An earthquake disaster mitigation simulation system for liquefiable ground

Abstract

The application relates to the technical field of computer modeling, and more particularly to an anti-seismic disaster mitigation simulation system for liquefiable ground. The system comprises a cyclic stress ratio field analysis unit, an excess pore water 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 relationship. The excess pore water pressure ratio evolution analysis unit is used for deducing an excess pore water pressure ratio and establishing an evolution relationship of the excess pore water pressure ratio with time and depth. The stress coupling correction unit is used for updating an effective vertical stress value based on the excess pore water pressure ratio and synchronously correcting a shear modulus according to a coupling relationship of a shear wave velocity and the excess pore water pressure ratio, and feeding back the corrected shear modulus to the excess pore water pressure ratio evolution analysis unit. The application effectively improves the scientificity and engineering applicability of the anti-seismic disaster mitigation of the liquefiable ground.

Description

Technical Field

[0001] This invention belongs to the field of earthquake modeling technology, specifically relating to an earthquake resistance and disaster reduction simulation system for liquefiable foundations. Background Technology

[0002] In the research and engineering application of seismic mitigation for 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 and the increase in large-scale development and construction in coastal areas, riverbanks, and areas with soft soil distribution, the risk of liquefaction of saturated loose sandy soil, which is widespread in these areas, has become more prominent. When liquefaction occurs, the effective stress of the foundation soil drops sharply, even approaching zero, leading to instantaneous loss of shear stiffness and strength degradation. This manifests as secondary earthquake disasters such as surface settlement, structural tilting, and even collapse, posing a significant threat to life and property. Existing anti-liquefaction technologies mainly include various methods such as in-situ shaking table tests, centrifuge model tests, pore pressure monitoring, and numerical simulations to assess the liquefaction potential of soil and its consolidation characteristics after liquefaction. For earthquake resistance and disaster reduction of 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 aim is to mitigate liquefaction damage and control post-earthquake settlement.

[0003] Currently, numerous studies both domestically and internationally have developed empirical models for liquefaction discrimination curves, dynamic strength envelopes, and excess porosity ratio evolution based on stress path methods and cyclic loading test data. For example, the traditional Seed cyclic stress ratio discrimination curve uses equivalent shear strain and shear modulus degradation test results to describe the threshold for soil liquefaction under specific cyclic loading. Furthermore, the cumulative evolution model of excess porosity ratio is usually based on the product of shear strain energy density or stress amplitude and the number of cycles, simplifying the liquefaction evolution process. However, most of these traditional models focus on the fitting stage of indoor tests, lacking a dynamic response process coupled with actual seismic conditions, and cannot reflect the dynamic attenuation of effective soil stress and the multi-stage evolution of shear stiffness under in-situ seismic time-history input. Simultaneously, traditional liquefaction discrimination models are usually based on a single number of cycles or a fixed amplitude, making it difficult to handle actual seismic inputs with complex pulse effects, multi-frequency components, and varying durations. Furthermore, after liquefaction occurs, quantifying the contribution of drainage and densification measures to the dissipation of residual excess pore pressure and the spatiotemporal distribution of post-earthquake settlement curves remains a major shortcoming of existing methods. Most empirical models can only provide the critical state at the instant of liquefaction detection, but cannot fully cover the real-time response throughout the earthquake and the secondary settlement calculation during the post-earthquake consolidation stage. Summary of the Invention

[0004] The main objective of this invention is to provide a seismic mitigation simulation system for liquefiable foundations. Through multidimensional coupling of three units—cyclic stress ratio analysis, excess pore pressure ratio evolution, and stress coupling correction—it dynamically simulates the liquefaction triggering and evolution of the foundation with depth and time. It provides real-time feedback on the coupling degradation process of effective stress and shear modulus, and introduces drainage improvement and densification parameter correction. Finally, it quantifies the post-earthquake surface settlement and compares it with the limit value, forming a high-precision dynamic prediction platform for the entire process from input seismic motion to output settlement curve, effectively improving the scientific nature and engineering applicability of seismic mitigation for liquefiable foundations.

[0005] To solve the above problems, the technical solution of the present invention is implemented as follows:

[0006] A seismic mitigation simulation system for liquefiable foundations includes: a cyclic stress ratio analysis unit, an excess pore pressure ratio evolution analysis unit, and a stress coupling correction unit. The cyclic stress ratio analysis unit is used to collect seismic parameters of the site after determining the design seismic 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 and time point in real time based on the cyclic stress ratio field to obtain the 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 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 shear wave velocity and excess pore pressure ratio, feeding back the corrected shear modulus to the excess pore pressure ratio evolution analysis unit.

[0007] Furthermore, the system also includes: a disaster reduction effectiveness assessment unit, used to correct the excess porosity using drainage improvement parameters and densification parameters to obtain a corrected excess porosity; after the site design earthquake event, the excess porosity, compression index, and original porosity are corrected by integrating along the foundation thickness to calculate the post-earthquake surface settlement and assess the disaster reduction effectiveness accordingly; 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.

[0008] Furthermore, the seismic parameters include: peak horizontal acceleration, total vertical stress, initial effective vertical stress, and shear wave velocity.

[0009] Furthermore, the specific execution process of the cyclic stress ratio field analysis unit includes: acquiring 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 by the corresponding depth, and the initial effective vertical stress is obtained by subtracting the initial pore water pressure from the total vertical stress; acquiring the shear wave velocity along the same depth direction; for any given depth, combining 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 to calculate the cyclic stress ratio, and using the result of the cyclic stress ratios corresponding to all depths as the cyclic stress ratio field.

[0010] Furthermore, the specific execution process of the excess porosity pressure ratio evolution analysis unit includes: calculating the cumulative shear strain energy density of shear stress and shear strain at different depths during the site design seismic event based on the cyclic stress ratio field; then, using the initial effective vertical stress and the critical shear strain value required to trigger liquefaction, determining the real-time growth trend of the excess porosity pressure ratio through the cumulative shear strain energy density, specifically including: at the beginning stage of the design seismic event, the excess porosity 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, at which point the excess porosity pressure ratio approaches the limit state; finally, obtaining the distribution results of the excess porosity pressure ratio at different depths as the duration of the design seismic event increases, thus obtaining the excess porosity pressure ratio distribution.

[0011] Furthermore, the specific execution process of the stress coupling correction unit includes: based on the excess pore pressure ratio, subtracting the excess pore pressure ratio 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, combined with the wet density at that depth and the original shear wave velocity test value in the field, synchronously correcting the shear modulus; subsequently, using the corrected shear modulus and the real-time effective vertical stress, recalculating the cyclic shear stress, and adding the product of the cyclic shear stress and the real-time shear strain to the cumulative shear strain energy density at 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 executed cyclically during the design earthquake event with a preset time step, thereby obtaining the coupling degradation history of the effective vertical stress and shear modulus with time and depth.

[0012] Furthermore, when correcting the shear modulus, the absolute value of the difference between the corrected shear modulus and the original shear modulus shall not be lower than the lower limit of the residual shear stiffness of the saturated soil at that depth; the lower limit of the residual shear stiffness shall be determined based on the ratio table of measured shear wave velocity and standard residual shear modulus; in addition, if the rate of decrease of the shear modulus at any depth in the coupled degradation process exceeds the set critical degradation threshold, an early warning indicator mechanism will be automatically triggered, and the input path of the excess pore pressure ratio evolution analysis unit will be frozen to prevent non-physical instability feedback from cascading and spreading in the next time step.

[0013] Furthermore, the disaster reduction effectiveness assessment unit combines the obtained real-time effective vertical stress and shear modulus coupled degradation history to determine the remaining excess porosity at each depth at the end of the design earthquake event; based on the compression index and initial void ratio, a volumetric reconsolidation analysis is performed on the remaining excess porosity, and the post-earthquake surface settlement within the foundation thickness range is calculated by integration; 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 deemed to be up to standard, and the simulation ends; otherwise, the disaster reduction effectiveness is deemed to be down to standard.

[0014] Furthermore, the process by which the disaster reduction effectiveness assessment unit determines the residual excess pore pressure ratio at each depth at the end of the design earthquake event includes: calling the effective vertical stress and shear modulus output by the stress coupling correction unit throughout the entire duration of the design earthquake event and extracting the effective vertical stress values ​​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 excess pore pressure ratio, the stress difference is taken as the residual excess pore pressure ratio at that depth at the end of the earthquake, representing the excess pore water pressure remaining after the soil structure failure and shear deformation caused by the earthquake without complete drainage or consolidation, reflecting the dynamic response results of the foundation soil under earthquake load.

[0015] This invention provides a seismic mitigation simulation system for liquefiable foundations, offering the following advantages: It enables continuous spatiotemporal tracking of the entire seismic load process, transforming traditional liquefaction analysis, which only provides single-point assessments, into dynamic predictions across the entire profile and multiple time periods. Utilizing a high-resolution subdivision strategy and vectorized parallel algorithms, the system transforms complex seismic inputs into millisecond-level feedback pore water pressure evolution surfaces while ensuring numerical stability. Furthermore, a freezing mechanism is used to suppress non-physical instability in real time, significantly improving computational reliability. Drainage improvement parameters and densification parameters are directly mapped to the excess pore pressure ratio reduction path, allowing the effectiveness of reinforcement measures to be reflected instantly in the simulation. Engineers can rapidly iterate on different drainage board spacings or preloading depths before construction, obtaining objective quantitative results comparing post-earthquake settlement with settlement limits, thus significantly shortening the design optimization cycle. The system's output of the remaining excess pore pressure ratio profile, shear modulus degradation curve, and settlement-time curve can all be corrected in real time with on-site monitoring data, providing a basis for dynamic adjustments during construction and reducing overly conservative or insufficient safety factors due to model deviations. In summary, this invention outperforms existing technologies in terms of accuracy, efficiency, and operability. It can not only identify high-risk weak interlayers in advance, but also assess the synergistic benefits of drainage and densification measures, providing an efficient, reliable, and closed-loop earthquake resistance and disaster reduction decision-making platform for complex engineering structures in coastal soft soil areas. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the system structure of a seismic mitigation simulation system for liquefiable foundations provided in an embodiment of the present invention;

[0017] Figure 2 The cyclic stress ratio field distribution with depth is provided for an embodiment of the present invention;

[0018] Figure 3 This is a graph showing the evolution of the permeability pressure ratio over time, provided in an embodiment of the present invention.

[0019] Figure 4 A comparison diagram of shear modulus before and after stress coupling correction provided in an embodiment of the present invention;

[0020] Figure 5 The post-earthquake surface subsidence and disaster reduction effectiveness assessment diagram provided for embodiments of the present invention. Detailed Implementation

[0021] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0022] refer to Figure 1 A seismic mitigation simulation system for liquefiable foundations is disclosed. 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 to collect seismic parameters of the site after determining the design seismic 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 shear stress and shear strain at each depth and time point in real time according to the cyclic stress ratio field to obtain the 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 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 shear wave velocity and excess pore pressure ratio, and feed back the corrected shear modulus to the excess pore pressure ratio evolution analysis unit.

[0023] From the very first step of engineering application, the cyclic stress ratio field analysis unit discretizes the site layer by layer after the seismic input conditions are determined. Each discrete depth point is assigned key seismic parameters corresponding to the site's design seismic event, such as peak horizontal acceleration, total vertical stress, initial effective vertical stress, and shear wave velocity. This unit reduces the surface peak horizontal acceleration to each depth point using a depth reduction relationship, and combines this with the ratio of total vertical stress to initial effective vertical stress, shear wave velocity, and the shear wave velocity exponential reduction function to calculate a continuously varying cyclic stress ratio field across the entire foundation thickness. Since the dynamic characteristics of liquefiable foundations are highly dependent on the initial stress state of the soil layers, a layer-by-layer scanning method is used to calibrate the difference between the total vertical stress and the initial effective vertical stress at the sampling depth, ensuring that the input accuracy of the cyclic stress ratio field is sufficient to support subsequent nonlinear coupled evolution calculations.

[0024] Once the cyclic stress ratio field is generated, it is automatically pushed to the excess porosity pressure ratio evolution analysis unit. During system initialization, this unit divides the time steps according to the duration of the seismic motion. In the first time step, it maps the cyclic stress ratio and the instantaneous shear stress and shear strain corresponding to the depth point to the shear strain rate and shear stress history curves. Then, through integration, the product of shear stress and shear strain is accumulated to obtain the cumulative shear strain energy density. There is a monotonically increasing correlation between the cumulative shear strain energy density and the critical cyclic shear strain, enabling the excess porosity pressure ratio evolution analysis unit to accurately estimate the increment of the excess porosity pressure ratio at each time step. When the cumulative shear strain energy density has not yet reached the energy threshold required to trigger liquefaction, the excess porosity pressure ratio increases gradually. Once the energy threshold approaches or is exceeded, the excess porosity pressure ratio rapidly rises to the upper limit of saturation and enters a plateau phase. This process exhibits significant advance or lag characteristics for saturated soil at different depths. Therefore, the system is designed with a multi-threaded parallel computing strategy to ensure that the deep coupling effect can be updated within milliseconds, avoiding numerical divergence caused by delayed updates.

[0025] As the excess porosity pressure ratio evolution analysis unit continuously outputs new excess porosity pressure ratio distribution results, the stress coupling correction unit synchronously receives and updates the effective vertical stress value in real time. Specifically, it multiplies the excess porosity pressure ratio by the initial effective vertical stress at the same depth and subtracts from the latter to obtain the real-time effective vertical stress at 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. Once the shear modulus changes, the shear wave velocity at the same depth adjusts accordingly, thus affecting the calculation of cyclic shear stress. To ensure that the coupling mechanism conforms to laboratory tests and field monitoring data, the unit also sets two safety thresholds: first, at any depth point, the corrected shear modulus must not be lower than the lower limit of the residual shear stiffness of saturated soil; second, throughout the entire time domain of the coupling degradation process, once the rate of decrease in shear modulus exceeds the critical degradation threshold, a freezing mechanism is immediately triggered, pausing the input of new cyclic shear stress and shear strain into the excess porosity pressure ratio evolution analysis unit to avoid cascading diffusion in subsequent time steps due to non-physical instability.

[0026] When the freeze mechanism is activated, the system outputs a warning to the user interface and saves the intermediate data files that caused the anomaly, facilitating engineers' subsequent retrieval of possible causes of instability. After the stress coupling correction unit completes its processing, the corrected shear modulus and real-time effective vertical stress are written back to the excess porosity pressure ratio evolution analysis unit, allowing it to continue iterating in the next time step. This process repeats until the timeline of the site design seismic event reaches its endpoint. During the entire seismic event duration, each time step corresponds to one update of the cyclic stress ratio field, one evolution of the excess porosity pressure ratio, and one coupling correction of the effective vertical stress and shear modulus, forming a dynamic data cube within a time-depth two-dimensional grid. The system uses memory-mapped files and asynchronous input / output technology in the background to fragment and store this data cube on a solid-state drive to ensure that data throughput does not become a bottleneck in large-scale computing scenarios. After the calculation is completed, the system automatically generates three types of three-dimensional distribution visualization files: effective vertical stress, shear modulus, and excess porosity pressure ratio. Users can directly view the response evolution process at each depth and time node on a professional graphics workstation.

[0027] Meanwhile, the system also reserves a data interface with the disaster reduction effectiveness assessment unit. Once it is necessary to assess the actual performance of drainage improvement or densification measures, users only need to input parameters such as horizontal permeability coefficient, equivalent drainage path length, drainage structure layout half-distance, initial void ratio, compression index, and reinforcement structure spacing into the interface. The system will then correct the excess porosity pressure ratio according to a linear or exponential decay model without recalculating the cyclic stress ratio field, thereby deriving the new effective vertical stress and shear modulus degradation process, and quickly outputting the post-earthquake surface settlement. If the post-earthquake surface settlement is less than the set settlement limit, the system determines that the disaster reduction effectiveness meets the standard and archives the simulation; if the settlement exceeds the limit, the system exports the settlement curve and depth distribution map for the design team to evaluate further optimization space of the reinforcement scheme. From the user's perspective, the entire simulation process is highly automated: the input end only needs to import the site's seismic time history or response spectrum, stratum static indicators, and improvement scheme parameters; the output end can obtain decision-making results that can be directly used for foundation disaster reduction design.

[0028] Furthermore, the system also includes: a disaster reduction effectiveness assessment unit, used to correct the excess porosity using drainage improvement parameters and densification parameters to obtain a corrected excess porosity; after the site design earthquake event, the excess porosity, compression index, and original porosity are corrected by integrating along the foundation thickness to calculate the post-earthquake surface settlement and assess the disaster reduction effectiveness accordingly; 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.

[0029] The disaster mitigation effectiveness assessment unit can receive and utilize drainage improvement parameters and densification parameters to perform multi-dimensional correction of excess porosity. Drainage improvement parameters mainly include horizontal permeability coefficient, equivalent drainage path length, and drainage structure layout spacing. In field engineering, these parameters are often achieved by installing sand wells, plastic drainage boards, or other drainage improvement measures to accelerate the dissipation of pore water pressure, increase the rate of decay of excess porosity, and slow down the accumulation of pore water pressure during liquefaction. Densification parameters include initial void ratio, compressibility index, and spacing of reinforced structures. These parameters are closely related to the compressibility of the reinforced soil and directly affect the volume shrinkage during the post-earthquake pore reconsolidation process. In actual operation, the disaster mitigation effectiveness assessment unit first correlates drainage improvement parameters with the depth-distributed excess porosity. Based on the length of the drainage path and the density of the drainage structure layout, it corrects the decay trend of excess porosity over time, reducing the residual excess porosity after the earthquake. Subsequently, the unit continues to call densification parameters and calculates post-earthquake surface settlement based on the coupling relationship between the initial void ratio and the compression index. This settlement is the integral result of the residual excess porosity ratio over volume change along the foundation thickness direction. To ensure the continuity of post-earthquake settlement calculation after the earthquake load ends, a data closed 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 load are input to ensure that the distribution of the residual excess porosity ratio is more consistent with the actual field 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 expected earthquake resistance and disaster reduction effect, thereby providing scientific decision-making for subsequent foundation reinforcement design. It is worth noting that during the correction process, the disaster reduction effectiveness assessment unit uses a layer-by-layer integration method to treat the corrected excess porosity ratio, initial void ratio, and compression index at each depth as a coupled whole, avoiding numerical oscillation problems caused by independent correction of parameter space, while ensuring the smoothness of the entire settlement curve.

[0030] Furthermore, the seismic parameters include: peak horizontal acceleration, total vertical stress, initial effective vertical stress, and shear wave velocity.

[0031] Furthermore, the specific execution process of the cyclic stress ratio field analysis unit includes: acquiring 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 by the corresponding depth, and the initial effective vertical stress is obtained by subtracting the initial pore water pressure from the total vertical stress; acquiring the shear wave velocity along the same depth direction; for any given depth, combining 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 to calculate the cyclic stress ratio, and using the result of the cyclic stress ratios corresponding to all depths as the cyclic stress ratio field.

[0032] The cyclic stress ratio field analysis unit acts as a bridge between seismic motion input and subsequent nonlinear response analysis. First, peak horizontal acceleration is acquired at the surface, then static information of the soil layers is collected 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 from the total vertical stress at the same depth point. The system simultaneously acquires the depth distribution of shear wave velocity through in-situ testing or existing exploration data and automatically matches it with a depth reduction factor database for joint use in subsequent steps. To ensure consistency between data sources, the cyclic stress ratio field analysis unit performs multiple quality controls in the background: firstly, Fourier filtering is applied to the peak horizontal acceleration time history to eliminate high-frequency noise; secondly, 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. After all necessary information has been registered in both the time and depth domains, the system performs combined calculations at each depth point on 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 to obtain the cyclic stress ratio at that depth point. To prevent numerical oscillations caused by abrupt parameter changes at soil interfaces, the analysis unit employs piecewise continuous interpolation to smooth the shear wave velocity at interlayer junctions, while simultaneously performing smooth interpolation of the same order on the depth reduction factor.

[0033] For any given depth Its corresponding cyclic stress ratio for:

[0034] ;

[0035] in, Peak horizontal acceleration; It is the acceleration due to gravity; For any given depth The total vertical stress; For any given depth The initial effective vertical stress; For any given depth The shear wave velocity.

[0036] This formula combines three types of information: seismic intensity, static stress state, and soil dynamics, enabling a quantitative description of the cyclic load sensitivity of liquefiable foundations at different depths. (Coefficient) Derived from statistical experience of the ratio of shear stress to shear strain amplitude in the main cycle of classical cyclic triaxial tests, this ratio directly reflects the conversion relationship between plane shear stress and principal shear stress; Peak ground horizontal acceleration is standardized to a dimensionless form to ensure numerical comparability across different design earthquake events; ratio Through total vertical stress With initial effective vertical stress The proportions characterize the relative contributions of static load and pore water pressure in the depth direction, where Obtained by multiplying the foundation saturation unit by the depth. Then at that depth point, the initial pore water pressure will be reduced from... The result obtained after deduction can accurately reflect the effective bearing capacity of saturated soil before liquefaction in the early stages of an earthquake; depth reduction item The combined effects of seismic wave amplitude attenuation and soil dynamic stiffness as the seismic wave propagates deeper were considered, including the linear factor. Using depth as the independent variable to describe the empirical law that dynamic stress decreases with depth, the exponential... Further with shear wave velocity The magnitude of the shear wave velocity relates to the deceleration rate and the consolidation stiffness of the soil. A higher shear wave velocity means that the soil is more compact and the energy decays faster, thus resulting in a lower cyclic stress ratio at the same depth.

[0037] The formula is implemented using vectorized matrix operations: the system first reads from the seismic motion input file. Subsequently, depth interpolation is performed on the saturated unit weight, pore water pressure, and shear wave velocity in the exploration database to form vectors of the same length; four multiplication, division, and cumulative multiplication steps are implemented element-wise in memory, and finally the result is output. Depth vector. To ensure that the attenuation term does not become negative at depth, the system performs constraint clipping on the depth range before interpolation, and... Nodes with values ​​less than zero are forced to zero to ensure the results are consistent with the actual physical meaning. After the cyclic stress ratio field analysis element completes the calculation, it will... The continuous distribution along the depth is stored in shared memory with a timestamp, for the ultrapore pressure ratio evolution analysis unit to call at each time step, which then... When calculating shear stress, there is no need to look up static stress or shear wave velocity again, thus avoiding redundant I / O overhead.

[0038] Furthermore, the specific execution process of the excess porosity pressure ratio evolution analysis unit includes: calculating the cumulative shear strain energy density of shear stress and shear strain at different depths during the site design seismic event based on the cyclic stress ratio field; then, using the initial effective vertical stress and the critical shear strain value required to trigger liquefaction, determining the real-time growth trend of the excess porosity pressure ratio through the cumulative shear strain energy density, specifically including: at the beginning stage of the design seismic event, the excess porosity 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, at which point the excess porosity pressure ratio approaches the limit state; finally, obtaining the distribution results of the excess porosity pressure ratio at different depths as the duration of the design seismic event increases, thus obtaining the excess porosity pressure ratio distribution.

[0039] The system first maps the cyclic stress ratio field to a shear stress history according to a preset time step, and then calculates the shear strain history with the same time resolution by combining the coupling results of the shear modulus and the real-time effective vertical stress. The two are multiplied point by point on the time axis and integrated over the occurred segments to obtain the cumulative shear strain energy density at different depths. Since the dynamic instability of liquefiable foundations is highly correlated with energy dissipation, the quantitative comparison between the cumulative shear strain energy density and the initial effective vertical stress and critical shear strain value becomes the sole basis for judging the growth rate of excess porosity pressure ratio: in the early stage of the design earthquake event, the cumulative shear strain energy density is at a low level, and the excess porosity pressure ratio only increases slowly; as the peak shear stress and shear strain amplitude continue to increase under the superposition effect, the energy consumption curve rises sharply, and the excess porosity pressure ratio accumulates rapidly. When the energy curve approaches the energy threshold jointly determined by the initial effective vertical stress and the critical shear strain value, the unit automatically switches to the limit approach algorithm, which compresses the time step and adopts an exponential approach method to ensure that the excess porosity pressure ratio approaches the limit state numerically smoothly without oscillation. To avoid abrupt changes in the depth dimension, the system employs spline smoothing in space, ensuring that the cumulative shear strain energy density presents a continuous piecewise curve along the depth direction. Simultaneously, the shear modulus degradation trajectory is updated synchronously, guaranteeing a closed-loop conservation between energy input, strain energy accumulation, and excess pressure ratio growth in each time iteration.

[0040] For any given depth ,time The pressure ratio of the pore at that time for:

[0041] ;

[0042] in, From the initial moment to time The cumulative shear strain energy density at that time; For any given depth The critical shear strain value;

[0043] ;

[0044] in, For time integration variables; For any given depth ,time Shear stress at that time; For any given depth ,time Shear strain rate at time;

[0045] ;

[0046] in, The relative density is equal to the difference between the loosest state porosity and the natural state porosity, divided by the difference between the loosest state porosity and the densest state porosity. Standard atmospheric pressure.

[0047] The overburden pressure ratio evolution analysis unit starts with the shear stress ratio from the cyclic stress ratio field analysis unit, and multiplies the ratio by the real-time effective vertical stress at each time step to obtain the result. Then, the shear modulus after coupling correction is obtained. Because the duration of earthquakes is subdivided into hundreds or even thousands of discrete steps, the system employs an explicit fourth-order Runge-Kutta method to ensure numerical stability during time integration. Simultaneously, the depth-oriented data structure is encapsulated as a column vector for parallel GPU computation, thereby enabling… It can be refreshed in milliseconds. As energy accumulates, the dimensionless ratio within the exponential function... Gradually increase from zero, initially hour The overpore pressure ratio increases quasi-linearly with energy, exhibiting near-linear decay; however, when shear stress amplitudes are superimposed or high-frequency pulses occur, it leads to... Approaching rapidly The exponential curve drops sharply, and the superpore pressure ratio increases nonlinearly; once The system automatically triggers the asymptotic approximation algorithm, reducing the time step to the original size. Times, and with an exponential approximation strategy Damping in In the vicinity, this avoids numerical oscillations while ensuring physical meaning. Spatially, deep high-stress zones are due to... big, Small and with low threshold energy The fastest growth rate was observed in shallow layers, which, due to their low total vertical stress and high pore water pressure, resulted in high threshold energy. The growth rate is relatively slow, forming a profile of peak excess pressure ratio that increases with depth. The system uses cubic splines to... Perform smoothing to ensure the shear modulus degradation curve has no abrupt jumps at interlayer transitions; simultaneously record... The timing sequence is used to quickly retrieve extreme moments when subsequent coupled correction elements calculate effective vertical stress, thereby capturing the critical point of instantaneous soil stiffness collapse. The energy threshold denominator contains... The coefficients are derived from the symmetry of the main circulation area of ​​shear stress and shear strain in unidirectional cyclic shearing, which not only matches the experimental statistics but also ensures the consistency of units. The exponential model avoids the problem of artificial truncation of the saturation upper limit in the high amplitude region of the traditional strain hyperbola model, making the increase of pore water pressure continuously differentiable.

[0048] Furthermore, the specific execution process of the stress coupling correction unit includes: based on the excess pore pressure ratio, subtracting the excess pore pressure ratio 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, combined with the wet density at that depth and the original shear wave velocity test value in the field, synchronously correcting the shear modulus; subsequently, using the corrected shear modulus and the real-time effective vertical stress, recalculating the cyclic shear stress, and adding the product of the cyclic shear stress and the real-time shear strain to the cumulative shear strain energy density at 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 executed cyclically during the design earthquake event with a preset time step, thereby obtaining the coupling degradation history of the effective vertical stress and shear modulus with time and depth.

[0049] The stress coupling correction unit plays a crucial role in converting the pore water pressure response into a degradation process of soil stiffness and bearing capacity. At each preset time step, the unit first reads the distribution of excess pore pressure ratio across the entire depth and then, for any depth point, directly subtracts this excess pore pressure ratio from the corresponding initial effective vertical stress to obtain the new real-time effective vertical stress. This operation implies that an increase in pore water pressure equivalently weakens the effective stress that the particle skeleton can bear. Subsequently, based on the one-to-one correspondence curve between shear modulus and real-time effective vertical stress established through experiments and field inversion, combined with the wet density and original shear wave velocity test values ​​at that depth, the system synchronously corrects the shear modulus, thereby ensuring that the decrease in dynamic stiffness and the reduction in effective stress are completed simultaneously within the same time step. Once the shear modulus is updated, it 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 by 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 overpore pressure ratio evolution analysis unit in the next time step. The entire process is executed cyclically with a fixed step size 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 coupling degradation matrix that is updated synchronously with time and depth. To avoid numerical divergence, the system checks whether the decrease in shear modulus exceeds the lower limit of residual shear stiffness in each time step; if the lower limit is triggered, the shear modulus at that depth point is immediately frozen, and a warning signal is issued to the upstream module to prevent the non-physical negative stiffness from cascading in the next step. Meanwhile, the stress coupling correction unit archives the real-time effective vertical stress, shear modulus, and cyclic shear stress corrected at 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, the system gradually depicts the coupled degradation surface of effective vertical stress and shear modulus with time and depth: in shallow layers, due to lower initial effective vertical stress, the excess pore pressure ratio increases faster, and the shear modulus decreases significantly; in deeper layers, due to higher constraint stress and relatively slower pore pressure rise, stronger residual stiffness is exhibited. After the design earthquake event ends, the unit freezes the last frame of data as the final degradation state, providing accurate initial mechanical values ​​for the disaster reduction effectiveness assessment unit to perform post-earthquake consolidation and settlement calculations.

[0050] For any given depth ,time Real-time effective vertical stress for:

[0051] ;

[0052] For any given depth ,time Corrected shear modulus at time for:

[0053] ;

[0054] in, These are the original shear wave velocity test values ​​from the field. For any given depth The wet density.

[0055] In the seismic mitigation simulation system for liquefiable foundations, the excess pore pressure ratio evolution analysis unit generates a new frame each time. The depth profile and stress coupling correction element immediately call the formula. The weakening of the soil skeleton bearing capacity by pore water pressure is transformed into a real-time reduction of effective vertical stress. It is the initial effective vertical stress corrected for hydrostatic pressure before the earthquake begins. This directly reflects the proportion of pore water pressure at the same depth relative to the initial effective vertical stress. When Still in the low value range, deduction items are... The effect is minor; when Approaching the limit, Significant compression, possibly even to less than 10% of the initial value, indicates that the soil microstructure can no longer maintain the original skeleton stress path.

[0056] Once the real-time effective vertical stress is updated, the system immediately uses the original on-site shear wave velocity test value. With wet density Calculate the corrected shear modulus This expression continues the trend in small-strain elasticity theory. The basic framework, while introducing As a nonlinear reduction factor, the square root form is chosen over the nonlinear form because the sensitivity of the equivalent stiffness dominated by shear wave velocity to pore water pressure decreases sublinearly: when Still lower than When the shear modulus decreases significantly; when achieve about, The increase began to push up the discount rate, making Entering a rapid decline phase; when Rise to above, It is close The reduction factor is less than At this point, the soil shear stiffness approaches the residual state. Because... Directly factored in, the increased wet density of the densified reinforced zone partially offsets the reduction in shear modulus, ensuring the system maintains a sensitive response to the dynamic stiffness improvement effect of the reinforcement measures; simultaneously The square term amplifies the stiffness advantage of layers with higher shear wave velocities, allowing them to maintain a relatively larger [stiffness] even with a faster increase in pore water pressure. This reflects the constrained hardening effect of deep sand layers. The stress-coupled correction element is updated... Subsequently, the cyclic shear stress is multiplied by the cyclic stress ratio field to obtain a new round of cyclic shear stress, which is then multiplied by the real-time shear strain and accumulated into the energy history curve. This provides input for the pore water pressure evolution in the next time step, completing the energy-pore pressure-stress-stiffness closed loop. The system uses a sparse tensor structure for storage in the background. The time series matrix is ​​used, and spline smoothing is applied to the depth dimension at each step to ensure that the shear modulus curve does not jump abruptly at the soil interface. To prevent instantaneous instability, when any depth point appears... The decrease exceeded the initial value for three consecutive time steps. or Once the residual shear stiffness drops to the lower limit, the system automatically shortens the time step and enters a limiting pressure regulation mode, limiting the pore water pressure increase rate within a set threshold to prevent numerical divergence. At the end of the seismic event, the element freezes the last frame. and The profile is passed to the disaster reduction effectiveness assessment unit for post-earthquake settlement and consolidation calculations.

[0057] Furthermore, when correcting the shear modulus, the absolute value of the difference between the corrected shear modulus and the original shear modulus shall not be lower than the lower limit of the residual shear stiffness of the saturated soil at that depth; the lower limit of the residual shear stiffness shall be determined based on the ratio table of measured shear wave velocity and standard residual shear modulus; in addition, if the rate of decrease of the shear modulus at any depth in the coupled degradation process exceeds the set critical degradation threshold, an early warning indicator mechanism will be automatically triggered, and the input path of the excess pore pressure ratio evolution analysis unit will be frozen to prevent non-physical instability feedback from cascading and spreading in the next time step.

[0058] Each correction to the shear modulus is subject to dual safety constraints: the lower limit of residual shear stiffness and the critical degradation threshold. Upon entering a given time step, the system first performs a weighted calculation of the real-time effective vertical stress and the original shear wave velocity based on the latest excess pore pressure ratio profile, obtaining a depth-discrete vector of the pre-correction shear modulus. Subsequently, the coupled algorithm performs a softening operation on this vector based on the increase in pore water pressure, generating candidate post-correction shear moduli. At this point, the system immediately calculates the absolute value of the difference between the two vectors and compares it element-by-element with the lower limit of residual shear stiffness in saturated soil at the same depth. The lower limit of residual shear stiffness is derived from the cross-interpolation of the measured shear wave velocity and the industry standard residual shear modulus ratio table; it reflects the minimum dynamic stiffness that the soil can maintain after large strain. If the difference at a certain depth is less than the corresponding lower limit, the system reverts the post-correction shear modulus at that depth to the minimum allowable value that meets the lower limit, and writes a "stiffness reversion" flag and the current timestamp to the log to maintain physical rationality and retain traceable evidence.

[0059] After determining the lower limit, the system enters the rate monitoring phase. It subtracts the shear modulus at each depth point in the current time step from the data of the previous time step and divides this difference by the step size to obtain the instantaneous rate of decrease. This rate is compared with a preset critical degradation threshold. If the rate at any depth point exceeds the threshold, the system immediately triggers an early warning mechanism. The early warning mechanism first highlights the abnormal depth and trigger time on the graphical interface, sending a mandatory review signal to the engineer. Second, it freezes the input path of the excess pore pressure ratio evolution analysis unit. Freezing means that the pore water pressure increment at that depth point is locked to zero in the subsequent time step, thus preventing numerical collapse that might be caused by non-physical coupling positive feedback. Simultaneously, an adaptive step-size contraction strategy is initiated, reducing the global calculation time step to one-tenth of its original size and repeating three subdivision iterations until the shear modulus rate of decrease recovers to within the threshold. If the three subdivisions still fail to recover, the system records a "persistent instability" state and automatically writes all intermediate field files for offline high-precision analysis to recalibrate the lower limit of residual shear stiffness or the critical degradation threshold. Through the dual insurance mechanism of the difference lower limit and the rate threshold, the system ensures at each time step that the degradation of the shear modulus is neither so small as to violate the physical meaning of the residual stiffness, nor so large as to exceed the energy dissipation rate that the soil structure can tolerate, thereby ensuring that the coupling chain between effective vertical stress, shear modulus, cyclic shear stress and energy accumulation is continuously controlled.

[0060] For any given depth ,time At that time, the excess porosity pressure ratio was corrected using drainage improvement parameters and densification parameters to obtain the corrected excess porosity pressure ratio. :

[0061]

[0062] in, For any given depth The horizontal permeability coefficient can be artificially increased by installing sand wells / PVD. The unit weight of water; For any given depth The equivalent drainage path half distance.

[0063] The denominator of the formula originates from the classical radial drainage consolidation theory, and its physical meaning is that the throttling effect of the drainage channel and the weight of water together determine the dissipation rate of pore water pressure: horizontal permeability coefficient. The larger the pore water depth, the smaller the lateral resistance to water flow within the same depth layer, and the faster the pore water pressure dissipates; the unit weight of water This factor acts as a proportionality factor to convert pore water pressure gradient into flow velocity, ensuring that seepage conservation and energy balance are simultaneously satisfied within the drainage channel; the equivalent drainage path half-distance The square of the value appears in the denominator, indicating that the length of the drainage path has a secondary amplification effect on the dissipation rate. If the spacing of the drainage structure is halved by increasing the density of sand wells or laying plastic drainage boards, the pore water pressure reduction rate can theoretically be increased by four times.

[0064] Time variable Being in the same position as the numerator in the denominator of a fraction means that as the consolidation time after the earthquake ends, the pressure reduction benefits from drainage improvements will accumulate in an exponentially decreasing manner. Engineers can monitor this in real time. The attenuation curve is used to determine whether post-earthquake drainage measures have achieved the expected results. The disaster reduction effectiveness assessment unit, during implementation, first reads the data from the freezing point of the coupled correction unit. The profile maps the depth, type, diameter, and spacing of each drainage component in the construction log to grid nodes, and calculates the corresponding... and The system for The assignment is performed in two steps: if a sand well or plastic drainage board exists at that depth, the original permeability coefficient is multiplied by an empirical coefficient based on the equivalent porosity model; if no reinforcement has been applied, the original value is retained to evaluate the comparison effect before and after the improvement. Equivalent drainage path half-distance By automatically identifying the spacing between adjacent drainage well nodes using finite element meshes and taking into account well diameter corrections, the geometric characteristics of the drainage channel network topology are fully reflected.

[0065] In the formula The system uses standard values ​​derived from on-site water temperature and density conversion. In high-altitude and cold regions, the system automatically adjusts to account for the combined effects of water temperature on viscosity and density. After all parameters are interpolated to the same depth resolution, the disaster mitigation effectiveness assessment unit performs parallel calculations node by node. Subsequently, spline smoothing is performed on the entire profile to ensure the continuity of the pore water pressure field. The results are then fed back to the coupled correction unit to update the real-time effective vertical stress and shear modulus, thereby maintaining the bidirectional coupling between dynamic response and static consolidation during the drainage consolidation stage. The system reflects the reduction in initial void ratio and compressibility index resulting from densification improvement through two paths: firstly, densification is usually accompanied by an increase in permeability, directly raising the... Secondly, in post-earthquake consolidation calculations, a smaller compression index will reduce the post-earthquake settlement, making the same... This also results in more limited surface settlement. Engineers can adjust the drainage structure layout spacing, sand well diameter, or pre-compaction density in real time on the interface, and the system immediately recalculates. , The modified excess pressure ratio profile shows the instantaneous changes in the sedimentation-time curve.

[0066] Furthermore, the disaster reduction effectiveness assessment unit combines the obtained real-time effective vertical stress and shear modulus coupled degradation history to determine the remaining excess porosity at each depth at the end of the design earthquake event; based on the compression index and initial void ratio, a volumetric reconsolidation analysis is performed on the remaining excess porosity, and the post-earthquake surface settlement within the foundation thickness range is calculated by integration; 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 deemed to be up to standard, and the simulation ends; otherwise, the disaster reduction effectiveness is deemed to be down to standard.

[0067] When the designed earthquake event ends Post-earthquake surface subsidence for:

[0068]

[0069] in, This refers to the thickness of the foundation. It is the compression index; This represents the initial void ratio.

[0070] The derivation of this formula stems from the linearization of volumetric strain in one-dimensional consolidation theory under the small-strain approximation: when pore water pressure has not completely dissipated, the remaining excess pore pressure ratio can be considered as instantaneous additional water pressure, and its equivalent effective stress increment on the soil skeleton is logarithmically related to the volumetric compression. Compression index Defined as the slope of the porosity-effective stress curve in the logarithmic effective stress coordinate system, therefore This can be interpreted as the volumetric strain coefficient caused by a unit effective stress increment. If we take... Multiplying by the initial effective vertical stress yields the equivalent effective stress increment, which, when multiplied by the volumetric strain coefficient, gives the instantaneous longitudinal strain. Since here we directly... Converted to Internally, at the formula level, what remains is a product of only the compressibility index, the initial porosity ratio, and the corrected excess porosity ratio. The integrand is physically the amount of settlement per unit depth.

[0071] During system implementation, the coupling degradation process is first frozen in the output frame. With the exploration profile Perform depth alignment, then discretize the foundation thickness according to the grid size. Thickness Applying the trapezoidal integral or Simpson's integral to each small interval yields... To reduce the sensitivity of the results to the initial porosity test error, the system... Cubic Hermite interpolation is employed with monotonic constraints applied to both sides of the interpolation function to prevent physically unreasonable rebounds or downward jumps in the porosity profile; for the compressibility index... If the survey report only provides representative values, the system will automatically assign values ​​based on saturated density and relative density to ensure that the high-density reinforced area has a relatively low compression index. (Corrected overpore pressure ratio) The system already includes the effects of drainage improvement and densification parameters on pore water pressure dissipation, so there's no need to consider the drainage time factor during integration. However, the system still records each contribution during integration in the background so users can query which depth segment contributes the most to the total settlement. When integration is complete... Subsequently, the disaster reduction effectiveness assessment unit compared it with the design settlement limit. Comparison: If If so, the output will be "Disaster reduction effectiveness meets standards"; if If the error occurs, the system will output "Disaster mitigation effectiveness not met" and highlight the area where the settlement curve exceeds the limit in red on the interface. Simultaneously, it will backtrack the data within that area. , and The system provides precise targets for engineers to adjust sand well spacing, increase horizontal permeability coefficients, or add densification treatments, based on the original values. It also supports sensitivity analysis, allowing users to batch input different drainage structure layout half-distances or compression index assumptions. The system will calculate multiple settlement curves in parallel and present them graphically, helping to quickly select the most economical improvement combination. Through this integral formula and its accompanying high-resolution numerical implementation, the seismic simulation system for liquefiable foundations links complex dynamic pore pressure response, consolidation volume deformation, and engineering settlement limits within a unified mathematical framework. This quantifies 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 schemes.

[0072] Furthermore, the process by which the disaster reduction effectiveness assessment unit determines the residual excess pore pressure ratio at each depth at the end of the design earthquake event includes: calling the effective vertical stress and shear modulus output by the stress coupling correction unit throughout the entire duration of the design earthquake event and extracting the effective vertical stress values ​​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 excess pore pressure ratio, the stress difference is taken as the residual excess pore pressure ratio at that depth at the end of the earthquake, representing the excess pore water pressure remaining after the soil structure failure and shear deformation caused by the earthquake without complete drainage or consolidation, reflecting the dynamic response results of the foundation soil under earthquake load.

[0073] In a seismic mitigation simulation system for liquefiable foundations, for the mitigation effectiveness assessment unit to accurately pinpoint the remaining excess pore pressure ratio at each depth at the end of the design earthquake event, it must first fully access the effective vertical stress and shear modulus coupled degradation database generated by the stress coupling correction unit throughout the dynamic calculation process. When establishing this database, the system leaves dual index tags for each time step and each depth node; therefore, the mitigation effectiveness assessment unit only needs to access the database via the termination timestamp. This allows you to retrieve the real-time effective vertical stress field in full-depth vectorization. Subsequently, the unit calls the static initial condition file and retrieves the corresponding initial effective vertical stress according to the depth. After the two stress profiles are precisely aligned in memory, the system directly performs a difference operation to obtain the result. The physical significance of this step lies in treating the stress attenuation in the skeletal structure caused by dynamic loads as water pressure still retained in the pore system. This water pressure has not yet been released when the seismic activity ceases, and is therefore stored in the soil as residual excess porosity. Based on the fundamental definition of excess porosity, the system divides this stress difference by the initial effective vertical stress to obtain the dimensionless residual excess porosity. Since the stress-coupled correction element ensures that the shear modulus reduction is not lower than the lower limit of the residual shear stiffness during the dynamic stage, the effective vertical stress degradation curves at these depths will not exhibit numerical jumps, thus guaranteeing the calculated results. Smoothness along depth distribution.

[0074] To further eliminate local anomalies, the disaster reduction effectiveness assessment unit... A wavelet denoising and spline smoothing process was performed to eliminate numerical discretization errors while preserving the true peak values ​​in weak areas such as soft interlayers. After completing this profile, the system used it as the initial pore water pressure field for post-earthquake consolidation analysis and visually displayed the relationship between the remaining excess pore pressure ratio and depth on the interface, allowing engineers to easily identify the depth sections with the highest risk. Simultaneously, the element... By cross-referencing with drainage improvement parameters and densification parameter libraries, the pore pressure decay half-life is automatically estimated, providing a time window for subsequent drainage layout optimization. Through this rigorous stress difference and excess pore pressure ratio conversion process, the disaster reduction effectiveness assessment unit not only fully inherits the stress degradation information from the dynamic stage, but also provides physically oriented initial conditions for post-earthquake settlement prediction in the static assessment stage. This ensures that the earthquake disaster reduction simulation system for liquefiable foundations can achieve data closure and reliable results throughout its entire life cycle.

[0075] The following is a complete embodiment demonstrating the entire process of a seismic mitigation simulation system for liquefiable foundations, from dynamic input to settlement determination. The site is located in a coastal alluvial plain, and the foundation thickness is [missing information]. The average saturated unit weight of the saturated sand layer is taken as follows. The water level is at the surface, and the unit weight of water is taken as follows. The design reference peak horizontal acceleration is defined as: The equivalent earthquake duration is taken as Install plastic drainage boards; the equivalent drainage path halfway is... , , The three sections are respectively , , Improved horizontal permeability coefficient Segmented , , The linear interpolation of in-situ segmented test values ​​of shear wave velocity is... (Surface) to ( (Wet density) Approximate. The compression index is uniformly taken as... The initial porosity decreases linearly with depth. (Surface) to ( The relative density is based on the site survey results. .

[0076] Step 1, Cyclic Stress Ratio Field:

[0077] With three representative depths Explain the calculation process. For example, the total vertical stress is The initial effective vertical stress is . formula

[0078] ;

[0079] Give . Same method , .

[0080] The second step is the evolution of the ultrapore pressure ratio:

[0081] Shear stress amplitude .by For example Assuming in equivalent The shear strain amplitude within the main cycle is taken as follows: ,but

[0082] ;

[0083] Critical shear strain value

[0084] ;

[0085] Give Energy threshold .then

[0086] .

[0087] Same method , .

[0088] The third step, drainage and densification correction: with For example:

[0089] .

[0090] The remaining depths were obtained after correction. , .

[0091] Step 4: Update the effective vertical stress and output the remaining excess pressure ratio:

[0092] ;

[0093] .

[0094] depth and have to and The values ​​are the same because the difference process with the same initial stress is already included in the formula.

[0095] Step 5, Shear modulus degradation: Initial shear modulus .

[0096] Revised ; Satisfies the lower limit of residual shear stiffness The difference between the thresholds is a safety line. The rate of descent did not exceed the threshold, and the system did not freeze.

[0097] Step 6, Settlement Calculation: Assume three-segment average The coefficients are as follows: .integral ;

[0098] .

[0099] Step 7, Performance Assessment: The site's allowable settlement limit is taken as... .because The system determines that the disaster reduction efficiency after the combination of drainage board and densification meets the standard, automatically ends the simulation and generates settlement-depth curve and residual excess pore pressure ratio profile for engineers to archive.

[0100] like Figure 1 As 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 illustrates the output of the cyclic stress ratio field analysis unit, reflecting the distribution of the cyclic stress ratio field generated using depth reduction relationships after determining the site's design seismic event. This is achieved by collecting seismic parameters such as peak horizontal acceleration, total vertical stress, initial effective vertical stress, and shear wave velocity. The figure shows that the cyclic stress ratio gradually increases with depth, approaching zero near the surface, and reaching a peak of approximately 0.6 at a depth of about 20 meters. This distribution characteristic is consistent with the stress distribution caused by the depth reduction factor during seismic wave propagation in the soil.

[0101] like Figure 2 As shown, the horizontal axis represents time in seconds, and the vertical axis represents excess porosity (EPS), which is dimensionless. This figure presents the analysis results of the EPS evolution analysis unit during the design earthquake event, including three evolution curves at different depths: 5 meters, 10 meters, and 15 meters. The solid line represents the EPS evolution at a depth of 5 meters, the dashed line represents the evolution at a depth of 10 meters, and the long and short dashed 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 EPS at all depths gradually increases with the increase of cumulative shear strain energy density. The EPS increase is more rapid in shallow soil, with the EPS at a depth of 5 meters approaching the limit state of 1.0 after approximately 15 seconds, while the EPS increase in deeper soil is relatively slower.

[0102] like Figure 3As shown, the horizontal axis represents depth in meters, and the vertical axis represents shear modulus in megapascals (MPa). This figure illustrates the effect of the stress-coupled correction element, using a bar chart to compare the changes in shear modulus before and after correction. White bars represent the shear modulus before correction, and black bars represent the shear modulus after correction. It is clearly observed from the figure that after stress-coupled correction, the shear modulus at all depths is significantly reduced. This 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 consistently remains above the lower limit of the residual shear stiffness of the saturated soil at that depth, ensuring the physical rationality of the calculation.

[0103] like Figure 4 As shown, the horizontal axis represents different site types, and the vertical axis represents post-earthquake surface settlement in centimeters. This figure illustrates the assessment results of the disaster reduction effectiveness evaluation unit, containing three curves comparing the effects of no disaster reduction measures, drainage improvement measures, and densification measures. The horizontal dashed line represents the settlement limit, set at 30 cm. The solid line represents post-earthquake surface settlement without disaster reduction measures, the short dashed line represents settlement after drainage improvement measures, and the long and short dashed lines represent settlement after densification measures. The figure indicates the compliance status of disaster reduction effectiveness. Sites without disaster reduction measures exceeding the settlement limit in saturated soil and other site types are deemed non-compliant, while sites using drainage improvement and densification measures meet the settlement limit requirements and are deemed compliant. This figure effectively verifies the function of the disaster reduction effectiveness evaluation unit in determining whether disaster reduction effectiveness is compliant by comparing post-earthquake surface settlement with the settlement limit.

[0104] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A seismic mitigation simulation system for liquefiable foundations, characterized in that, The system includes: Cyclic stress ratio field analysis unit, overpore pressure ratio evolution analysis unit, and 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 seismic event and generate a cyclic stress ratio field using the depth reduction relationship. The specific execution process of the excess porosity pressure ratio evolution analysis unit includes: calculating the cumulative shear strain energy density of shear stress and shear strain at different depths during the site design seismic event based on the cyclic stress ratio field; then, using the initial effective vertical stress and the critical shear strain value required to trigger liquefaction, determining the real-time growth trend of the excess porosity pressure ratio through the cumulative shear strain energy density, specifically including: at the beginning stage of the design seismic event, the excess porosity 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, at which point the excess porosity pressure ratio approaches the limit state; finally, obtaining the distribution results of the excess porosity pressure ratio at different depths as the duration of the design seismic event increases, obtaining the excess porosity pressure ratio distribution, and establishing the evolution relationship of the excess porosity pressure ratio with time and depth; The stress coupling correction unit is used to subtract the excess pressure ratio from the corresponding initial effective vertical stress at each depth based on the excess pressure ratio, thereby obtaining 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, and combined with the wet density at that depth and the original on-site shear wave velocity test value, the shear modulus is synchronously corrected. Subsequently, using the corrected shear modulus and the real-time effective vertical stress, the cyclic shear stress is recalculated, and the product of the cyclic shear stress and the real-time shear strain is added to the cumulative shear strain energy density at the same time step, serving as the input for the evolution of the excess pressure ratio in the next time step. This process is repeated cyclically during the design earthquake event with a preset time step to obtain the coupling degradation history of the effective vertical stress and shear modulus with time and depth.

2. The earthquake resistance and disaster reduction simulation system for liquefiable foundations as described in claim 1, characterized in that, The system also includes: a disaster reduction effectiveness assessment unit, used to correct the excess porosity using drainage improvement parameters and densification parameters to obtain a corrected excess porosity; after the site design earthquake event, the excess porosity, compression index, and original porosity are corrected by integrating along the foundation thickness to calculate the post-earthquake surface settlement and assess the disaster reduction effectiveness accordingly; 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 resistance and disaster reduction simulation system for liquefiable foundations as described in claim 2, characterized in that, Earthquake parameters include: peak horizontal acceleration, total vertical stress, initial effective vertical stress, and shear wave velocity.

4. The earthquake resistance and disaster reduction simulation system for liquefiable foundations as described in claim 3, characterized in that, The specific execution process of the cyclic stress ratio field analysis unit includes: acquiring 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 by the corresponding depth, and the initial effective vertical stress is obtained by subtracting the initial pore water pressure from the total vertical stress; acquiring the shear wave velocity along the same depth direction; for any given depth, combining 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 to calculate the cyclic stress ratio, and using the result of the cyclic stress ratios corresponding to all depths as the cyclic stress ratio field.

5. The earthquake resistance and disaster reduction simulation system for liquefiable foundations as described in claim 4, characterized in that, When correcting the shear modulus, the absolute value of the difference between the corrected shear modulus and the original shear modulus shall not be lower than the lower limit of the residual shear stiffness of the saturated soil at that depth. The lower limit of the residual shear stiffness shall be determined based on the ratio of measured shear wave velocity to standard residual shear modulus. In addition, if the rate of decrease of the shear modulus at any depth in the coupled degradation process exceeds the set critical degradation threshold, an early warning mechanism will be automatically triggered, and the input path of the excess pore pressure ratio evolution analysis unit will be frozen to prevent non-physical instability feedback from cascading and spreading in the next time step.

6. The earthquake resistance and disaster reduction simulation system for liquefiable foundations as described in claim 5, characterized in that, The disaster reduction effectiveness assessment unit combines the real-time effective vertical stress and shear modulus coupled degradation history to determine the remaining excess porosity at each depth at the end of the design earthquake event. Based on the compression index and the initial void ratio, a volumetric reconsolidation analysis is performed on the remaining excess porosity, and the post-earthquake surface settlement within the foundation thickness range is calculated by integration. 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 be up to standard, and the simulation ends; otherwise, the disaster reduction effectiveness is determined to be down to standard.

7. The earthquake resistance and disaster reduction simulation system for liquefiable foundations as described in claim 6, characterized in that, The process of determining the residual excess pore pressure ratio at each depth at the end of the design earthquake event by the disaster reduction effectiveness assessment unit includes: calling the coupling degradation history of the effective vertical stress and shear modulus output by the stress coupling correction unit throughout 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; according to the physical definition of excess pore pressure ratio, the stress difference is taken as the residual excess pore pressure ratio at that depth at the end of the earthquake, which represents the excess pore water pressure remaining after the soil structure failure and shear deformation caused by the earthquake without complete drainage or consolidation, reflecting the dynamic response result of the foundation soil under earthquake load.

Images