. Material nonlinearities are assigned to discrete hinge locations or distributed plasticity, where plastic rotation occurs according to FEMA-356 or another set of code-based or user-defined standards.

[0156] It is worth noting that although this method is based on the measured velocity, that is, the blasting seismic wave load is defined based on the measured velocity, and in some analyses is used as an external force equivalent to the blasting seismic wave. However, for static pushover analysis, what is needed is the capacity curve of the structure, that is, it only cares about the response of the structure under different loads. During the analysis, the shape and size of the load are defined by the engineer according to the control form or indirectly calculated, and have nothing to do with the earthquake to be analyzed and measured. Based on the simplicity and intuitiveness of the analysis and the accuracy of the model assumptions, when analyzing the finite element of static pushover analysis and calculating the equivalent SDOF, let the seismic load be considered as the pseudo-absolute acceleration S of the structure. A It can be obtained from the acceleration response spectrum mentioned above.

[0157] (1) Theoretical determination

[0158] First, determine the dynamic characteristics (natural frequency, vibration mode) of the elastic multi-degree-of-freedom system (MSOF). The basic motion differential equation of the free vibration equation of the elastic multi-degree-of-freedom structure is:

[0159]

[0160] Where [M] is the mass matrix of the structure, [C] is the damping matrix of the structure, and [K] is the stiffness matrix of the structure. Now assume that the effect of damping on the natural vibration of the structure is ignored, and we get:

[0161]

[0162] The solution to this differential equation is the displacement vector of the structure, which is of the form Substituting into the above formula and simplifying it, we can get:

[0163]

[0164] Its characteristic equation is:

[0165] |-ω2 M+K|=0

[0166] Solve the characteristic equation to obtain the characteristic value ω of the structural system j , substitute the eigenvalue into the equation to solve and get the eigenvector The obtained eigenvalue ω j 2 is the natural frequency of the structure, and the eigenvector This is the natural vibration mode of the structure.

[0167] The multi-degree-of-freedom system is reduced in degrees of freedom. Based on the orthogonality between the vibration modes, that is, When p≠k, the relative displacement vector of the structure blasting response can be Use vibration mode To expand and obtain a series of independent vibration equations, the vibration of the MDOF system is decomposed into independent vibrations under each vibration mode.

[0168]

[0169] Substitute it into the basic motion differential equation of the corresponding vibration equation of the elastic multi-degree-of-freedom structure subjected to explosion and multiply the equation on the left get:

[0170]

[0171] in is a unit vector.

[0172] Because of the orthogonality mentioned above, we know that for p≠k items, When p = k, the result of this forward and backward multiplication is always a positive number. If the stiffness matrix is ​​used, it is called the modal stiffness. If a mass matrix is ​​used, it is called modal mass Through vibration mode The linear change makes It is not difficult to find that this has no effect on the calculation results.

[0173] For the damping term, the equivalent damping ratio ξ is used. i , the basic differential equation of motion can be simplified to the following formula, where [I] and [J] are unit matrices.

[0174]

[0175] It can be found that the multi-degree-of-freedom system is decoupled, and the coupled equations in spatial coordinates become an uncoupled ordinary second-order differential equation system, which is equivalent to the differential equation system controlling the single-degree-of-freedom motion:

[0176]

[0177] The equivalent damping ratio ξ i Obtained from actual structural analysis, and is the participation coefficient of the i-th order vibration mode of the structure Its satisfaction m j is the mass of the structural particle j; φ ij is the amplitude of the i-order vibration mode at particle j.

[0178]

[0179] If the MDOF structure is equivalent to multiple SDOF structures, the blasting ground acceleration needs to be reduced according to the vibration mode participation coefficient.

[0180] By using Duhamel integration method, we can get:

[0181]

[0182] Calculate q i (t) after the displacement u i (t) can be obtained by q i (t) and the eigenvectors are obtained

[0183] Based on the theory of the SDOF elastic system mentioned above, the damping ξ i and the natural frequency ω i The structure is shaken by the ground Displacement response under action:

[0184]

[0185] You can use q i (t) is simplified to:

[0186] q i (t) = Γ i D i (t)

[0187] You can find D i (t) Depends only on ground motion and modal damping ξ i and frequency ω i Rather than the mode shape. At the same time, D i The maximum value of (t) can be read directly from the response spectrum if there is an available ground motion Once the modal coordinates are calculated, the displacement of each mass as a function of time can be calculated using modal superposition:

[0188]

[0189] The displacement of one mass is where Δ is the scale vector of the structure and the vector represents the vibration shape of the structure, which is related to the modes and participation conventions.

[0190] Similarly, the acceleration of the particle relative to the ground under the control of mode i in the MDOF system can be obtained:

[0191]

[0192] According to the acceleration of the particle, the inertial force of the blasting action of vibration mode j on particle i is:

[0193]

[0194] The total base shear force of the structure is:

[0195]

[0196] in is the equivalent mass of vibration mode i,

[0197]

[0198] And satisfy

[0199]

[0200] Substituting this into the total base shear force, we obtain

[0201]

[0202] Its form is that the contribution of the i-th order vibration mode of the structure to the base shear force under blasting is the equivalent mass The SDOF system moves on the ground The inertial force under the inertial force is the result of decoupling the equation of motion of the MDOF system according to the equivalent mass of the structure.

[0203] By decoupling the equivalent mass of the structure, the relationship between the inertial force on mass point j and the base shear force under vibration mode i is obtained:

[0204]

[0205] Because the seismic force under earthquake action does the same work in the MDOF system and the equivalent SDOF system, we can get:

[0206]

[0207] D j eff For MDOF system, the equivalent mass The displacement of the equivalent SDOF system after decoupling, Fij , V j Substitute the expression into the above equation:

[0208]

[0209] Simplified

[0210]

[0211]

[0212] This shows that according to the principle of mode superposition, after the structural elastic MDOF system is decomposed according to the equivalent mass under the blasting action, the total response of the structure is the superposition of the responses of multiple SDOF systems.

[0213] The equivalent stiffness of the effective single degree of freedom system is the secant stiffness corresponding to the maximum displacement, such as Figure 7 As shown, the maximum displacement is the equivalent displacement. According to the principle of structural dynamics, the equivalent stiffness K of the equivalent single degree of freedom system can be expressed as:

[0214]

[0215] in is the equivalent period of the equivalent SDOF, and the solution process is mentioned below. The relationship between the equivalent displacement and the base is obtained as follows:

[0216] (2) Model building

[0217] Establish a finite element model and use a multi-degree-of-freedom structural model. In addition to the data required for normal elastic analysis, such as elastic modulus, shear modulus, specific gravity, etc., the basic data for establishing the model also requires the nonlinear force-deformation relationship of the structural unit under monotonic load, such as the nonlinear stress-strain curve of concrete, using a bilinear or trilinear moment-rotation relationship. When establishing the unit model, beam units with plastic hinges at both ends and shell units are selected to simulate masonry behavior. (Fiber beam models and contact units can be used instead when accuracy is required). For the structure with multiple degrees of freedom, the inertial mass m of each degree of freedom is used. i (It can be a uniformly distributed mass or a concentrated mass. For a uniformly distributed load, the inertial mass is calculated according to the degree of freedom distribution) model so that an eigenvalue analysis can be performed to update the shape of the load vector.

[0218] (3) Determination of structural characteristics

[0219] Determine the load-displacement relationship of the structure, and thus determine the structural stiffness. Then calculate the natural frequency ω based on the mechanical model and stiffness characteristics of the structure. i , vibration shape Participation coefficient Γ i And the equivalent mass m corresponding to each vibration mode j .

[0220] (4) Apply load

[0221] 1. Displacement load vector Size

[0222] The analysis begins by defining a standard displacement load vector Its size can be chosen arbitrarily, since it defines the structural nodes to which the loads are applied. For uniformly distributed loads, the size and shape of this vector are less relevant, since it does not affect the obtained results during subsequent calculations by automatically scaling the load vector to meet the analysis objectives.

[0223] For any time during the analysis, the load vector P is calculated by directly scaling the applied force vector with the load factor λ and the standard load vector The product of gets:

[0224]

[0225] The load factor λ is automatically increased using a load-controlled or response-controlled increment strategy and can be considered an independent variable. A series of loads can be generated for λ, and the response of the structure can be calculated by the model, thereby obtaining a load-displacement response curve. This curve is repeated until the predefined analysis goal is reached or the numerical value fails.

[0226] 2. Displacement load vector Shape

[0227] As mentioned in the previous theoretical analysis, the normalized modal scale vector It can be used to determine the shape of the load vector (or load increment vector) at each step. It needs to be calculated at the beginning of each load increment in order to make the scale vector reflect the actual stiffness state of the structure calculated at the end of the previous load increment. First, the structural characteristics determined by the eigenvalue analysis in step 3 are used. For the normalized modal scale vector This method provides two solution methods.

[0228] First: directly solve the scale vector and perform modal combination. To this end, the Lanczos algorithm is used to determine the modal vibration shape and participation factor of any given predefined modal number. At the same time, the scale vector is calculated with the S of the instantaneous period of the modal. d The values ​​are weighted to take into account the effect of the frequency content of a particular input time history or spectrum on the response of the structure being analyzed.

[0229] Δ j =φ ijΓ i S d

[0230] In order to consider the influence of multiple vibration modes (their maximum accelerations do not appear at the same time and should not be directly superimposed), according to actual engineering experience, when local damage (generally caused by high-order modes) needs to be considered, since the high-order modes have similar modal frequencies or frequency coupling, the CQC rule is used to combine the vibration modes. For the jth layer of the structure, it is obtained as follows:

[0231]

[0232] Second: based on the superposition of inter-story displacements. For the maximum displacement of the j structure, it is essentially the relative displacement between the floor and the ground, which cannot fully understand the actual degree of damage suffered by the building under seismic loads. On the contrary, the displacement between floors, as the difference between the floor displacements of two consecutive floors, has a clearer and more direct relationship with the horizontal deformation demand of the building. Therefore, another scaling scheme was developed, that is, the maximum inter-story displacement value is obtained directly from the modal analysis, rather than from the difference between the maximum floor displacement values ​​that are not necessarily simultaneous, for calculating the scaled displacement vector. Therefore, by using the eigenvalue vector to determine the modal delta ij The inter-story displacement of each vibration mode is combined using the CQC rule. For the j-th layer of the structure, the following formula is obtained. The displacement mode Δ of the i-th layer is obtained by summing the inter-story displacements of the modal combinations of the layers below the layer. j Similarly, the inter-story displacement is calculated with the instantaneous period S of the modal d The values ​​are weighted to take into account the effect of the frequency content of a particular input time history or spectrum on the response of the structure being analyzed.

[0233]

[0234] In general, the accuracy of increasing the inter-story displacement is higher than directly solving the scale vector, but the scale vector has low computational requirements and is used in structures that do not require high accuracy or are relatively easy to detect.

[0235] Since the purpose of determining the normalized modal scale vector Δ is to obtain the load shape rather than the magnitude, only the relative value of the floor position is meaningful. j Perform normalization and obtain

[0236]

[0237] It is worth noting that this algorithm tends to produce unrealistically high load concentrations at a given floor as it begins to fail due to damage accumulation, leading to equally unrealistically high drift values. Therefore, for this reason, it seems reasonable to adopt a constant load vector shape within the post-peak softening structural response range.

[0238] 3. Increase of load vector

[0239] The load increase for static pushover analysis is achieved through incremental update. The load vector (of the balanced displacement load) is incrementally added to the newly derived displacement load vector to obtain the load vector for a given analysis step t The new load factor is the current load factor increment Δλ t Scaling vector with current modality and the nominal load vector The product between

[0240]

[0241] (5) Analysis and calculation

[0242] The horizontal lateral loading pattern used in the static elastoplastic analysis represents the distribution of seismic inertial forces on the structure. The horizontal lateral force is calculated in step (4). The load is applied to the model and a finite element simulation is performed with increasing λ. As the lateral load increases, the components in the weak parts of the structure yield. At this time, the stiffness of the yielding components is corrected:

[0243] A. Set the ends of flexural members such as beams, columns, shear walls, etc. that have reached flexural strength as hinge points;

[0244] B. Remove the shear walls on the floors that have reached the shear strength;

[0245] C. Remove supporting members that have buckled and whose strength decreases rapidly after buckling;

[0246] D. For components whose stiffness has been reduced but can withstand more loads, modify their stiffness characteristics.

[0247] Then repeat steps (3) and (4) and continue to increase the lateral load until a new component yields. Finally, the target displacement can be determined by the displacement response spectrum. By accumulating the forces and deformations at each loading stage, the total internal forces and total deformations of all components at all loading stages can be obtained.

[0248] The load is continuously increased and the structural vibration characteristics and the new load are calculated until the lateral displacement of the structure reaches the predetermined target displacement, or too many plastic hinges appear in the structure and become a mechanism. The load-response relationship VD curve is obtained by recording the total internal force and total deformation. Figure 8 shown.

[0249] 5. Equivalent SDOF (elastic single degree of freedom system) model and capacity curve

[0250] According to theoretical analysis, the MDOF (elastic multi-degree-of-freedom system) system can be decoupled by the participation coefficient Γ. The differential equation of motion based on orthogonality is transformed into the basic form of the solution:

[0251]

[0252] Define m* as the equivalent mass of the system, which is Ignore the effect of damping, that is, when the earthquake load is regarded as inertial force, the external force on the structure is only the elastic restoring force of the structure. Simplifying, we get:

[0253]

[0254] The equivalent displacement is D * =D i / Γ, the equivalent force is F * =V / Γ, the total base shear force of the structure is

[0255]

[0256] It can be seen that the transformations of displacement and force are based on the same constant Γ. Therefore, the force-displacement relationship determined for the MDOF system (VD plot) also applies to the equivalent SDOF system (F*-D* plot) by dividing both the force and displacement by Γ. This can be visualized by changing the scales on both axes of the force-displacement plot. The initial stiffness of the equivalent SDOF system remains the same as that defined by the base shear-top displacement plot of the MDOF system.

[0257] When solving a bilinear system, it is usually assumed that the stiffness after yielding is equal to zero. This is because the reduction factor R μ is defined as the ratio of the required elastic strength to the yield strength. Therefore, the effects of moderate strain hardening are incorporated into the demand spectrum. At the same time, moderate strain hardening has no significant effect on the displacement demand, and the proposed spectrum is approximately applicable to systems with zero or small strain hardening. The elastic period of the ideal bilinear system T can be determined as:

[0258]

[0259] D y * and F y * represent the yield displacement and force of the system, respectively.

[0260] And because For the equivalent force, it can be expressed by acceleration, that is, by F * =m * S a , S aIt is obtained from the acceleration response spectrum. In this way, the multi-degree-of-freedom MDOF system (VD diagram) can be converted into an SDOF system (S a -D* graph). Finally we get the capability curve graph (such as Figure 9 shown).

[0261] 6. Seismic Demand Equivalent SDOF System

[0262] By combining the demand curve and the capacity curve in the same coordinate system, we can get Figure 10 shown.

[0263] The resistance of the equivalent SDOF system to blasting can be determined using the graphical procedure shown in the figure. Elastic period T of the ideal bilinear system * The corresponding radial line and elastic demand spectrum S ae The intersection of defines the acceleration demand (strength) and the corresponding elastic displacement demand required for elastic behavior. ay It represents both the acceleration requirement of the inelastic system and the load-bearing capacity of the inelastic system. μ It can be determined as the ratio of the accelerations corresponding to the elastic and inelastic systems.

[0264]

[0265] R μ This differs from the reduction factor R used in seismic codes. The code reduction factor R takes into account energy dissipation and so-called overstrength.

[0266] If the structure needs to be reinforced, modified or redesigned for blasting resistance (if a relevant database is established as mentioned above to clarify the relationship between blasting volume, blasting method and acceleration), the design acceleration S ad Usually less than the yield acceleration S ay When the elastic period T is greater than or equal to T c When the inelastic displacement demand S a Equal to the elastic displacement demand S de As can be seen from the triangle in the figure, the ductility requirement is defined as μ = S ad / D y * , which is equal to R μ :

[0267] S d =S de (T * ), T c ≤T *

[0268] μ=R μ

[0269] When the elastic period T is less than T c When , the structural ductility requirement is:

[0270]

[0271] In both cases, the inelastic demands for acceleration and displacement correspond to the intersection of the capacity diagram and the demand spectrum for the ductility demand μ. The ductility factor determined from the capacity diagram is equal to the ductility factor associated with the intersecting demand spectrum. A graphical approach is not required; therefore, all steps in the process can be performed digitally without using graphics. However, the graphical process may help to better understand the relationships between the basic quantities.

[0272] Summary: 1) Based on the blasting seismic wave velocity measured on site, a method and process for establishing the blasting response demand spectrum is clearly established, which is rare in the past. (2) The analysis method is optimized so that the analysis can not only determine whether the structure will be damaged as a whole, but also analyze the local damage situation and location. (3) For the load application method, the analysis process is controlled based on force and the dynamic response is continuously updated. The modal combination is based on the CQC rule, so that the results are closer to the actual situation. (4) The method is based on velocity, and its advantages are mentioned in the background. (5) Because the regulations also evaluate the structural response based on velocity, it can be used as a supplement to the regulations judgment. At the same time, compared with the regulations judgment method, it can more accurately reflect the damage situation and process, local damage situation and structural response, which is convenient for subsequent blasting optimization and structural reinforcement. Compared with dynamic time history analysis, it can be more easily implemented and greatly save computing power. (6) It can be implemented through graphical methods, which is more convenient and intuitive. (7) It can be found that the capacity spectrum and demand spectrum of this method are calculated separately and have no direct correlation (the calculation of demand spectrum does not limit the specific structure, and the calculation of capacity spectrum does not specify the specific blasting seismic wave input. The calculation process is only related to S a The maximum absolute acceleration is not directly related to the explosion situation, so it can be used as a coefficient to establish different structures for different S a capacity curve), so it is possible to establish a database of capacity spectrum and demand spectrum for a certain blasting type and existing structure respectively, which can be achieved directly through graphics without numerical simulation.

[0273] Compared with the nonlinear static analysis method based on acceleration (1) in simulating earthquake loads, although the results based on acceleration are more accurate than those based on velocity, it is more difficult to measure acceleration on site and has higher requirements on instruments. Therefore, in the field of actual blasting engineering, the field data is mainly based on velocity. (2) The main regulations "Safety Regulations for Blasting" (GB6722-2010) use particle vibration velocity and main frequency as the basis for judging whether it is safe and take into account the importance of the building. Therefore, if the results need additional analysis to supplement the results, the velocity-based method does not need to measure other data and reduce the amount of engineering. (3) Ground velocity can more directly reflect the energy transmitted by earthquake waves, which is more related to the kinetic energy and stress that the structure may bear. The greater the velocity, the more kinetic energy the earthquake wave carries, and the greater the destructive force on the structure. The medium and low frequency characteristics of blasting earthquake waves (4) The earthquake generated by the blasting The waves are mainly composed of medium and low frequency components. For fluctuations of this type of frequency, changes in ground velocity can better reflect the actual impact of the wave, while acceleration is usually used to capture high-frequency components and its response to medium and low frequencies is not as obvious as that of velocity. (5) The ground velocity waveform is usually smoother and more representative than the acceleration waveform, and can more clearly reflect the propagation characteristics of the blasting seismic wave. (6) The acceleration signal usually contains more high-frequency noise, which may interfere with the authenticity of the signal, making it more difficult to judge the impact of the blasting. In contrast, the ground velocity signal is less affected by noise, and it is easier to obtain stable and meaningful measurement data.

Claims

1. A nonlinear static analysis method for the impact of blasting vibration on surrounding buildings based on on-site vibration velocity measurement, characterized in that: The nonlinear static analysis method includes the following steps: Step 1: On-site detection and data collection to obtain the vibration velocity of the target structure and the blasting seismic wave velocity vibration curve at the target structure; Step 2: Calculate the structural inelastic pseudo-absolute acceleration-relative displacement S A,e -S D,e curve, i.e., the demand curve of the target structure; Step 3: Establish a multi-degree-of-freedom structural model and perform static pushover analysis on it to obtain the load-displacement response relationship VD curve of the structure, and deform it to obtain the capacity curve of the equivalent SDOF structure; Step 4: The demand curve and capacity curve of the target structure are moved to the same coordinate system. The intersection of the demand curve and the capacity curve reflects the local damage of the structure. The process of determining the capability curve of the structure in step 3 includes: Step 301: Establish a multi-degree-of-freedom structural model; Step 302: Determine the characteristics of the multi-degree-of-freedom structural model: determine the structural stiffness and calculate the natural frequency ω based on the mechanical model and stiffness characteristics of the structure i , vibration shape Participation coefficient Γ i And the equivalent mass m corresponding to each vibration mode j ; Step 303: Apply displacement loads to the multi-degree-of-freedom structural model to perform nonlinear displacement analysis. During each iteration, the load shape for each iteration is calculated based on the structural characteristics determined in step 302. The load magnitude is increased by continuously increasing the load coefficient λ. As the load increases, components in weak locations of the structure yield, and the stiffness of the yielded components is corrected. Step 304: After the correction, repeat steps 302 and 303, and continuously increase the load until the lateral displacement of the structure reaches the predetermined target displacement or too many plastic hinges appear in the structure to form a mechanism. By recording the total internal force and total deformation, the load-displacement response relationship VD curve is obtained; Step 305: Convert the VD curve of the structural MDOF system into the S curve of the structural SDOF system. a -D* graph, that is, the capacity curve of the structure; The specific process of step 303 includes: Step 3031: Determine the displacement load vector Size Displacement load vector at any time during the analysis By directly scaling the applied force vector with the load factor λ and the standard displacement load vector The product of gets: The load factor λ is automatically increased by load control or response control increment strategy. A series of loads can be obtained for λ. The response of the structure is obtained through model calculation, thus obtaining the load-response relationship curve. Step 3032: Determine the displacement load vector shape; Step 3033: Add displacement load vector. The displacement load is added by incremental update, that is, the balanced displacement load in the previous iteration process is added. The displacement load vector for a given iteration step t is obtained by adding the load vector of New displacement load vector Current load factor increment Δλ t Scaling vector with current modality and the nominal displacement load vector The product between P0 represents the defined standard load vector; Step 3034: Analyze and calculate that as the lateral load increases, the components in the weak parts of the structure reach yield. The stiffness of the yielded components is corrected and the next round of iteration begins.

2. The nonlinear static analysis method for the impact of blasting vibration on surrounding buildings based on on-site vibration velocity measurement according to claim 1 is characterized in that: The specific process of step 2 includes: Step 201: Establish a single degree of freedom system, and apply the blasting seismic wave to the single degree of freedom system based on the vibration velocity obtained in step 1 and the blasting seismic wave velocity vibration curve; Step 202: Use numerical methods to solve formula (1) to obtain the pseudo-absolute acceleration of the structure with given stiffness k and mass m and time S A,e -t curve, similarly, we can get the relative displacement and time S D,e -t curve; In the above formula, represents the absolute acceleration, represents the absolute velocity, y represents the absolute displacement, Represents the measured ground velocity function, x g (t) represents the ground displacement function, c represents the ground-to-ground damping; Step 203: Maintaining the mass m of the single-degree-of-freedom system, by changing the stiffness k of the single-degree-of-freedom system, obtain the pseudo-absolute acceleration and time S of the single-degree-of-freedom system with different natural frequencies. A,e -t curve, similarly, we can get the relative displacement and time S D,e -t curve; Step 204: Take each S A,e -t curve S A,e The maximum value is obtained, and the pseudo-absolute acceleration and period of the single degree of freedom system S A,e -T curve; similarly, the relative displacement and period of the single degree of freedom system S D,e -The curve between T; Step 205: Pseudo-absolute acceleration response spectrum S A,e -T curve and relative displacement response spectrum S D,e -T curve is converted to obtain the inelastic pseudo-absolute acceleration-relative displacement S A,e -S D,e curve.

3. The nonlinear static analysis method for the impact of blasting vibration on surrounding buildings based on on-site vibration velocity measurement according to claim 2 is characterized in that: In step 204, the structure is pseudo-absolute acceleration and period of the single degree of freedom system S A,e The expression of the curve between -T is as follows: In the above formula, ξ represents the critical damping of the structure, For flexible systems with ξ<0.05, Then ω d represents the natural frequency of the single-degree-of-freedom system, and τ is the Duhamel integration variable.

4. The nonlinear static analysis method for the impact of blasting vibration on surrounding buildings based on on-site vibration velocity measurement according to claim 3 is characterized in that: The single degree of freedom system S of the relative displacement and period of the structure in step 204 D,e The curve between -T is expressed as follows:

5. The nonlinear static analysis method for the impact of blasting vibration on surrounding buildings based on on-site vibration velocity measurement according to claim 4 is characterized in that: The specific process of step 205 is: (1) For the elastic SDOF system, it can be seen from the differential relationship that S A,e =ω d 2 S D,e , S V,e =ω d S D,e , we can get: For elastic SDOF systems with the same structural stiffness and mass, T is the same, and the corresponding elastic S can be obtained. A,e -S D,e relation; (2) For an inelastic SDOF system with a bilinear force-deformation relationship, the inelastic acceleration spectrum S A,i and inelastic displacement spectrum S D,i Determined as: In the above formula, μ is the ductility coefficient of the ratio of maximum displacement to yield displacement, R μ is the ductility reduction factor, and the ductility reduction factor R is expressed using a bilinear spectrum. μ : When T c <T R μ =μ, when T c >T In the above formula, Tc is the characteristic period of blasting earthquake motion, which is defined as the transition period from the constant acceleration section to the constant velocity section of the response spectrum, that is, the transition period from the short-period range to the medium-term range. c >T, R μ =μ, in the medium and long period range S D,i =S D,e , that is, the displacement of the inelastic system is equal to the displacement of the corresponding elastic system in the same period. Based on the above relationship, the inelastic pseudo-absolute acceleration-relative displacement S can be obtained A,e -S D,e curve.

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