Earthquake resistance and disaster reduction simulation system for liquefiable foundation

Abstract

The invention relates to the technical field of computer modeling, in particular to an earthquake resistance and disaster reduction simulation system for a liquefiable foundation. The system comprises a cyclic stress ratio field analysis unit, an excess pore pressure ratio evolution analysis unit and a stress coupling correction unit, the cyclic stress ratio field analysis unit is used for generating a cyclic stress ratio field by using a depth reduction relation; the excess pore pressure ratio evolution analysis unit is used for deducing an excess pore pressure ratio and establishing an evolution relation of the excess pore pressure ratio along with time and depth; and the stress coupling correction unit is used for updating the effective vertical stress value based on the excess pore pressure ratio, synchronously correcting the shear modulus according to the coupling relationship between the shear wave velocity and the excess pore pressure ratio, and feeding back the corrected shear modulus to the excess pore pressure ratio evolution analysis unit. According to the method, the scientificity and engineering applicability of earthquake resistance and disaster reduction of the liquefiable foundation are effectively improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of earthquake modeling, and in particular relates to an earthquake-resistant disaster reduction simulation system for a liquefiable foundation. Background Art

[0002] In the research and engineering application of earthquake-resistant disaster reduction of liquefiable foundations, earthquake-induced foundation liquefaction and the resulting post-earthquake settlement have always been important research topics in earthquake engineering and geotechnical engineering. With the acceleration of urbanization, large-scale development and construction in coastal areas, river banks and soft soil areas have increased, making the liquefaction risk of saturated loose sandy soil, which is widespread in these areas, more prominent. When liquefaction occurs, the effective stress of the foundation soil drops sharply or even approaches zero, resulting in instantaneous loss of shear stiffness and strength degradation of the soil, which manifests as secondary earthquake disasters such as surface settlement, structural tilting and even collapse, posing a huge threat to the safety of life and property. Existing anti-liquefaction technical means mainly include on-site shaking table tests, centrifuge model tests, pore pressure monitoring and numerical simulation, etc., to evaluate the liquefaction potential of soil and the consolidation characteristics after liquefaction. To mitigate earthquake disasters in liquefiable foundations, on-site drainage improvement measures (such as sand wells and plastic drainage boards) and densification measures (such as dynamic compaction and preloading reinforcement) have been widely adopted in engineering practice. By improving the shear strength of the soil and accelerating the dissipation of excess pore water pressure, the purpose of slowing down liquefaction damage and controlling post-earthquake settlement is achieved.

[0003] Currently, numerous studies, both domestically and internationally, have developed empirical models for liquefaction discriminant curves, dynamic strength envelopes, and the evolution of excess pore pressure ratios based on stress path methods and cyclic loading test data. For example, conventional Seed et al. cyclic stress ratio discriminant curves utilize equivalent shear strain and shear modulus degradation test results to describe the threshold for soil liquefaction under specific cyclic loading. Furthermore, cumulative evolution models of excess pore pressure ratios are typically based on the product of shear strain energy density or stress amplitude and the number of cycles, simplifying the liquefaction evolution process. However, these conventional models are mostly focused on the fitting stage of laboratory tests and lack dynamic response processes coupled with actual earthquake conditions. Consequently, they are unable to reflect the dynamic attenuation of effective stress and the multi-stage evolution of shear stiffness under field ground motion time history inputs. Furthermore, conventional liquefaction discriminant models are typically based on a single number of cycles or a fixed amplitude, making them difficult to handle actual ground motion inputs with complex impulse effects, multi-frequency components, and varying durations. Furthermore, quantifying the contribution of drainage and densification measures to the dissipation of residual excess pore pressure ratios after liquefaction occurs, as well as the spatial and temporal distribution of post-earthquake settlement curves, remains a major shortcoming of existing methods. Most empirical models can only provide critical states at the instantaneous point of liquefaction identification, but cannot fully account for the real-time response throughout the earthquake or calculate secondary settlement during the post-earthquake consolidation phase. Summary of the Invention

[0004] The main purpose of the present invention is to provide a seismic disaster reduction simulation system for liquefiable foundations. Through the multi-dimensional coupling of three units, namely cyclic stress ratio field analysis, excess pore pressure ratio evolution and stress coupling correction, the system dynamically simulates the triggering of foundation liquefaction and its evolution with depth and time, and provides real-time feedback on the coupled degradation process of effective stress and shear modulus. It also introduces drainage improvement and densification parameter correction, and finally quantifies the post-earthquake surface settlement and compares it with the limit value, forming a full-process high-precision dynamic prediction platform from input seismic motion to output settlement curve, which effectively improves the scientific nature and engineering applicability of seismic disaster reduction for liquefiable foundations.

[0005] In order to solve the above problems, the technical solution of the present invention is achieved as follows: A seismic disaster reduction simulation system for liquefiable foundations, comprising: a cyclic stress ratio field analysis unit, an excess pore pressure ratio evolution analysis unit, and a stress coupling correction unit; the cyclic stress ratio field analysis unit is used to collect seismic parameters of the site after determining the site design earthquake event, and generate a cyclic stress ratio field using a depth reduction relationship; the excess pore pressure ratio evolution analysis unit is used to integrate shear stress and shear strain at each depth at each time point in real time based on the cyclic stress ratio field to obtain cumulative shear strain energy density, compare the cumulative shear strain energy density with the critical cyclic shear strain, infer the excess pore pressure ratio, and establish an evolution relationship of the excess pore pressure ratio with time and depth; the stress coupling correction unit is used to update the effective vertical stress value based on the excess pore pressure ratio, and synchronously correct the shear modulus according to the coupling relationship between the shear wave velocity and the excess pore pressure ratio, and feed the corrected shear modulus back to the excess pore pressure ratio evolution analysis unit.

[0006] Furthermore, the system also includes: a disaster reduction effectiveness evaluation unit, which is used to correct the excess pore pressure ratio using drainage improvement parameters and densification parameters to obtain a corrected excess pore pressure ratio; after the site design earthquake event ends, the excess pore pressure ratio, compression index and original porosity are corrected by integrating along the foundation thickness, and the post-earthquake surface settlement is calculated, and the disaster reduction effectiveness is evaluated accordingly; the drainage improvement parameters include: horizontal permeability coefficient, equivalent drainage path length and half-distance of drainage structure layout; the densification parameters include: initial porosity, compression index and reinforcement structure spacing.

[0007] Furthermore, the earthquake parameters include: peak horizontal acceleration, total vertical stress, initial effective vertical stress and shear wave velocity.

[0008] Furthermore, the specific execution process of the cyclic stress ratio field analysis unit includes: collecting the peak horizontal acceleration of the site under the design earthquake event; obtaining the total vertical stress and the initial effective vertical stress along the depth direction; the total vertical stress is obtained by multiplying the saturated unit weight of the foundation and the corresponding depth, and the initial effective vertical stress is obtained by deducting the initial pore water pressure from the total vertical stress; obtaining the shear wave velocity along the same depth direction; for any given depth, combining the ratio of the peak horizontal acceleration to the gravity acceleration, the ratio of the total vertical stress to the initial effective vertical stress, and the depth reduction factor to calculate the cyclic stress ratio, and taking the result composed of the cyclic stress ratios corresponding to all depths as the cyclic stress ratio field.

[0009] Furthermore, the specific execution process of the excess pore pressure ratio evolution analysis unit includes: calculating the cumulative shear strain energy density of shear stress and shear strain at different depths during the design earthquake event of the site over time based on the cyclic stress ratio field; then using the initial effective vertical stress and the critical shear strain value required to trigger liquefaction, the real-time growth trend of the excess pore pressure ratio is determined through the cumulative shear strain energy density, specifically including: at the beginning of the design earthquake event, the excess pore pressure ratio gradually increases with the increase of the cumulative shear strain energy density until it approaches the critical energy threshold defined by the initial effective vertical stress, and the excess pore pressure ratio approaches the limit state; finally, the distribution results of the excess pore pressure ratio at different depths that increase with the duration of the design earthquake event are obtained, and the excess pore pressure ratio distribution is obtained.

[0010] Furthermore, the specific execution process of the stress coupling correction unit includes: according to the excess pore pressure ratio, the excess pore pressure ratio is deducted from the corresponding initial effective vertical stress at each depth to obtain the real-time effective vertical stress at the same depth; based on the deterministic correspondence between the shear modulus and the real-time effective vertical stress, the shear modulus is synchronously corrected in combination with the wet density at the depth and the original shear wave velocity test value on site; then, the cyclic shear stress is recalculated using the corrected shear modulus and the real-time effective vertical stress, and the product of the cyclic shear stress and the real-time shear strain is added to the cumulative shear strain energy density of the same time step as the input of the evolution of the excess pore pressure ratio in the next time step; the above process is cyclically executed with a preset time step during the design earthquake event, so as to obtain the coupled degradation history of the effective vertical stress and shear modulus with time and depth.

[0011] Furthermore, when the shear modulus is corrected, the absolute value of the difference between the corrected shear modulus and the uncorrected shear modulus is not less than the lower limit of the residual shear stiffness of the saturated soil at that depth; the lower limit of the residual shear stiffness is determined based on the table of the ratio of the measured shear wave velocity to the standard residual shear modulus; in addition, if the shear modulus decrease rate at any depth in the coupled degradation process exceeds the set critical degradation threshold, the early warning identification mechanism will be automatically triggered, and the input path of the excess pore pressure ratio evolution analysis unit will be frozen to prevent the cascading spread of non-physical instability feedback in the next time step.

[0012] Furthermore, the disaster reduction effectiveness evaluation unit combines the obtained real-time effective vertical stress with the shear modulus coupled degradation process to determine the residual excess pore pressure ratio at each depth at the end of the design earthquake event; based on the compression index and the initial porosity ratio, the residual excess pore pressure ratio is subjected to volume reconsolidation analysis, and the post-earthquake surface settlement within the foundation thickness is obtained by integral calculation; the post-earthquake surface settlement is compared with the settlement limit; if the post-earthquake surface settlement meets the settlement limit, the disaster reduction effectiveness is judged to have met the standard and the simulation is terminated; otherwise, the disaster reduction effectiveness is judged to have failed to meet the standard.

[0013] Furthermore, the process of the disaster reduction effectiveness evaluation unit determining the residual excess pore pressure ratio at each depth at the end of the design earthquake event includes: calling the stress coupling correction unit to output the coupling degradation history of the effective vertical stress and shear modulus with time and depth during the entire duration of the design earthquake event, and extracting the effective vertical stress value at each depth at the end of the design earthquake event; then, the initial effective vertical stress value before the design earthquake event and the real-time effective vertical stress value at the end of the design earthquake event are compared at the same depth, and the stress difference between the two is calculated; based on the physical definition of the excess pore pressure ratio, the stress difference is used as the residual excess pore pressure ratio at the depth at the end of the earthquake action, indicating the excess pore water pressure remaining due to the soil structure damage and shear deformation caused by the earthquake in the absence of complete drainage or consolidation, reflecting the dynamic response of the foundation soil under the action of earthquake loads.

[0014] The seismic disaster reduction simulation system for liquefiable foundations disclosed herein has the following beneficial effects: it enables continuous spatiotemporal tracking of the entire earthquake load process, transforming traditional liquefaction analysis, which can only provide single-point judgments, into dynamic predictions for the entire cross-section and multiple time periods. The system utilizes a high-resolution segmentation strategy and a vectorized parallel algorithm to convert complex seismic input into a pore-water pressure evolution surface with millisecond-level feedback, while ensuring numerical stability. It also uses a freezing mechanism to curb non-physical instabilities in real time, significantly improving computational reliability. Drainage improvement parameters and densification parameters are directly mapped to the excess pore pressure ratio reduction path, enabling the effects of reinforcement measures to be immediately reflected in the simulation. Engineers can quickly iterate different drainage board spacings or preloading depths before construction, obtaining objective quantitative results comparing post-seismic settlement with settlement limits, significantly shortening the design optimization cycle. The residual excess pore pressure ratio profile, shear modulus degradation curve, and settlement-time curve output by the system can be calibrated in real time with field monitoring data, providing a basis for dynamic adjustments during construction and reducing overly conservative or insufficient safety factors due to model bias. In summary, the present invention is superior to existing technologies in terms of accuracy, efficiency, and operability. It can not only identify high-risk weak interlayers in advance, but also evaluate the synergistic benefits of drainage and densification measures, providing an efficient, reliable, closed-loop seismic disaster reduction decision-making platform for complex engineering structures in coastal soft soil areas. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 A schematic diagram of the system structure of a liquefiable foundation earthquake disaster reduction simulation system provided by an embodiment of the present invention; Figure 2 A diagram showing the distribution of cyclic stress ratio field with depth provided by an embodiment of the present invention; Figure 3 A graph showing the evolution of excess pore pressure ratio over time provided by an embodiment of the present invention; Figure 4 A comparison chart of shear modulus before and after stress coupling correction provided by an embodiment of the present invention; Figure 5 This is a post-earthquake surface settlement and disaster reduction effectiveness assessment diagram provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0016] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0017] refer to Figure 1: A seismic disaster reduction simulation system for liquefiable foundation, the system comprising: a cyclic stress ratio field analysis unit, an excess pore pressure ratio evolution analysis unit and a stress coupling correction unit; the cyclic stress ratio field analysis unit is used to collect the seismic parameters of the site after determining the site design earthquake event, and generate a cyclic stress ratio field using the depth reduction relationship; the excess pore pressure ratio evolution analysis unit is used to integrate the shear stress and shear strain at each depth at each time point in real time according to the cyclic stress ratio field, obtain the cumulative shear strain energy density, and compare the cumulative shear strain energy density with the critical cyclic shear strain, infer the excess pore pressure ratio, and establish the evolution relationship of the excess pore pressure ratio with time and depth; the stress coupling correction unit is used to update the effective vertical stress value based on the excess pore pressure ratio, and synchronously correct the shear modulus according to the coupling relationship between the shear wave velocity and the excess pore pressure ratio, and feed the corrected shear modulus back to the excess pore pressure ratio evolution analysis unit.

[0018] Starting from the first step of engineering application, the cyclic stress ratio field analysis unit discretizes the site into layers after the seismic input conditions are determined. Each discrete depth point is assigned key seismic parameters such as peak horizontal acceleration, total vertical stress, initial effective vertical stress, and shear wave velocity corresponding to the site's design earthquake event. The unit reduces the surface peak horizontal acceleration to each depth point through the depth reduction relationship, and combines the proportional relationship between total vertical stress and initial effective vertical stress, shear wave velocity and shear wave velocity exponential reduction function, etc. to calculate the cyclic stress ratio field that varies continuously throughout the entire foundation thickness. Because the dynamic characteristics of liquefiable foundations are highly dependent on the initial stress state of the soil layer, a layer-by-layer scanning method is used here to calibrate the difference between the total vertical stress and the initial effective vertical stress at the sampling depth to ensure that the input accuracy of the cyclic stress ratio field is sufficient to support subsequent nonlinear coupled evolution calculations.

[0019] Once generated, the cyclic stress ratio field is automatically fed into the excess pore pressure ratio evolution analysis unit. During the system initialization phase, this unit divides the time steps according to the duration of the ground motion. In the first time step, the cyclic stress ratio and the instantaneous shear stress and strain corresponding to the depth point are mapped to the shear strain rate and shear stress history curve. The product of shear stress and strain is then integrated to form the cumulative shear strain energy density. The cumulative shear strain energy density shows a monotonically increasing relationship with the critical cyclic shear strain, enabling the excess pore pressure ratio evolution analysis unit to accurately estimate the excess pore pressure ratio increment at each time step. When the cumulative shear strain energy density has not yet reached the energy threshold required to trigger liquefaction, the excess pore pressure ratio increases gradually. Once the energy threshold is approached or exceeded, the excess pore pressure ratio rapidly rises to the saturation upper limit and enters a plateau. This process exhibits significant advance and lag characteristics for saturated soils at different depths. Therefore, the system was designed to utilize a multi-threaded parallel computing strategy to ensure that the depth coupling effect is updated in milliseconds, avoiding numerical divergence caused by delayed updates.

[0020] As the excess pore pressure ratio evolution analysis unit continuously outputs new excess pore pressure ratio distribution results, the stress coupling correction unit simultaneously receives these results and updates the effective vertical stress value in real time. Specifically, the excess pore pressure ratio is multiplied by the initial effective vertical stress at the same depth and subtracted from the initial effective vertical stress to obtain the real-time effective vertical stress for the current time step. The real-time effective vertical stress, in turn, acts on the shear modulus through the coupling relationship between the shear modulus and the effective stress. Changes in the shear modulus adjust the shear wave velocity at the same depth, which in turn affects the calculation of the cyclic shear stress. To ensure that the coupling mechanism is consistent with laboratory tests and field monitoring data, the unit also sets two safety thresholds: first, at any depth, the corrected shear modulus must not fall below the lower limit of the saturated soil residual shear stiffness. Second, if the shear modulus decreases at a critical degradation threshold throughout the entire time domain of the coupled degradation process, a freezing mechanism is triggered, suspending the input of new cyclic shear stresses and shear strains into the excess pore pressure ratio evolution analysis unit to prevent the cascading propagation of subsequent time steps due to non-physical instabilities.

[0021] When the freeze mechanism is activated, the system displays a warning indicator to the user interface and saves the intermediate data files that caused the anomaly, allowing engineers to later identify the possible causes of instability. After the stress coupling correction unit completes processing, the corrected shear modulus and real-time effective vertical stress are written back to the excess pore pressure ratio evolution analysis unit, allowing iteration to continue at the next time step. This cycle repeats until the timeline of the site design earthquake event reaches its end. During the entire duration of the earthquake, each time step corresponds to an update of the cyclic stress ratio field, an evolution of the excess pore pressure ratio, and a coupled correction of the effective vertical stress and shear modulus, forming a dynamic data cube within a two-dimensional time-depth grid. The system fragments this data cube and stores it on a solid-state drive using memory-mapped files and asynchronous input and output technology in the background, ensuring that data throughput does not become a bottleneck in large-scale computational scenarios. After the calculation is complete, the system automatically generates three-dimensional visualization files of the effective vertical stress, shear modulus, and excess pore pressure ratio. Users can directly view the response evolution at each depth and time point on a professional graphics workstation.

[0022] The system also provides a data interface with the disaster reduction effectiveness assessment unit. To evaluate the performance of drainage improvement or densification measures, the user simply inputs parameters such as horizontal permeability, equivalent drainage path length, drainage structure half-distance, initial porosity, compression index, and reinforcement structure spacing. The system then applies a linear or exponential decay model to the excess pore pressure ratio, without recalculating the cyclic stress ratio field. This model then derives new degradation histories for effective vertical stress and shear modulus, and rapidly outputs post-earthquake surface settlement. If post-earthquake surface settlement is less than the set settlement limit, the system determines that the disaster reduction effectiveness has been met and archives the simulation. If settlement exceeds the limit, the system outputs settlement curves and depth distribution maps for the design team to evaluate for potential optimization of the reinforcement solution. The entire simulation process is highly automated from a user's perspective: The input requires only the site seismic motion history or response spectrum, geostatic indices, and improvement plan parameters, while the output provides decisive results for direct application in foundation disaster reduction design.

[0023] Furthermore, the system also includes: a disaster reduction effectiveness evaluation unit, which is used to correct the excess pore pressure ratio using drainage improvement parameters and densification parameters to obtain a corrected excess pore pressure ratio; after the site design earthquake event ends, the excess pore pressure ratio, compression index and original porosity are corrected by integrating along the foundation thickness, and the post-earthquake surface settlement is calculated, and the disaster reduction effectiveness is evaluated accordingly; the drainage improvement parameters include: horizontal permeability coefficient, equivalent drainage path length and half-distance of drainage structure layout; the densification parameters include: initial porosity, compression index and reinforcement structure spacing.

[0024] The disaster reduction effectiveness assessment unit can receive and use drainage improvement parameters and densification parameters to make multi-dimensional corrections to the excess pore pressure ratio. Drainage improvement parameters mainly include the horizontal permeability coefficient, the equivalent drainage path length, and the half-distance of the drainage structure layout. These parameters are often achieved in on-site projects by installing sand wells, plastic drainage boards, or other drainage improvement measures. The purpose is to accelerate the dissipation of pore water pressure, increase the decay rate of the excess pore pressure ratio, and slow down the accumulation of pore water pressure during the liquefaction process. Densification parameters include the initial porosity, compression index, and reinforcement structure spacing. These parameters are closely related to the compressive properties of the soil after reinforcement treatment and directly affect the volume shrinkage during the post-earthquake pore reconsolidation process. In actual operation, the disaster reduction effectiveness assessment unit first associates the drainage improvement parameters with the depth-distributed excess pore pressure ratio. Based on the length of the drainage path and the density of the drainage structure layout, the decay trend of the excess pore pressure ratio over time is corrected to reduce the residual excess pore pressure ratio after the earthquake. The unit then uses the densification parameters to calculate post-earthquake surface settlement based on the coupled relationship between the initial porosity and the compressibility index. This settlement is the integration of the residual excess pore pressure ratio over the volume change along the foundation thickness. To ensure continuity in the post-earthquake settlement calculation after the earthquake loading ends, a closed-loop data loop is formed between the disaster reduction effectiveness assessment unit and the stress coupling correction unit. The degradation evolution curves of the effective vertical stress and shear modulus during the earthquake loading period are input, ensuring that the distribution of the residual excess pore pressure ratio more closely matches the actual site conditions. By comparing the post-earthquake surface settlement with the preset settlement limit, the system automatically determines whether the current drainage improvement and densification measures have achieved the desired seismic disaster reduction effect, thus providing scientific decision-making for subsequent foundation reinforcement design. Notably, during the correction process, the disaster reduction effectiveness assessment unit utilizes a layer-by-layer integration approach, treating the corrected excess pore pressure ratio, initial porosity, and compressibility index at each depth as a coupled entity. This avoids numerical oscillations caused by independent parameter space corrections while ensuring the smoothness of the overall settlement curve.

[0025] Furthermore, the earthquake parameters include: peak horizontal acceleration, total vertical stress, initial effective vertical stress and shear wave velocity.

[0026] Furthermore, the specific execution process of the cyclic stress ratio field analysis unit includes: collecting the peak horizontal acceleration of the site under the design earthquake event; obtaining the total vertical stress and the initial effective vertical stress along the depth direction; the total vertical stress is obtained by multiplying the saturated unit weight of the foundation and the corresponding depth, and the initial effective vertical stress is obtained by deducting the initial pore water pressure from the total vertical stress; obtaining the shear wave velocity along the same depth direction; for any given depth, combining the ratio of the peak horizontal acceleration to the gravity acceleration, the ratio of the total vertical stress to the initial effective vertical stress, and the depth reduction factor to calculate the cyclic stress ratio, and taking the result composed of the cyclic stress ratios corresponding to all depths as the cyclic stress ratio field.

[0027] The cyclic stress ratio field analysis unit serves as a bridge between seismic input and subsequent nonlinear response analysis. It first acquires peak horizontal acceleration at the surface, then collects soil static information layer by layer along the depth direction. The total vertical stress at each discrete depth point is directly calculated by multiplying the saturated unit weight of the foundation by the corresponding depth. The initial effective vertical stress is obtained by subtracting the initial pore water pressure at the same depth from the total vertical stress. The system simultaneously acquires the depth distribution of shear wave velocity from in-situ testing or existing survey data and automatically matches it to a database of depth reduction factors for combined use in subsequent steps. To ensure consistency between various data sources, the cyclic stress ratio field analysis unit performs multiple quality control checks in the background. First, the peak horizontal acceleration time history is Fourier filtered to eliminate high-frequency noise. Second, the initial pore water pressure derived from hydrostatic pressure is cross-checked with the laboratory porosity ratio-pressure relationship curve to avoid distortion of the cyclic stress ratio due to abnormal pore water pressure input. Once all necessary information is aligned in both the time and depth domains, the system combines the ratio of peak horizontal acceleration to gravitational acceleration, the ratio of total vertical stress to initial effective vertical stress, and the depth reduction factor at each depth point to calculate the cyclic stress ratio at that depth point. To prevent numerical oscillations caused by sudden changes in parameters at soil layer interfaces, the analysis unit employs piecewise continuous interpolation, smoothing the shear wave velocity at interlayer junctions and simultaneously performing smooth interpolation of the same order for the depth reduction factor.

[0028] For any given depth , the corresponding cyclic stress ratio for: ; in, is the peak horizontal acceleration; is the acceleration due to gravity; For any given depth Total vertical stress; For any given depth The initial effective vertical stress of For any given depth shear wave velocity.

[0029] This formula combines three types of information: earthquake intensity index, static stress state index and soil dynamic index, and realizes a quantitative description of the sensitivity of liquefiable foundation to cyclic loads at different depths. It comes from the statistical experience of the ratio of the main cycle amplitude of shear stress to shear strain in the classic cyclic triaxial test, which can directly reflect the conversion relationship between plane shear stress and main shear stress; Normalize the peak horizontal acceleration of the ground into a dimensionless form to ensure that different design earthquake events are comparable in numerical scale; Through the total vertical stress and initial effective vertical stress The ratio of describes the relative contribution of static load and pore water pressure in the depth direction, where Obtained by multiplying the foundation saturation unit by the depth, At this depth, the initial pore water pressure is reduced from The deduction from the depth can truly reflect the effective bearing capacity of saturated soil before liquefaction in the early stage of earthquake; At the same time, the combined effects of the amplitude attenuation of seismic waves propagating deep into the soil and the dynamic stiffness of the soil are considered, where the linear factor Using depth as the independent variable to describe the empirical law of dynamic stress decreasing with depth, the exponent Further shear wave velocity The magnitude of will link the deceleration rate with the soil consolidation stiffness. The higher the shear wave velocity means the denser the soil and the faster the energy decay, which makes the cyclic stress ratio present a lower value at the same depth.

[0030] The formula is implemented by vectorized matrix operations: the system first reads the seismic input file Then, the saturated unit weight, pore water pressure and shear wave velocity in the survey database are deeply interpolated to form vectors of the same length; four multiplication and division steps are implemented element by element in the memory, and finally output Depth vector. To ensure that the attenuation term does not have negative values ​​in the deep part, the system performs constraint clipping on the depth range before interpolation and Nodes with values ​​less than zero are forced to be zero to make the results consistent with the actual physical meaning. The continuous distribution with depth is stored in shared memory with a time stamp, and is called by the excess pore pressure ratio evolution analysis unit at each time step. When calculating shear stress, there is no need to query static stress or shear wave velocity again, thus avoiding repeated I / O overhead.

[0031] Furthermore, the specific execution process of the excess pore pressure ratio evolution analysis unit includes: calculating the cumulative shear strain energy density of shear stress and shear strain at different depths during the design earthquake event of the site over time based on the cyclic stress ratio field; then using the initial effective vertical stress and the critical shear strain value required to trigger liquefaction, the real-time growth trend of the excess pore pressure ratio is determined through the cumulative shear strain energy density, specifically including: at the beginning of the design earthquake event, the excess pore pressure ratio gradually increases with the increase of the cumulative shear strain energy density until it approaches the critical energy threshold defined by the initial effective vertical stress, and the excess pore pressure ratio approaches the limit state; finally, the distribution results of the excess pore pressure ratio at different depths that increase with the duration of the design earthquake event are obtained, and the excess pore pressure ratio distribution is obtained.

[0032] The system first maps the cyclic stress ratio field into a shear stress history at a preset time step. The shear modulus and the real-time effective vertical stress are then coupled to convert the shear strain history to the same time resolution. The two are then multiplied point-by-point on the time axis and integrated over the existing segments to obtain the cumulative shear strain energy density at different depths. Because dynamic instability in liquefiable foundations is highly correlated with energy dissipation, the quantitative comparison of the cumulative shear strain energy density with the initial effective vertical stress and critical shear strain values ​​provides the only basis for determining the growth rate of the excess pore pressure ratio. In the early stages of the design earthquake event, the cumulative shear strain energy density is low, and the excess pore pressure ratio increases only slowly. As the shear stress peak and shear strain amplitude continue to increase under the combined effect, the energy dissipation curve rises steeply, accelerating the accumulation of the excess pore pressure ratio. When the energy curve approaches the energy threshold determined by the initial effective vertical stress and critical shear strain, the unit automatically switches to a limit approach algorithm, compressing the time step and employing an exponential approach to ensure that the excess pore pressure ratio approaches the limit state smoothly without oscillation. To avoid sudden changes in the depth dimension, the system uses spline smoothing in space to make the cumulative shear strain energy density present a continuous segmented curve along the depth direction. At the same time, the shear modulus degradation trajectory is updated synchronously to ensure closed-loop conservation between energy input, strain energy accumulation and excess pore pressure ratio growth in each time iteration.

[0033] For any given depth ,time Excess pore pressure ratio for: ; in, From the initial moment to time The cumulative shear strain energy density at ; For any given depth The critical shear strain value; ; in, is the time-integrated variable; For any given depth ,time Shear stress at ; For any given depth ,time Shear strain rate when ; in, is the relative density, which is equal to the difference between the porosity in the loosest state and the porosity in the natural state, divided by the difference between the porosity in the loosest state and the porosity in the densest state; is standard atmospheric pressure.

[0034] The excess pore pressure ratio evolution analysis unit starts with the shear stress ratio transmitted by the cyclic stress ratio field analysis unit and multiplies the ratio by the real-time effective vertical stress at each time step to obtain , and then use the coupled corrected shear modulus to obtain Since the duration of earthquake motion is subdivided into hundreds or even thousands of discrete steps, the system uses an explicit fourth-order Runge-Kutta method to ensure numerical stability during time integration, and encapsulates the depth-direction data structure into a column vector for GPU parallel computing, thereby making It can be refreshed in milliseconds. As energy accumulates, the dimensionless ratio in the exponential function Gradually increase from zero, initially hour The excess pore pressure ratio increases quasi-linearly with energy. When the shear stress amplitude is superimposed or high-frequency pulses occur, Rapid Approach , the exponential curve drops sharply, and the excess pore pressure ratio increases nonlinearly; once , the system automatically triggers the asymptotic approximation algorithm and reduces the time step to the original times, and use the exponential approximation strategy to Damping In the spatial dimension, the deep high stress area is big, Small and low threshold energy, The growth rate is the fastest, and the shallow layer has a high threshold energy due to the low total vertical stress and high pore water pressure. The growth rate is relatively slow, forming a peak profile of excess pore pressure ratio that increases with depth. Smooth the shear modulus degradation curve to ensure that there is no sudden jump at the transition between layers; at the same time record The time sequence of the energy threshold is used to quickly retrieve the extreme value moment when the subsequent coupling correction unit calculates the effective vertical stress, thereby capturing the critical point of instantaneous collapse of soil stiffness. The coefficient is derived from the symmetry of the main circulation area of ​​shear stress and shear strain in unidirectional cyclic shear, which is consistent with experimental statistics and ensures unit consistency. The exponential model as a whole avoids the problem of artificial truncation of the saturation upper limit of the traditional strain hyperbola model in the high amplitude zone, making the growth of pore water pressure continuous and differentiable.

[0035] Furthermore, the specific execution process of the stress coupling correction unit includes: according to the excess pore pressure ratio, the excess pore pressure ratio is deducted from the corresponding initial effective vertical stress at each depth to obtain the real-time effective vertical stress at the same depth; based on the deterministic correspondence between the shear modulus and the real-time effective vertical stress, the shear modulus is synchronously corrected in combination with the wet density at the depth and the original shear wave velocity test value on site; then, the cyclic shear stress is recalculated using the corrected shear modulus and the real-time effective vertical stress, and the product of the cyclic shear stress and the real-time shear strain is added to the cumulative shear strain energy density of the same time step as the input of the evolution of the excess pore pressure ratio in the next time step; the above process is cyclically executed with a preset time step during the design earthquake event, so as to obtain the coupled degradation history of the effective vertical stress and shear modulus with time and depth.

[0036] The stress coupling correction unit is responsible for converting the pore water pressure response into the degradation process of soil stiffness and bearing capacity. At each preset time step, the unit first reads the distribution result of the excess pore pressure ratio at the full depth, and uses the excess pore pressure ratio to directly deduct the corresponding initial effective vertical stress for any depth point to obtain a new real-time effective vertical stress in real time. This operation means that the increase in pore water pressure will equivalently weaken the effective stress that the particle skeleton can bear. Subsequently, the system makes a synchronous correction to the shear modulus based on the one-to-one correspondence curve between the shear modulus and the real-time effective vertical stress established through experiments and field inversion, combined with the wet density and the original shear wave velocity test value at that depth, to ensure that the dynamic stiffness attenuation and the effective stress reduction are completed in coordination within the same time step. Once updated, the shear modulus participates in the recalculation of cyclic shear stress: the ratio given by the cyclic stress ratio field analysis unit is multiplied by the new shear modulus to obtain the new cyclic shear stress. The system immediately multiplies this cyclic shear stress with the real-time shear strain at the same time step, adds it to the current cumulative shear strain energy density, and stores the increment in the energy history curve, providing input for the excess pore pressure ratio evolution analysis unit at the next time step. The entire process is executed in a fixed-step loop in the time dimension, and each discrete depth point is processed independently and in parallel in the spatial dimension, forming a real-time effective vertical stress and shear modulus coupled degradation matrix that updates synchronously with time and depth. To avoid numerical divergence, the system checks at each time step whether the drop in shear modulus exceeds the lower limit of the residual shear stiffness. If the lower limit is triggered, the shear modulus at that depth point is immediately frozen, and a warning flag is issued to upstream modules to prevent the cascading propagation of unphysical negative stiffness. At the same time, the stress coupling correction unit archives the corrected real-time effective vertical stress, shear modulus, and cyclic shear stress for each time step, and exchanges timestamps with the excess pore pressure ratio evolution analysis unit to ensure that the two units always maintain data synchronization. As the design earthquake event continues to advance, the system gradually depicts the coupled degradation surface of the effective vertical stress and shear modulus with time and depth: the shallow layer has a lower initial effective vertical stress, the excess pore pressure ratio increases faster, and the shear modulus decays more significantly; the deep layer exhibits stronger residual stiffness due to the high constraint stress and relatively slow rise in pore pressure. After the design earthquake event ends, the unit freezes the last frame of data as the final degradation state, providing accurate mechanical initial values ​​for the disaster reduction effectiveness assessment unit to perform post-earthquake consolidation and settlement calculations.

[0037] For any given depth ,time Real-time effective vertical stress for: ; For any given depth ,time The corrected shear modulus for: ; in, is the original shear wave velocity test value on site; For any given depth wet density.

[0038] In the earthquake disaster reduction simulation system of liquefiable foundation, the excess pore pressure ratio evolution analysis unit generates a new frame Depth profile, stress coupling correction unit immediately calls the formula The weakening of soil skeleton bearing capacity by pore water pressure is converted into the attenuation of real-time effective vertical stress. is the initial effective vertical stress corrected by the hydrostatic pressure before the earthquake begins. It directly reflects the proportion of pore water pressure at the same depth relative to the initial effective vertical stress. Still in the low range, the deduction items are The effect is slight; when Approaching the limit, It is significantly compressed and may even drop to less than 10% of the initial value, indicating that the soil microstructure can no longer maintain the original skeleton stress path.

[0039] Once the real-time effective vertical stress is updated, the system immediately calculates the original shear wave velocity test value based on the field and wet density Calculate the corrected shear modulus , which continues the small strain elasticity theory The basic framework of The square root form is chosen instead of the linear form because the sensitivity of the equivalent stiffness dominated by shear wave velocity to pore water pressure decays sublinearly: when Still lower than When , the shear modulus decays insignificantly; when achieve about, The increase in Entering a rapid decline phase; when Rise to above, Close , the reduction factor is only less than , at this time the soil shear stiffness approaches the residual state. Directly taking into account, the densified reinforced area will partially offset the shear modulus reduction due to the increase in wet density, so that the system can maintain sensitive feedback on the dynamic stiffness improvement effect of the reinforcement measures; at the same time The square term of α amplifies the stiffness advantage of the higher shear wave velocity layer, and even if the pore water pressure increases rapidly, it can maintain a relatively larger , reflecting the confined hardening effect of deep sand layers. The stress coupling correction unit is updated After that, it is multiplied with the cyclic stress ratio field to obtain a new round of cyclic shear stress, which is then multiplied with the real-time shear strain and accumulated into the energy history curve to provide input for the pore water pressure evolution of the next time step, completing the energy-pore pressure-stress-stiffness closed loop. The system uses sparse tensor structure storage in the background Time series matrix, and perform spline smoothing on the depth dimension at each step to ensure that the shear modulus curve has no sudden jumps at the soil interface. In order to prevent instantaneous instability, when any depth point appears The decrease exceeds the initial value for three consecutive time steps or When the residual shear stiffness drops to the lower limit, the system automatically shortens the time step and enters the limit pressure stabilization mode, limiting the pore water pressure growth rate to within the set threshold to avoid numerical divergence. and The profile is transferred to the disaster reduction effectiveness assessment unit for post-earthquake settlement and consolidation calculations.

[0040] Furthermore, when the shear modulus is corrected, the absolute value of the difference between the corrected shear modulus and the uncorrected shear modulus is not less than the lower limit of the residual shear stiffness of the saturated soil at that depth; the lower limit of the residual shear stiffness is determined based on the table of the ratio of the measured shear wave velocity to the standard residual shear modulus; in addition, if the shear modulus decrease rate at any depth in the coupled degradation process exceeds the set critical degradation threshold, the early warning identification mechanism will be automatically triggered, and the input path of the excess pore pressure ratio evolution analysis unit will be frozen to prevent the cascading spread of non-physical instability feedback in the next time step.

[0041] Each correction of the shear modulus is subject to the dual safety constraints of a lower limit for residual shear stiffness and a critical degradation threshold. At each time step, the system first performs a weighted conversion of the real-time effective vertical stress and the original shear wave velocity based on the latest excess pore pressure ratio profile, generating a pre-corrected shear modulus vector discretized by depth. The coupled algorithm then softens this vector based on the pore water pressure increase to produce a candidate post-correction shear modulus. The system then immediately calculates the absolute value of the difference between the two vectors and compares it element-by-element with the lower limit for residual shear stiffness of saturated soil at the same depth. The lower limit for residual shear stiffness is derived from a cross-interpolation of field-measured shear wave velocities and an industry-standard residual shear modulus ratio table. It reflects the minimum dynamic stiffness that the soil can maintain after large strains. If the difference at a depth point falls below the corresponding lower limit, the system rolls back the corrected shear modulus at that depth to the minimum allowable value that meets the lower limit. A "stiffness rollback" flag and the current timestamp are recorded in the log to maintain physical plausibility and preserve traceability.

[0042] After determining the lower limit, the system enters the rate monitoring phase. The shear modulus at each depth in the current time step is subtracted from the data at the previous time step and divided by the step size to obtain the instantaneous rate of decline. This rate is then compared with a preset critical degradation threshold. If the rate at any depth exceeds the threshold, the system immediately triggers a warning indicator. The warning indicator first highlights the abnormal depth and the triggering moment in the graphical interface, prompting engineers to conduct a mandatory review. Second, the input path of the excess pore pressure ratio evolution analysis unit is frozen. This freeze locks the pore water pressure increment at that depth to zero for the next time step, thus preventing numerical corruption caused by non-physical coupling positive feedback. This freeze also initiates an adaptive step-size reduction strategy, shortening the global calculation time step to one-tenth of its original value. Three subdivision iterations are repeated until the shear modulus decline rate returns to within the threshold. If recovery after three subdivisions is not achieved, the system records a "persistent instability" state and automatically writes all intermediate field files for offline high-precision analysis to recalibrate the residual shear stiffness lower limit or critical degradation threshold. Through the dual insurance mechanism of the lower limit of the difference and the rate threshold, the system ensures that the degradation amplitude of the shear modulus at each time step is neither too small to violate the physical meaning of the residual stiffness, nor too large to exceed the tolerable energy dissipation rate of the soil structure, thereby ensuring that the coupling chain between the effective vertical stress, shear modulus, cyclic shear stress and energy accumulation is continuously controlled.

[0043] For any given depth ,time When the excess pore pressure ratio is corrected using drainage improvement parameters and densification parameters, the corrected excess pore pressure ratio is obtained. : in, For any given depth The horizontal permeability coefficient can be artificially increased by installing sand wells / PVD; is the unit weight of water; For any given depth The equivalent drainage path half distance.

[0044] The denominator of the formula is derived from the classical radial drainage consolidation theory. Its physical meaning is that the throttling effect of the drainage channel and the weight of water jointly determine the dissipation rate of pore water pressure: horizontal permeability The larger the water density, the smaller the lateral migration resistance of water flow in the same depth layer, and the faster the pore water pressure dissipates; the unit weight of water is It plays the role of converting the pore water pressure gradient into a proportional factor of flow velocity, so that the conservation of seepage and energy balance in the drainage channel are satisfied at the same time; the equivalent drainage path half distance The square of appears in the denominator, indicating that the drainage path length has a quadratic amplification effect on the dissipation rate. If the drainage structure layout distance is halved by densifying sand wells or laying plastic drainage boards, the pore water pressure reduction rate can theoretically be increased four times.

[0045] Time variable Being in the same position as the numerator of the fractional denominator means that as the consolidation time passes after the earthquake ends, the pressure reduction benefit brought by drainage improvement will accumulate in an exponentially decreasing manner. Engineers can monitor the pressure reduction effect through real-time monitoring. The attenuation curve of the post-earthquake drainage measures is used to judge whether the post-earthquake drainage measures have achieved the expected results. When the disaster reduction effectiveness evaluation unit is implemented, it first reads the freezing time of the coupling correction unit. The depth, type, diameter and layout spacing of each drainage component in the construction log are mapped to the grid nodes, and the corresponding and . System The assignment of is performed in two steps: if there is a sand well or plastic drainage board at this depth, the original permeability coefficient is multiplied by the empirical coefficient according to the equivalent porosity model; if it has not been reinforced, the original value is retained to evaluate the comparative effect before and after the improvement. The finite element mesh automatically identifies the distance between adjacent drainage well nodes and takes into account the well diameter correction to ensure that the geometric characteristics of the drainage channel network topology are fully reflected.

[0046] In the formula The standard value after the conversion of water temperature and density on site is taken. The system will automatically adjust in cold areas to convert the combined effect of water temperature on viscosity and density. After all parameters are interpolated to the same depth resolution, the disaster reduction effectiveness evaluation unit is calculated in parallel by node. ; Then the entire profile is spline smoothed to ensure the continuity of the pore water pressure field, and the results are fed back to the coupling correction unit to update the real-time effective vertical stress and shear modulus, so as to continue to maintain the two-way coupling between dynamic response and static consolidation during the drainage consolidation stage. For the initial porosity reduction and compression index reduction caused by densification improvement, the system is reflected in two ways: First, densification is usually accompanied by an increase in permeability, which directly raises Second, in the calculation of post-earthquake consolidation, a smaller compression index will reduce the post-earthquake settlement, making the same It can also bring more limited surface pull settlement. Engineers can adjust the drainage structure layout half distance, sand well diameter or pre-compression density in real time on the interface, and the system will recalculate immediately. 、 The modified excess pore pressure ratio section shows the immediate changes in the settlement-time curve.

[0047] Furthermore, the disaster reduction effectiveness evaluation unit combines the obtained real-time effective vertical stress with the shear modulus coupled degradation process to determine the residual excess pore pressure ratio at each depth at the end of the design earthquake event; based on the compression index and the initial porosity ratio, the residual excess pore pressure ratio is subjected to volume reconsolidation analysis, and the post-earthquake surface settlement within the foundation thickness is obtained by integral calculation; the post-earthquake surface settlement is compared with the settlement limit; if the post-earthquake surface settlement meets the settlement limit, the disaster reduction effectiveness is judged to have met the standard and the simulation is terminated; otherwise, the disaster reduction effectiveness is judged to have failed to meet the standard.

[0048] At the end of the design earthquake event , post-earthquake surface settlement for: in, is the foundation thickness; is the compression index; is the initial void ratio.

[0049] The derivation of this formula comes from the linearization of volume strain in one-dimensional consolidation theory under the small strain approximation: when the pore water pressure has not completely dissipated, the residual excess pore pressure ratio can be regarded as an instantaneous additional water pressure, and the equivalent effective stress increment exerted on the soil skeleton is logarithmically related to the volume compression. is defined as the slope of the porosity-effective stress curve in the logarithmic effective stress coordinate, so It can be interpreted as the volumetric strain coefficient caused by the unit effective stress increment. Multiplying by the initial effective vertical stress can get the equivalent effective stress increment, and then multiplying by the volume strain coefficient can get the instantaneous longitudinal strain. Convert to Internally, what is left at the formula level is a product containing only the compression index, the initial porosity and the modified excess pore pressure ratio. The integrand is physically the settlement per unit depth layer.

[0050] When the system is implemented, the coupled degradation process is first frozen in the frame output. With the survey section Do depth alignment, and then discretize the foundation thickness according to the grid size Thickness For each interval, we can apply trapezoidal integral or Simpson integral to obtain In order to reduce the sensitivity of the initial porosity test error to the results, the system Cubic Hermite interpolation is used and monotonicity constraints are imposed on both sides of the interpolation function to prevent physically unreasonable rebound or downward jump in the porosity profile; for the compression index If the survey report only gives representative values, the system will automatically assign values ​​based on the saturated density and relative density to ensure that the high-density reinforcement area has a relatively low compression index. The system already includes the effects of drainage improvement parameters and densification parameters on pore water pressure dissipation, so there is no need to consider the drainage time factor during the integration process; however, the system still records each contribution during the integration in the background so that users can query which depth segment contributes the most to the total settlement. After that, the disaster reduction effectiveness assessment unit will compare it with the design settlement limit Compare: If , then output “disaster reduction efficiency meets standards”; if , then the output is "disaster reduction efficiency does not meet the standard", and the interface shows the interval where the settlement curve exceeds the limit in red, and the interval is traced back. 、 and The original value provides precise targeting for engineers to adjust the spacing between sand wells, increase the horizontal permeability coefficient, or add densification treatment. The system also supports sensitivity analysis functions. Users can batch input different drainage structure layout half-distance or compression index assumptions. The system will calculate multiple settlement curves in parallel and present them in interactive graphics to help quickly screen the most economical improved combination. Through this integral formula and its supporting high-resolution numerical implementation, the seismic disaster reduction simulation system for liquefiable foundations associates the complex dynamic pore pressure response, consolidation volume deformation, and engineering settlement limits within a unified mathematical framework, realizing the quantification of the entire process from microscopic pore structure softening to macroscopic surface settlement, providing a reliable and intuitive basis for judging the safety and economy of foundation treatment solutions.

[0051] Furthermore, the process of the disaster reduction effectiveness evaluation unit determining the residual excess pore pressure ratio at each depth at the end of the design earthquake event includes: calling the stress coupling correction unit to output the coupling degradation history of the effective vertical stress and shear modulus with time and depth during the entire duration of the design earthquake event, and extracting the effective vertical stress value at each depth at the end of the design earthquake event; then, the initial effective vertical stress value before the design earthquake event and the real-time effective vertical stress value at the end of the design earthquake event are compared at the same depth, and the stress difference between the two is calculated; based on the physical definition of the excess pore pressure ratio, the stress difference is used as the residual excess pore pressure ratio at the depth at the end of the earthquake action, indicating the excess pore water pressure remaining due to the soil structure damage and shear deformation caused by the earthquake in the absence of complete drainage or consolidation, reflecting the dynamic response of the foundation soil under the action of earthquake loads.

[0052] In the earthquake disaster reduction simulation system for liquefiable foundations, the disaster reduction effectiveness evaluation unit must first fully access the effective vertical stress and shear modulus coupling degradation database generated by the stress coupling correction unit during the entire dynamic calculation process in order to accurately lock the residual excess pore pressure ratio at each depth at the end of the design earthquake event. When establishing this database, the system leaves a double index label for each time step and each depth node, so the disaster reduction effectiveness evaluation unit only needs to use the end timestamp to obtain the residual excess pore pressure ratio at each depth. The full-depth vectorized real-time effective vertical stress field can be retrieved Then, the unit calls the static initial condition file and calls out the corresponding initial effective vertical stress according to the depth. After the two stress profiles are precisely aligned in memory, the system directly performs the difference to obtain The physical significance of this step is to regard the skeleton stress attenuation caused by dynamic load as the water pressure still retained in the pore system. They have not been discharged when the earthquake stops, and are therefore stored in the soil in the form of residual excess pore pressure ratio. According to the basic definition of excess pore pressure ratio, the system divides this stress difference by the initial effective vertical stress to obtain the dimensionless residual excess pore pressure ratio. Since the stress coupling correction unit has ensured that the shear modulus decrease is not less than the lower limit of the residual shear stiffness in the dynamic stage, the effective vertical stress degradation curves at these depths will not show numerical jumps, thus ensuring the calculated Smoothness distribution along depth.

[0053] In order to further eliminate local anomalies, the disaster reduction effectiveness assessment unit Performing wavelet denoising and spline smoothing not only eliminates numerical discretization errors but also preserves the true peak values ​​of weak areas such as weak interlayers. After completing the profile, the system uses it as the starting pore water pressure field for post-seismic consolidation analysis and intuitively displays the relationship curve between the residual excess pore pressure ratio and depth on the interface, allowing engineers to identify the depth section with the greatest risk at a glance. Cross-comparison with the drainage improvement parameter and densification parameter libraries automatically estimates the pore pressure decay half-life, providing a time window for subsequent drainage layout optimization. Through this rigorous stress differential and excess pore pressure ratio conversion process, the disaster reduction effectiveness assessment unit not only fully inherits the stress degradation information from the dynamic phase but also provides physically specific initial conditions for post-earthquake settlement prediction during the static assessment phase. This ensures that the seismic disaster reduction simulation system for liquefiable foundations achieves a closed-loop data cycle and reliable results throughout its lifecycle.

[0054] The following is a complete example to demonstrate the whole process of the earthquake disaster reduction simulation system for liquefiable foundation from power input to settlement determination. The site is located in the coastal alluvial plain, and the foundation thickness is The average saturation unit of saturated sand layer is re-taken , the water level is on the surface, the unit of water is taken The design basis ground motion peak horizontal acceleration is set as , the equivalent earthquake duration is . Lay out plastic drainage board, the equivalent drainage path half distance 、 、 The three sections are 、 、 ; Improved horizontal permeability coefficient Segmented 、 、 The linear interpolation of the shear wave velocity in situ segmented test value is (surface) to ( ). Wet density Approximation. The compression index is uniformly taken The initial porosity decreases linearly with depth: (surface) to ( ). The relative density is based on the site survey results. .

[0055] The first step is the cyclic stress ratio field: Three representative depths Explain the calculation process. For example, the total vertical stress is , the initial effective vertical stress is . formula ; Give . Same method , .

[0056] The second step is the evolution of excess pore pressure ratio: Shear stress amplitude .by For example . Assume that the equivalent The shear strain amplitude in each main cycle is ,but ; Critical shear strain value ; Give Energy threshold .then .

[0057] Same method , .

[0058] The third step is drainage and densification correction: For example: .

[0059] The rest of the depth is corrected , .

[0060] Step 4: Update the effective vertical stress and output the residual excess pore pressure ratio: ; .

[0061] depth and have to and The values ​​are the same because the differencing process with the same initial stress is already included in the formula.

[0062] Step 5, shear modulus degradation: initial shear modulus .

[0063] After correction ; meet the lower limit of residual shear stiffness The difference between the two is the safety line. The descent rate does not exceed the threshold and the system does not freeze.

[0064] Step 6: Settlement calculation: Set the average of the three sections The coefficients are .integral ; .

[0065] Step 7: Efficiency determination: The allowable settlement limit of the site is .because ,The system determines that the disaster reduction efficiency of the combination of drainage board and densification meets the standard, automatically ends the simulation and generates the settlement-depth curve and residual excess pore pressure ratio profile for the engineer to archive.

[0066] like Figure 1As shown in the figure, the horizontal axis represents depth in meters, and the vertical axis represents the cyclic stress ratio, which is dimensionless. This figure shows the output of the cyclic stress ratio field analysis unit. It reflects the cyclic stress ratio field distribution law generated by collecting seismic parameters such as the peak horizontal acceleration, total vertical stress, initial effective vertical stress, and shear wave velocity of the site after determining the design earthquake event of the site, using the depth reduction relationship. As can be seen from the figure, the cyclic stress ratio gradually increases with increasing depth. The cyclic stress ratio is close to zero near the surface. As the depth increases to about 20 meters, the cyclic stress ratio reaches a peak of about 0.6. This distribution feature is consistent with the stress distribution law generated by the influence of the depth reduction factor when seismic waves propagate in the soil layer.

[0067] like Figure 2 As shown in the figure, the horizontal axis represents time in seconds, and the vertical axis represents the excess pore pressure ratio, which is dimensionless. The figure shows the analysis results of the excess pore pressure ratio evolution analysis unit during the design earthquake event, which contains three evolution curves at different depths, corresponding to depths of 5 meters, 10 meters and 15 meters respectively. The solid line represents the evolution of the excess pore pressure ratio at a depth of 5 meters, the short dash line represents the evolution at a depth of 10 meters, and the long and short dash lines represent the evolution at a depth of 15 meters. It can be observed from the figure that at the beginning of the design earthquake event, the excess pore pressure ratio at each depth gradually increases with the increase of the cumulative shear strain energy density. Among them, the excess pore pressure ratio of the shallow soil increases more rapidly. At a depth of 5 meters, the excess pore pressure ratio is close to the limit state of 1.0 at about 15 seconds, while the excess pore pressure ratio of the deep soil increases relatively slowly.

[0068] like Figure 3 As shown, the horizontal axis represents the depth in meters, and the vertical axis represents the shear modulus in megapascals. This figure shows the correction effect of the stress coupling correction unit, and uses a bar graph to compare the changes in the shear modulus before and after the correction. The white bar graph represents the shear modulus before correction, and the black bar graph represents the shear modulus after correction. It can be clearly observed from the figure that after the stress coupling correction, the shear modulus at each depth is significantly reduced, which reflects the influence of the excess pore pressure ratio on the effective vertical stress and the deterministic correspondence between the shear modulus and the real-time effective vertical stress. The corrected shear modulus value always remains above the lower limit of the residual shear stiffness of the saturated soil at this depth, ensuring the physical rationality of the calculation.

[0069] like Figure 4As shown in the figure, the horizontal axis represents different site types, and the vertical axis represents post-earthquake surface settlement, measured in centimeters. This figure displays the results of the Disaster Reduction Effectiveness Assessment Unit, consisting of three curves comparing the effectiveness of no disaster reduction measures, drainage improvement measures, and densification measures. The horizontal dashed line represents the settlement limit, set at 30 centimeters. The solid line represents post-earthquake surface settlement without disaster reduction measures, the short dashed line represents settlement with drainage improvement measures, and the long and short dashed line represents settlement with densification measures. The figure also indicates compliance with disaster reduction effectiveness standards. Sites with no disaster reduction measures, such as saturated soil, that exceed the settlement limit are considered non-compliant. Sites with drainage improvement and densification measures meet the settlement limit and are considered compliant. This figure effectively demonstrates the ability of the Disaster Reduction Effectiveness Assessment Unit to determine compliance with disaster reduction effectiveness by comparing post-earthquake surface settlement with the settlement limit.

[0070] As described above, the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that the technical solutions described in the above embodiments can still be modified, or some of the technical features thereof can be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A seismic disaster reduction simulation system for liquefiable foundation, characterized in that: The system includes: a cyclic stress ratio field analysis unit, an excess pore pressure ratio evolution analysis unit and a stress coupling correction unit; the cyclic stress ratio field analysis unit is used to collect the seismic parameters of the site after determining the site design earthquake event, and generate a cyclic stress ratio field using the depth reduction relationship; the excess pore pressure ratio evolution analysis unit is used to integrate the shear stress and shear strain at each depth at each time point in real time according to the cyclic stress ratio field to obtain the cumulative shear strain energy density, and compare the cumulative shear strain energy density with the critical cyclic shear strain to infer the excess pore pressure ratio and establish the evolution relationship of the excess pore pressure ratio with time and depth; the stress coupling correction unit is used to update the effective vertical stress value based on the excess pore pressure ratio, and synchronously correct the shear modulus according to the coupling relationship between the shear wave velocity and the excess pore pressure ratio, and feed the corrected shear modulus back to the excess pore pressure ratio evolution analysis unit.

2. The earthquake-resistant disaster reduction simulation system for liquefiable foundation according to claim 1, characterized in that: The system also includes: a disaster reduction effectiveness assessment unit, which is used to correct the excess pore pressure ratio using drainage improvement parameters and densification parameters to obtain a corrected excess pore pressure ratio; after the site design earthquake event ends, the excess pore pressure ratio, compression index and original porosity are integrated along the foundation thickness to correct the post-earthquake surface settlement, and the disaster reduction effectiveness is evaluated based on this; the drainage improvement parameters include: horizontal permeability coefficient, equivalent drainage path length and drainage structure layout half-distance; the densification parameters include: initial porosity, compression index and reinforcement structure spacing.

3. The earthquake-resistant disaster reduction simulation system for liquefiable foundation according to claim 2, characterized in that: Seismic parameters include: peak horizontal acceleration, total vertical stress, initial effective vertical stress, and shear wave velocity.

4. The earthquake-resistant disaster reduction simulation system for liquefiable foundation according to claim 3, characterized in that: The specific execution process of the cyclic stress ratio field analysis unit includes: collecting the peak horizontal acceleration of the site under the design earthquake event; obtaining the total vertical stress and the initial effective vertical stress along the depth direction; the total vertical stress is obtained by multiplying the saturated unit weight of the foundation and the corresponding depth, and the initial effective vertical stress is obtained by deducting the initial pore water pressure from the total vertical stress; obtaining the shear wave velocity along the same depth direction; for any given depth, combining the ratio of the peak horizontal acceleration to the gravity acceleration, the ratio of the total vertical stress to the initial effective vertical stress, and the depth reduction factor to calculate the cyclic stress ratio, and the result of the cyclic stress ratio corresponding to all depths is used as the cyclic stress ratio field.

5. The earthquake-resistant disaster reduction simulation system for liquefiable foundation according to claim 4, characterized in that: The specific execution process of the excess pore pressure ratio evolution analysis unit includes: calculating the cumulative shear strain energy density of shear stress and shear strain at different depths during the design earthquake event of the site based on the cyclic stress ratio field; then using the initial effective vertical stress and the critical shear strain value required to trigger liquefaction, the real-time growth trend of the excess pore pressure ratio is determined through the cumulative shear strain energy density, specifically including: at the beginning of the design earthquake event, the excess pore pressure ratio gradually increases with the increase of the cumulative shear strain energy density until it approaches the critical energy threshold defined by the initial effective vertical stress, and the excess pore pressure ratio approaches the limit state; finally, the distribution results of the excess pore pressure ratio at different depths as the duration of the design earthquake event increases are obtained, and the excess pore pressure ratio distribution is obtained.

6. The earthquake-resistant disaster reduction simulation system for liquefiable foundation according to claim 5, characterized in that: The specific execution process of the stress coupling correction unit includes: according to the excess pore pressure ratio, the excess pore pressure ratio is deducted from the corresponding initial effective vertical stress at each depth to obtain the real-time effective vertical stress at the same depth; based on the deterministic correspondence between the shear modulus and the real-time effective vertical stress, the shear modulus is synchronously corrected in combination with the wet density at the depth and the original shear wave velocity test value in situ; then, the cyclic shear stress is recalculated using the corrected shear modulus and the real-time effective vertical stress, and the product of the cyclic shear stress and the real-time shear strain is added to the cumulative shear strain energy density of the same time step as the input for the evolution of the excess pore pressure ratio in the next time step; the above process is cyclically executed with a preset time step during the design earthquake event to obtain the coupled degradation history of the effective vertical stress and shear modulus with time and depth.

7. The earthquake-resistant disaster reduction simulation system for liquefiable foundation according to claim 6, characterized in that: When correcting the shear modulus, the absolute value of the difference between the corrected and uncorrected shear moduli must not be lower than the lower limit of the residual shear stiffness of the saturated soil at that depth. This lower limit is determined based on a table comparing the measured shear wave velocity to the standard residual shear modulus. Furthermore, if the shear modulus decrease rate at any depth during the coupled degradation process exceeds the set critical degradation threshold, an early warning mechanism is automatically triggered, freezing the input path of the excess pore pressure ratio evolution analysis unit to prevent the cascading propagation of non-physical instability feedback in the next time step.

8. The earthquake-resistant disaster reduction simulation system for liquefiable foundation according to claim 7, characterized in that: The disaster reduction effectiveness assessment unit combines the obtained real-time effective vertical stress with the shear modulus coupled degradation process to determine the residual excess pore pressure ratio at each depth at the end of the design earthquake event; based on the compression index and the initial porosity ratio, a volume reconsolidation analysis is performed on the residual excess pore pressure ratio, and the post-earthquake surface settlement within the foundation thickness is obtained by integral calculation; the post-earthquake surface settlement is compared with the settlement limit. If the post-earthquake surface settlement meets the settlement limit, the disaster reduction effectiveness is determined to have met the standard and the simulation is terminated; otherwise, the disaster reduction effectiveness is determined to have failed to meet the standard.

9. The earthquake-resistant disaster reduction simulation system for liquefiable foundation according to claim 8, characterized in that: The process of the disaster reduction effectiveness assessment unit determining the residual excess pore pressure ratio at each depth at the end of the design earthquake event includes: calling the coupling degradation history of the effective vertical stress and shear modulus output by the stress coupling correction unit over time and depth during the entire duration of the design earthquake event, and extracting the effective vertical stress value at each depth at the end of the design earthquake event; then, comparing the initial effective vertical stress value before the design earthquake event with the real-time effective vertical stress value at the end of the design earthquake event at the same depth, and calculating the stress difference between the two; based on the physical definition of the excess pore pressure ratio, the stress difference is used as the residual excess pore pressure ratio at the depth at the end of the earthquake action, indicating the excess pore water pressure remaining due to the soil structure damage and shear deformation caused by the earthquake in the absence of complete drainage or consolidation, reflecting the dynamic response of the foundation soil under the action of earthquake loads.

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