A nonlinear static analysis method and system for the impact of blasting vibration on surrounding buildings based on acceleration

Abstract

The present invention discloses a nonlinear static analysis method and system for the impact of blasting vibration on surrounding buildings based on acceleration, belonging to the field of engineering blasting technology. The safety assessment method comprises the following steps: Step 1: On-site detection and data acquisition to obtain the blasting acceleration characteristics and the blasting seismic wave acceleration vibration curve of the blasting; Step 2: Calculate the inelastic pseudo-absolute acceleration-relative displacement S of the structure. A，e ‑S D，e The curve is the structural 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 structural 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 present invention belongs to the technical field of engineering blasting, and in particular relates to a nonlinear static analysis method and system for the influence of blasting vibration on surrounding buildings based on acceleration. Background Art

[0002] Currently, research on the impact of blasting vibration on surrounding buildings is incomplete. The primary regulation, the "Safety Code for Blasting" (GB6722-2010), solely uses particle velocity and dominant frequency as criteria for safety assessment, while also considering factors such as building importance and quality. However, given the common occurrence of blasting operations in real-world projects, where both high- and low-frequency components are present in blasting waves, a single dominant frequency corresponding to the maximum amplitude is inappropriate and incomplete. Furthermore, this regulation, which solely 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, potentially leading to overly conservative assumptions. 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 standards 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 assessment 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] In a first aspect, the present invention provides a nonlinear static analysis method for the impact of blasting vibration on surrounding buildings based on acceleration. The safety assessment method comprises the following steps:

[0007] Step 1: On-site testing and data collection to obtain the blasting acceleration characteristics and the blasting seismic wave acceleration vibration curve of the blasting;

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

[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 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 blasting acceleration characteristics obtained in step 1 and the blasting seismic wave acceleration vibration curve of the blasting;

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

[0015] 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 and S of relative displacement and time D,e -t curve;

[0016] 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;

[0017] Step 205: Pseudo-absolute acceleration response spectrum S A,e -T curve and relative displacement response spectrum SD,e -T curve is converted to obtain the inelastic pseudo-absolute acceleration-relative displacement S A,e -S D,e curve.

[0018] Furthermore, in step 204, the structure is pseudo-absolute acceleration and periodic single degree of freedom system S A,e The expression of the curve between -T is as follows:

[0019]

[0020] In the above formula, ξ represents the critical damping of the structure, ω represents the natural frequency of the single degree of freedom system, is the acceleration function of blasting seismic wave; τ is the Duhamel integral variable.

[0021] 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:

[0022]

[0023] In the above formula,

[0024] Furthermore, the specific process of step 205 is as follows:

[0025] (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:

[0026]

[0027] For elastic SDOF systems with the same structural stiffness and mass, T is the same, and the corresponding elastic SA can be obtained. ,e -S D,e relation;

[0028] (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:

[0029]

[0030] 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 :

[0031] When T c <T

[0032] R μ =μ, when T c >T

[0033] 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.

[0034] Furthermore, the process of determining the capability curve of the structure in step 3 includes:

[0035] Step 301: Establish a multi-degree-of-freedom structural model;

[0036] 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 ;

[0037] Step 303: Apply loads to the multi-degree-of-freedom structural model to perform static pushover 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.

[0038] 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 accumulating the forces and deformations in each loading stage, the total internal forces and total deformations of all components in all loading stages are obtained, and then the load-displacement response relationship VD curve is obtained;

[0039] 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.

[0040] Furthermore, the specific process of step 303 includes:

[0041] Step 3031: Determine the size of the load vector P

[0042] The load vector P at any time during the analysis is obtained by directly scaling the applied force vector by the load factor λ multiplied by the normalized load vector P0:

[0043]

[0044] 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 and displacement response relationship curve;

[0045] Step 3032: Determine the shape of the load vector P

[0046] Based on the structural characteristics determined in step 302 and taking into account the elastic acceleration response spectrum, we obtain:

[0047] F ij =-m j φ ij Γ i S a

[0048] When local damage is considered, the high-order modes show modal frequencies that are close or have frequency coupling. Using the CQC rule to combine the vibration modes, the result for the j-th layer of the structure is:

[0049]

[0050] F ij To determine the shape of the load, the F j After normalization, we get:

[0051]

[0052] Step 3033: Add load vector. For static pushover analysis, the load vector in the previous iteration is completely replaced by the newly derived load vector. The new load vector 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;

[0053] 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.

[0054] Furthermore, the specific process of correcting the stiffness of the component in step 3034 is as follows:

[0055] (1) The end of the bending member that has reached the bending strength is set as the hinge point;

[0056] (2) Remove the shear walls on the floors that have reached the shear strength;

[0057] (3) Remove the supporting members that have buckled and whose strength decreases rapidly after buckling;

[0058] (4) For components whose stiffness has been reduced but can bear more loads, modify their stiffness characteristics.

[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 * is 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. Simplifying, we get:

[0063]

[0064] The equivalent displacement is D * =D i / Γ, the equivalent force is F * =V / Γ, the total base shear force of the structure is

[0065] 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.

[0066] When a solution is required based on a bilinear system, the elastic period of the ideal bilinear system T can be determined as:

[0067]

[0068] D y * and Fy * Represent the yield displacement and force of the system respectively. 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.

[0069] In a second aspect, the present invention provides a safety assessment system for surrounding buildings under blasting vibration based on acceleration, the system comprising:

[0070] The acquisition module is used to realize on-site detection and data collection to obtain the blasting acceleration characteristics and the blasting seismic wave acceleration vibration curve of the blasting;

[0071] The first analysis module establishes a single degree of freedom system and applies the blasting seismic wave uploaded by the acquisition module to the single degree of freedom system to calculate the inelastic pseudo-absolute acceleration-relative displacement S of the structure. A,e -S D,e curve, i.e. the structural demand curve;

[0072] The second analysis module establishes a multi-degree-of-freedom structural model and performs static pushover analysis on it to obtain the load-displacement response relationship VD curve of the structure, and deforms it to obtain the capacity curve of the equivalent SDOF structure;

[0073] The processing module is used to move the demand curve and the capacity curve into a unified coordinate system, find the intersection of the demand curve and the capacity curve, and determine the local damage situation and location of the structure.

[0074] Compared with the prior art, the present invention has the following advantages:

[0075] 1. Traditional analysis methods only involve the seismic response demand spectrum. However, the present invention clarifies the method and process of establishing the blasting response demand spectrum through the optimization of the evaluation method. At the same time, it introduces the capacity curve of the structure. The demand curve determined by the demand response spectrum and the capacity curve of the structure obtained by static pushover analysis are used for comprehensive analysis. This can not only determine whether the structure will be completely damaged, but also analyze the local damage situation and location.

[0076] 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.

[0077] 3. The present invention is based on acceleration, which can better simulate the effect of force and the actual force and response of the structure during the blasting process compared to the velocity measurement, which makes the structure more realistic.

[0078] 4. 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.

[0079] 5. The present invention can be implemented through a graphical method, which is more convenient and intuitive.

[0080] 6. 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. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 It is a schematic diagram of the formation of earthquake response spectrum;

[0082] Figure 2 is the response spectrum curve after bilinearization;

[0083] Figure 3 It is a typical smooth elastic acceleration spectrum and the corresponding elastic displacement spectrum.

[0084] Figure 4 is the elastic response spectrum S A,e -S D,e curve chart.

[0085] Figure 5 is the inelastic quasi-absolute acceleration-relative displacement S A,e -S D,e Curve diagram,

[0086] Figure 6 It is a schematic diagram of the load vector increase law.

[0087] Figure 7 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 8 It is the capability curve of the SDOF system.

[0089] Figure 9 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 based on acceleration of the impact of blasting vibration on surrounding buildings. Figure 1-9 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 acceleration testing was performed on the tunnel blasting vibration test. The maximum acceleration amplitude and main frequency in different directions at different blast center distances were obtained. The Sadovsky formula was then used to perform regression analysis on the peak acceleration data of the tunnel surface particles to obtain the vibration velocity attenuation formula for the blasting. Based on the test data, the blasting acceleration characteristics and the typical blasting seismic wave vibration acceleration time history curve were obtained to obtain the blasting seismic wave acceleration vibration curve for the blasting (of course, it would be best if the actual blasting seismic wave acceleration vibration curve could be detected and recorded). At the same time, the monitoring data was subjected to blasting seismic wave spectrum analysis to determine the frequency bands that contribute most to the blasting vibration energy, and the main frequency characteristics of the horizontal vibration were compared and analyzed.

[0094] 2. Establish the seismic response spectrum of the single degree of freedom system

[0095] (1) Theoretical derivation

[0096] Assume that there is an elastic single degree of freedom system (elastic SDOF) with mass m, damping c, and stiffness k. For the elastic single degree of freedom system, under a given blasting seismic wave (acceleration function is Under the action, the relative velocity displacement of the elastic single degree of freedom system is y, and the relative velocity of x is The relative acceleration is The differential equation of motion according to D'Alembert's principle can be expressed as:

[0097]

[0098] It can be simplified:

[0099]

[0100] 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 motion function of the mass of the elastic SDOF system can be expressed as

[0101]

[0102] According to the integral relationship, we can get

[0103]

[0104] 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 velocity and absolute acceleration functions obtained by differentiating the displacement function:

[0105]

[0106] Assume that the elastic relative displacement response spectrum is S D,e =|y| 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 .

[0107] 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 is used to verify the structure. The inertial force of blasting that the structure experiences during the blasting process is:

[0108]

[0109] Opposite the flexible structure, neglect The elastic restoring force of the structure is equal to the inertial force:

[0110] F(t)=ky(t)=mω 2 y(t) (7)

[0111] y(t)=F(t) / k=F(t)δ (8)

[0112] 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.

[0113] For flexible systems with ξ < 0.05, Then ω0≈ω d Therefore, ω is used to represent the natural frequency of the system, and integrating equations 5 and 6, we can obtain:

[0114]

[0115] For the maximum horizontal earthquake action F e,max =mS A,e , S A,e It can be expressed as:

[0116]

[0117] Same S D,e It can be expressed as:

[0118]

[0119] It can be seen from formula (2) that when the blasting input is acceleration, the structure only has inertial force and elastic restoring force caused by its own absolute acceleration. In theoretical simplification and subsequent numerical calculations, formula (10) can be obtained. Of course, if the blasting action is simulated by velocity or explosive quantity, a pseudo-absolute acceleration expression can be obtained.

[0120] (2) Establish the pseudo-absolute acceleration spectrum response curve and relative displacement response spectrum curve of elastic explosion

[0121] In the first step, the detection data is used to obtain the blasting acceleration characteristics (peak value and frequency) and the typical blasting seismic wave vibration acceleration time history curve to obtain the blasting seismic wave acceleration vibration curve of the blasting. Based on the theory in (1), by actually using numerical methods (such as the central difference method and the Newmark method), we can directly solve the assumed single-degree-of-freedom motion equation (Equation 1) and obtain the structural quasi-absolute acceleration and time S at a given stiffness k and mass m. A,e -t curve between.

[0122] Now keep the mass of single degree of freedom, and take each S by changing the stiffness of the structure. 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 curve is as follows Figure 1 As shown. Finally, we get the single degree of freedom system S with quasi-absolute acceleration and different stiffness. A,e -T, where T is the natural vibration period of the single degree of freedom system, and T is related to the stiffness k of the single degree of freedom system. This curve is the pseudo-absolute acceleration response spectrum curve of this elastic explosion. Using a similar method, the elastic relative displacement response spectrum S can be obtained. D,e -T curve. Through bilinearization, a smooth S A,e -T and S D,e -T curve.

[0123] 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 2 shown.

[0124] 3. Obtain quasi-absolute acceleration-relative displacement S A,e -S D,e Curve (demand curve)

[0125] 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:

[0126]

[0127] Where S A,e and S D,e are 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 3 shown.

[0128] 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 4 shown.

[0129] 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:

[0130]

[0131] 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 :

[0132] When T c <T

[0133] R μ =μ, when T c >T

[0134] 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 5 As shown. For example, S D,e :

[0135] 4. Static pushover analysis

[0136] Pushover analysis is performed by subjecting the structure to a gravity load and a monotonically increasing lateral force pattern. The lateral force simulates the inertial forces the structure would experience when subjected to ground vibrations. Under the increasing load, the elastic and inelastic behavior of the individual components increases, and the various structural elements yield sequentially.

[0137] Therefore, with each event, the structure experiences a loss of stiffness. 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 chosen. 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. Selecting the appropriate lateral load distribution is an important step in pushover analysis. There is no unique solution.

[0138] (1) Theoretical determination

[0139] 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:

[0140]

[0141] 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:

[0142]

[0143] 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:

[0144]

[0145] Its characteristic equation is:

[0146]

[0147] 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.

[0148] 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.

[0149]

[0150] 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:

[0151]

[0152] in is a unit vector.

[0153] 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.

[0154] 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 [J] is the unit matrix.

[0155]

[0156] 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:

[0157]

[0158] 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.

[0159]

[0160] 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.

[0161] By using the Duhamel integral method we can get:

[0162]

[0163] Calculate q i (t) after the displacement u i (t) can be obtained by q i (t) and the eigenvectors are obtained

[0164] 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:

[0165]

[0166] You can use q i (t) is simplified to:

[0167] q i (t) = Γ i D i (t)

[0168] 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:

[0169]

[0170] Similarly, the acceleration of the particle relative to the ground under the control of mode i in the MDOF system can be obtained:

[0171]

[0172] The total base shear force of the structure is:

[0173]

[0174] in is the equivalent mass of vibration mode i,

[0175]

[0176] And satisfy

[0177]

[0178] Substituting this into the total base shear force, we obtain

[0179]

[0180] 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.

[0181] By decoupling the equivalent mass of the structure, the relationship between the inertial force and the base shear force acting on mass point j under vibration mode i is obtained:

[0182]

[0183] Because the seismic force under earthquake action does the same work in the MDOF system and the equivalent SDOF system, we can get:

[0184]

[0185] For MDOF system, the equivalent mass The displacement of the equivalent SDOF system after decoupling, F ij ,V j Substitute the expression into the above equation:

[0186]

[0187] Simplified

[0188]

[0189] 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.

[0190] (2) Model building

[0191] 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. j(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.

[0192] (3) Determination of structural characteristics

[0193] 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 .

[0194] (4) Apply load

[0195] 1. The size of the load vector P

[0196] At the beginning of the analysis, a standard load vector P0 is defined. Its size can be arbitrarily chosen, as it defines the structural nodes to which the load is applied. Initially, this P0 can be a uniformly distributed load. The size and shape of this vector are less relevant, as it will not affect the obtained results, as it will be automatically scaled during the subsequent calculations to meet the analysis objectives.

[0197] The load vector P for any time during the analysis is obtained by directly scaling the applied force vector by the product of the load factor λ and the standard load vector P0:

[0198]

[0199] 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.

[0200] During the analysis, when the computing power is limited, a special load control node can be selected to record the load and displacement response relationship to obtain a curve to reduce the amount of calculation. For blasting, if the damage response control is achieved through the base shear force, the base shear force and the equivalent inertia force F can be determined according to the theory. ij relation Determine the load control node And convert the base shear increment into load factor λ n According to the mainstream loading methods (triangular loading method and modulation, function loading method and exponential loading method), a specific load control node load vector P is selected based on actual engineering and engineering experience. n , and get the corresponding λ n .

[0201] 2. Shape of the load vector

[0202] Normalized modal scaling blasting equivalent inertial force F ij It is used to determine the shape of the load vector (or loading increment vector) for each step and is calculated at the beginning of each loading increment. Based on the structural characteristics determined in step 3 and considering the elastic acceleration response spectrum (obtained from the structural natural vibration period difference diagram in the first part of this article), it is obtained:

[0203] F ij =-m j φ ij Γ i S a

[0204] In order to consider the influence of multiple vibration modes (their maximum accelerations do not occur at the same time and should not be directly superimposed), according to actual engineering experience, when local damage needs to be considered (generally caused by high-order modes), 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:

[0205]

[0206] Considering F ij It is always used to determine the shape of the load. j After normalization, we get:

[0207]

[0208] This algorithm tends to produce unrealistically high load concentrations at a given floor when 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.

[0209] 3. Increase of load vector

[0210] like Figure 6 As shown in Figure 1, the load increase for a static pushover analysis is performed by completely replacing the existing equilibrium load (the load vector of the previous step) with the newly derived load vector at a given analysis step n. The new load vector P n :

[0211]

[0212] (5) Analysis and calculation

[0213] 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 the finite element simulation is performed while continuously increasing λ. As the lateral load increases, the components in the weak parts of the structure reach yield. At this time, the stiffness of the yielding components is corrected:

[0214] A. Set the ends of flexural members such as beams, columns, shear walls, etc. that have reached flexural strength as hinge points;

[0215] B. Remove the shear walls on the floors that have reached the shear strength;

[0216] C. Remove supporting members that have buckled and whose strength decreases rapidly after buckling;

[0217] D. For components whose stiffness has been reduced but can withstand more loads, modify their stiffness characteristics.

[0218] 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.

[0219] 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. By recording the total internal force and total deformation, the load and displacement response relationship VD curve is obtained, such as Figure 7 shown.

[0220] 5. Equivalent SDOF (elastic single degree of freedom system) model and capacity curve

[0221] 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:

[0222]

[0223] Define m * is 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:

[0224]

[0225] The equivalent displacement is D * =D i / Γ, the equivalent force is F* =V / Γ, the total base shear force of the structure is

[0226] 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.

[0227] 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:

[0228]

[0229] D y * and F y * represent the yield displacement and force of the system, respectively.

[0230] And because For the equivalent force, it can be expressed by acceleration, that is, by F * =m * S a , S a It 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 8 shown).

[0231] 6. Seismic Demand Equivalent SDOF System

[0232] By combining the demand curve and the capacity curve in the same coordinate system, we can get Figure 9 shown.

[0233] 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 aeThe 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.

[0234]

[0235] 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.

[0236] 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 When the elastic period T is greater than or equal to When the inelastic displacement demand 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 :

[0237] S d =S de (T * ), T c ≤T *

[0238] μ=R μ

[0239] When the elastic period T is less than T c When , the structural ductility requirement is:

[0240]

[0241] 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.

[0242] Summary: (1) The method and process of establishing the blasting response demand spectrum are clearly defined, which was previously only the earthquake response demand spectrum. (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 force-based control and continuous update of dynamic response are adopted during the analysis process, and the modes are combined through the CQC rule to make the results closer to the actual situation. (4) The method is based on acceleration, which simulates the effect of force and the actual force and response of the structure during the blasting process more than the velocity measurement method, which makes the structure more realistic. (5) Compared with the procedural 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.

[0243] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the scope of protection of the present invention. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention can be modified or replaced by equivalents without departing from the essence and scope of the technical solutions of the present invention.

Claims

1. A nonlinear static analysis method for the impact of blasting vibration on surrounding buildings based on acceleration, characterized in that: The method comprises the following steps: Step 1: On-site testing and data collection to obtain the blasting acceleration characteristics and the blasting seismic wave acceleration vibration curve of the blasting; Step 2: Calculate the structural inelastic pseudo-absolute acceleration-relative displacement S A,e S D,e curve, i.e. the structural demand curve; 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 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 loads to the multi-degree-of-freedom structural model to perform static pushover finite element 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 accumulating the forces and deformations in each loading stage, the total internal forces and total deformations of all components in all loading stages are obtained, and then 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 size of the load vector P The load vector P at any time during the analysis is obtained by directly scaling the applied force vector by the load factor λ multiplied by the normalized load vector P0: 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 and displacement response relationship curve; Step 3032: Determine the shape of the load vector P Based on the structural characteristics determined in step 302 and taking into account the elastic acceleration response spectrum, we obtain: F ij =-m j f ij C i S a When local damage is considered, the high-order modes show that the modal frequencies are close or there is frequency coupling. Using the CQC rule to combine the vibration modes, the result for the j-th layer of the structure is: F ij To determine the shape of the load, the F j After normalization, we get: Step 3033: Add load vector. For static pushover analysis, the load vector in the previous iteration is completely replaced by the newly derived load vector. The new load vector 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; 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 of the acceleration-based blasting vibration effect on surrounding buildings 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 blasting acceleration characteristics obtained in step 1 and the blasting seismic wave acceleration vibration curve of the blasting; Step 202: Use numerical methods to obtain the pseudo-absolute acceleration of the structure with given stiffness k and mass m and time S A,e -t curve and S of relative displacement and time D,e -t curve; 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 and S of relative displacement and time 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 of the acceleration-based blasting vibration effect on surrounding buildings 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, ω represents the natural frequency of the single degree of freedom system, is the acceleration function of blasting seismic wave; τ is the Duhamel integral variable.

4. The nonlinear static analysis method for the impact of blasting vibration on surrounding buildings based on acceleration 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: In the above formula, 5. The nonlinear static analysis method of the acceleration-based blasting vibration effect on surrounding buildings 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.

6. The nonlinear static analysis method of the acceleration-based blasting vibration effect on surrounding buildings according to claim 1 is characterized in that: The specific process of correcting the stiffness of the component in step 3034 is as follows: (1) The end of the bending member that has reached the bending strength is set as the hinge point; (2) Remove the shear walls on the floors that have reached the shear strength; (3) Remove the supporting members that have buckled and whose strength decreases rapidly after buckling; (4) For components whose stiffness has been reduced but can bear more loads, modify their stiffness characteristics.

7. A system based on the nonlinear static analysis method of the acceleration-based blasting vibration effect on surrounding buildings according to any one of claims 1 to 6, characterized in that: The system includes: The acquisition module is used to realize on-site detection and data collection to obtain the blasting acceleration characteristics and the blasting seismic wave acceleration vibration curve of the blasting; The first analysis module establishes a single degree of freedom system and applies the blasting seismic wave uploaded by the acquisition module to the single degree of freedom system to calculate the inelastic pseudo-absolute acceleration-relative displacement S of the structure. A,e -S D,e curve, i.e. the structural demand curve; The second analysis module establishes a multi-degree-of-freedom structural model and performs static pushover analysis on it to obtain the load-displacement response relationship VD curve of the structure, and deforms it to obtain the capacity curve of the equivalent SDOF structure; The processing module is used to move the demand curve and the capacity curve into a unified coordinate system, find the intersection of the demand curve and the capacity curve, and determine the local damage situation and location of the structure.

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