Uncertainty Of Soil Parameters Research Articles

Performance-based design of strip foundation considering the full effect of ground improvement

Ground improvement is an effective way to improve the bearing capacity of a shallow foundation. However, the benefit of reducing uncertainties in soil parameters for shallow foundation design is rarely recognized. This study investigated the full effect of rapid impact compaction (RIC) on a strip foundation design. The finite difference method coupled Monte Carlo simulation were used to calculate the failure probability and the required width of the strip foundation, where the friction angle of soil was treated as a random variable. The results show that the foundation width reduces by 48.5% when considering the full effect of RIC, and a significant part of the reduction came from the decrease in the uncertainty of friction angle. Although the adopted relationship between the friction angle and tip resistance of cone penetration test affects the designed width of the foundation, the full effect of ground improvement contributed by the uncertainty reduction of soil parameters is still significant. The implication of the present study provides a basis for the performance-based bearing capacity design of shallow foundations.

Expected Changes in Rainfall-Induced Landslide Activity in an Italian Archaeological Area

Cultural heritage is one of the most exceptional resources characterizing the Italian territory. Archaeological heritage, i.e., the archaeological sites with different types of archaeological artifacts, strongly contributes to enriching the national and international cultural heritage. Nevertheless, it is constantly exposed to external factors, such as natural deterioration, anthropic impact, and climate-related hazards, which may compromise its conservation. In Italy, many archaeological areas are affected by significant soil settlements that involve a large part of monuments. This paper focuses on the landslide hazard assessment of the archaeological site of Pietrabbondante (Molise region, Italy). The impact of the expected rainfall regimes, according to the EURO-CORDEX projections, on slope stability conditions were evaluated through the application of a physically based model that couples a hydraulic and a mechanical model to evaluate slope stability evolution due to pore pressure changes. Given the unavoidable lack of knowledge of the geotechnical soil properties in an archaeological heritage area, the proposed method considered the random uncertainty of soil parameters by means of a probabilistic approach in order to assess the stability conditions in terms of probability of occurrence of a landslide. The results of this study provide a reference for the safety assessment and preventive conservation of archaeological areas characterized by high cultural value.

Convolutional neural network-based seismic fragility analysis of subway station structure considering spatial variation of site shear-wave velocity

Prior research demonstrated that the uncertainty of soil parameter can significantly impact the seismic response analysis and seismic performance evaluation of underground structures. To this end, the seismic response of a three-story, three-span subway station embedded in a typical layered engineering site was investigated in this study and the uncertainty of soil parameters was explicitly considered using the shear-wave velocity interlayer correlation model. In addition, an incremental dynamic analysis considering the uncertainty of the shear-wave velocity was performed using the one-dimensional convolutional neural network (1D-CNN) model as a surrogate model for the traditional finite element method. The results indicate that the uncertainty of soil shear-wave velocity increases the average PGA values for minor, moderate, and severe failures with a probability of exceeding 50% by about 10%, and increases the logarithmic standard deviation by about 40%. When considering the uncertainty of shear-wave velocity, the discreteness of the fragility curve will increase. Moreover, the rightward shift of the fragility curve midpoint leads to a comparatively more safety seismic performance evaluation of the structure under significant seismic input.

Optimal intensity measure selection and probabilistic seismic demand model of pile group supported bridges in sandy soil considering variable scour effects

Scour of pile group foundations is a common hazard for cross-river bridges and can produce considerable damage to piles in earthquake-prone regions. The fragility-based performance assessment for pile group supported bridges subjected to earthquake and scour hazards has drawn increasing attention from engineering practice and academic communities. Such assessment requires numerical models that are computationally efficient and accurate in describing the mechanical behavior associated with the complex soil-pile interaction of these soil-bridge systems. Additionally, selecting an optimal ground motion intensity measure (IM) is generally required for such assessments. However, modeling the pile group effect for seismically excited pile groups and the optimal IM for the scoured bridges have not been well addressed in previous related studies. To this end, a practical pile group effect modeling approach is adopted in this study and validated by a set of shake table tests on scoured pile group bridge available in the literature. Based on the validated numerical modeling approach for the soil pile interaction, a series of coupled soil-bridge models are generated considering the structural and soil parameter uncertainty and analyzed in the OpenSees platform. The optimal IM for various engineering demand parameters (EDPs) is identified from thirty-nine scalar IM candidates through the criteria of efficiency, practicality, sufficiency, and hazard computability. Finally, a straightforward form of probabilistic seismic demand model (PSDM), incorporating the effect of scour depth changes, is developed for pile group supported bridges. Results show that the increase of scour depth significantly increases the curvature demand of a pile group and statistically reduces the embedded depth of the belowground plastic hinge of the pile shaft. The rank of optimal IM candidates directly depends on the selection criteria of an optimal IM and the selection of EDP. In addition, the scour depth slightly affects the rank of optimal IMs. Generally, VSI, PGV, and Sv,1.0 are recommended for the probabilistic seismic demand analysis of pile group supported bridges in sandy soils with scour potentials.

Estimation of Uncertainties in Soil Using MCMC Simulation and Effect of Model Uncertainty

The simulation of field conditions for seismically induced slope failures incorporates model uncertainties, which account for the difference between simulated and observed slope behaviour. The quantification of this uncertainty is mandatory to understand the field response of the geotechnical system and make decisions for geotechnical systems. Previous studies have partially studied uncertainty for slope systems under seismic loading. To this aim, this study proposes a methodology based on probabilistic back analysis to estimate uncertainties in soil parameters considering the observed slope response under seismic loading. The proposed method involves support vector regression (SVR) model to map the relationship between soil parameters and seismically induced slope displacement. The SVR model is generated using the data from the numerical simulation of slope system under seismic loading using FLAC 2D. Further, the developed SVR model is used for probabilistic back analysis using Markov Chain Monte Carlo (MCMC) simulation. The Noto Hanto earthquake in 2007 and the subsequent slope failure along Noto Yuryo Road, Japan, are considered as a case study to validate the proposed methodology. The results of the case study show that the updated or inferred soil parameters have less variability than the prior distribution. Further, the uncertainties in the slope system influence the inferred soil parameters. Hence, a parametric study is conducted to investigate the effect of model uncertainty on the posterior statistics of soil parameters. The study results facilitate a better understanding of the slope deformation mechanism and the effect of model uncertainty on the updated statistics of soil parameters.

Reduce uncertainty in soil hydrological modeling: A comparison of soil hydraulic parameters generated by random sampling and pedotransfer function

Numerical simulation of unsaturated soil hydrology relies on calibrated soil hydraulic parameters, which are subject to uncertainty due to imperfect information during the inverse modelling. This study investigates the effectiveness of reducing parameter uncertainty using the recently developed Rosetta 3 pedotransfer function. The GLUE method was employed for numerical modeling using the Darcy-Richards equation under two strategies for sampling Mualem-van Genuchten (MvG) parameters: the first uses conventional random generation of MvG parameters (GLUE-random), while the second adopts Rosetta 3 to transfer soil particle composition to MvG parameter (GLUE-Rosetta). Both approaches were used for inverse modeling of 9 typical soils, each with a recommended parameter set defined as true values and associated soil moisture dynamics as observations. The posterior parameters selected with both GLUE-random and GLUE-Rosetta show an equifinality phenomenon. GLUE-random fails to provide well-constrained posterior parameters to recover the pre-defined true values, and its posterior results of soil water characteristic curve (SWCC) and soil hydraulic conductivity function (HCF) are poorly constrained. In contrast, GLUE-Rosetta significantly improves the accuracy of the inversely-estimated soil hydraulic parameters, and the ensemble of posterior SWCC and HCF also encompasses the predefined true curves. The results demonstrate the effectiveness of using Rosetta 3 to reduce the dimensionality of the optimization problem, which results in reliable estimation of soil hydraulic parameters and soil particle compositions. Moreover, GLUE-Rosetta outperforms GLUE-random in predicting soil moisture dynamics under different rainfall intensities. Overall, it is recommended to integrate Rosetta 3 with existing optimization tools to reduce the uncertainty of soil parameters and support more reliable modeling of unsaturated soil hydrology.

Effects of Uncertain Soil Parameters on Seismic Responses of Fixed Base and Base-Isolated Liquid Storage Tanks

ABSTRACT Effects of soil-structure interaction (SSI) on the seismic performance of cylindrical ground-supported liquid storage tanks are studied. The present study attempts to investigate the effects of uncertainties, associated with the critical soil parameters, on the seismic behavior of liquid storage tanks. Random multi-layered soil models coupled with the fixed base liquid storage tank are developed and analyzed. Further, the tank structure is considered base-isolated with lead rubber bearing and analyzed with the same set of soil models, to investigate the seismic behavior of base-isolated tank under uncertain soil condition. A set of three ground motions are selected from a large suite through a mean spectral matching scheme for investigating the effect of soil uncertainties on the seismic response. Distributions of the peak seismic response quantities observed herein show that the uncertainties in soil parameters critically affect the seismic responses of fixed base and base-isolated liquid storage tanks. Sloshing displacement of fixed base and base-isolated tanks is affected by both uncertainty in the soil parameters and ground motion characteristics. Nevertheless, for ground-supported tank, relatively larger dispersion or variability of base shear and overturning moment, as compared to that of the sloshing response, is observed.

A new method to select the cross-sectional shape of stabilizing piles from the perspective of design robustness

Stabilizing piles with different cross-sectional shapes, e.g., circular, rectangular, and trapezoidal, have been widely used in landslide treatment. Indeed, the selection of the cross-sectional shape of the stabilizing piles usually relies on a designer’s experience or a quantitative evaluation of the ultimate lateral resistance of the piles, considering the constant soil parameters. However, the observed uncertainties in the soil parameters may affect the estimation of the ultimate lateral resistance. Hence, a quantitative method, that considers the uncertainties in soil parameters, for the selection of the optimal cross-sectional shape for stabilizing piles based on the design robustness is developed in this study. An illustrative example is also presented to demonstrate and verify the proposed method. It is concluded that a rectangular pile has the preferred cross-sectional shape from the perspective of design robustness. The influence of the initial confining stresses, geometric parameters of the cross-section, coefficient of variation (COV) and correlation coefficients of the soil parameters on the selection of the cross-sectional shape is also further discussed. This work establishes a theoretical basis for the selection of the cross-sectional shape and provides further insights into the optimization of the stabilizing piles in landslide treatments.

Probabilistic method for the size design of energy piles considering the uncertainty in soil parameters

Energy piles have attracted increasing attention as profitable solutions for the utilization of shallow geothermal energy. Although various complex geotechnical design models of energy piles have been proposed, a simplified sizing method that considers the uncertainty propagation in the soil is required. In this study, a Monte Carlo Simulation-based method was proposed for the size design of energy piles considering the uncertainty of parameters in the soil, such as thermal conductivity and friction angle. The small-sample analysis method of Markov chain Monte Carlo simulation combined with the Bayesian theoretical framework was developed to generate equivalent samples. Subsequently, the thermal response function and thermomechanical load transfer methods were employed to address the failure probability of the energy pile in the serviceability limit state and ultimate limit state. In addition, a case study was presented to illustrate the implementation of the proposed probabilistic sizing method. The analysis results of the case study confirm the necessity of modeling the soil uncertainty in the energy pile size design.

Polynomial chaos surrogate and bayesian learning for coupled hydro-mechanical behavior of soil slope

As rainfall infiltrates into soil slopes, the hydraulic and mechanical behaviors of soils are interacted. In this study, an efficient probabilistic parameter estimation method for coupled hydro-mechanical behavior in soil slope is proposed. This method integrates the Polynomial Chaos Expansion (PCE) method, the coupled hydro-mechanical modeling, and the Bayesian learning method. A coupled hydro-mechanical numerical model is established for the simulation of behaviors of unsaturated soil slope under rainfall infiltration, following by training a cheap-to-run PCE surrogate to replace it. Probabilistic estimation of soil parameters is conducted based on the Bayesian learning technique with the Markov Chain Monte Carlo (MCMC) simulation. A numerical example of an unsaturated slope under rainfall infiltration is presented to illustrate the proposed method. The effects of measurement durations and response types on parameter estimation are addressed. The result shows that with the increase of measurement duration, the uncertainties of soil parameters are significantly reduced. The uncertainties of hydraulic properties are reduced significantly using the pore water pressure data, while the uncertainties of soil strength parameters are reduced greatly using the measured displacement data.

Application of interval field method to the stability analysis of slopes in presence of uncertainties

Spatial uncertainty of soil parameters has a significant impact on the analysis of slope stability. Interval field analysis is emerging as a complementary tool of the conventional random field method that can take spatial uncertainty into account, which, however, has not been investigated in slope stability analysis. The present paper proposes a new method, named the interval field limit equilibrium method (IFLEM), for assessing the stability of slope in the presence of the interval field. In this method, the modified exponential function is introduced to characterize the spatial uncertainty of the interval field and the Karhunen–Loève-like decomposition is employed to generate the interval field. Then, in a single calculation, the deterministic slope stability analyzed by the Morgenstern–Price approach is implemented in order to estimate the safety factor. Subsequently, the upper and lower bounds of the interval of safety factor are efficiently evaluated by a kind of surrogate-assisted global optimization algorithms, such as Bayesian global optimization used in this study. Finally, the effectiveness of the proposed method is verified by three numerical examples. The results indicate that the proposed method can provide reasonable accuracy and efficiency, which is potentially applicable to a number of geotechnical systems.

Uncertainty quantification of tunnel seismic deformations in random soils

Tunnel damages are increasing worldwide in major earthquakes, some of which may result from the underestimated seismic actions and uncertainties associated with the design parameters. Opposite to traditionally performed deterministic analysis, this paper introduces stochastic dynamic time-history analysis to quantify the variability of seismic-induced tunnel deformations in a probabilistic framework. Two-dimensional nonlinear finite difference models combined with the Monte Carlo simulation are employed to assess the influence of parameter uncertainty. Analyses are performed for a wide range of soil shear wave velocities, ground motion intensities, lining Young’s moduli, correlation structures, distribution types, and coefficients of variation. The results indicate that the parameter uncertainty can have a significant impact on tunnel seismic deformations. Increased motion intensity leads to an increased standard deviation, especially for flexible tunnels. The influence of shear strength parameters is insignificant, despite a slightly larger standard deviation appears for the positive correlation. The distribution type effect increases sharply for the cases with high variation degrees, and the lognormal distribution generally predicts a lower mean, standard deviation, and probability of exceedance. The results also show that the soil parameter uncertainty can be properly considered by introducing a factor of safety. These findings may provide a useful reference for the reliability-based seismic design of tunnels.

Probabilistic slope stability analysis of Heavy-haul freight corridor using a hybrid machine learning paradigm

With the rising freight demand, specialized heavy-haul railway corridors allow heavier trains to transport heavy freight, improving productivity and lowering unit costs. Generally, a heavy-haul corridor necessitates a significant investment, thus the risk assessment of a rail-track system must be extensively evaluated during the design phase. From the standpoint of serviceability, this study presents a probabilistic slope stability analysis of heavy-haul freight corridor using an efficient hybrid computational technique. The present approach, i.e., ANN-MPA, is an amalgamation of an artificial neural network (ANN) and marine predators algorithm (MPA). The newly constructed ANN-MPA was used to perform probabilistic analysis of a 12.293 m high embankment of heavy-haul freight corridor of Indian Railways with a design axle load of 32.5 MT. The concept of probability theory and statistics were used to map the soil uncertainties through the first-order second-moment method. The results of the proposed ANN-MPA model were evaluated and compared with other hybrid ANNs constructed with seven distinct swarm intelligence algorithms. In the validation phase, the proposed ANN-MPA outperformed (R2 = 0.9931 and RMSE = 0.0233) other hybrid ANNs and was used to perform probabilistic analysis of a 12.293 m high embankment. The reliability index and the probability of failure were computed under seismic and non-seismic conditions, taking into consideration the influence of uncertainties in soil parameters. Using the proposed approach, the failure probability of the 12.293 m high soil slope under different seismic conditions can be evaluated rationally and efficiently.

Estimating epistemic uncertainty in soil parameters for nonlinear site response analyses: Introducing the Latin Hypercube Sampling technique

This study quantifies the effects of epistemic uncertainty in soil parameters on nonlinear (NL) site response analysis (SRA) results, validated against the data recorded at a well-instrumented geotechnical downhole array located in Japan. To this end, a one-dimensional soil column model of the Service Hall Array (SHA) near the Kashiwazaki-Kariwa Nuclear Power Plant (KKNPP) is developed using the finite element (FE) program LS-DYNA. The dynamic stress–strain relationship is characterized by a modified two-stage hyperbolic (MTH) NL backbone curve formulation capable of capturing soil behavior at both small- and large-shear strains. The model is then validated against the ground motion recordings to capture the model bias. The uncertainties associated with the shear-wave velocity profile (a small-strain soil property) and soil shear strength (a large-strain soil property) are incorporated in NL SRA to quantify their separate and joint randomization effects on the results. This study proposes using the Latin Hypercube Sampling (LHS) method as an efficient alternative to commonly used methods, such as Standard Monte Carlo (SMC), to account for uncertainty propagation in such reliability analysis. Both low-intensity and design-level records from the recordings at the SHA are applied to study the contribution of the small- and large-strain NL dynamic soil properties. Results from 46,200 NL FE analyses (23,100 per input motion) are presented. Measured and predicted site response, using recorded ground motions at this downhole array, is compared to assess the significance of soil parameter uncertainty on the observed ground motion dispersions. It is demonstrated that increasing the number of soft realizations and implementing higher level earthquake intensity lead to higher ground motion dispersion. Unlike past studies in randomization of Vs profiles with the SMC method, the LHS method is shown to have no significant effect on the predicted median surface response spectra and amplification factors (AFs) for this case study.

Probabilistic back analysis for rainfall-induced slope failure using MLS-SVR and Bayesian analysis

ABSTRACT Measurement and model uncertainties in soil parameters account for the difference between slope behaviour in the field and expected behaviour. The probabilistic back analysis is an effective approach to quantify these uncertainties in soil parameters. A new methodology for probabilistic back analysis is proposed to evaluate the uncertainties in soil parameters for observed data for slope. The proposed methodology implements multi-output least square support vector regression (MLS-SVR) to replicate the numerical model for slope under precipitation. This methodology also utilises a multi-objective genetic algorithm and Bayesian analysis to estimate updated statistics of soil parameters for observed data for slope. The rainfall-induced slope failure at Malin, Pune, India, in 2014 is used as a case study to validate the proposed methodology. The mean values of soil parameters are updated using multi-objective genetic algorithm for the expected values of safety factor. The uncertainties in soil parameters are estimated using Bayesian analysis. The updated statistics of input parameters suggest that matric suction governs the slope behaviour under rainfall precipitation. The results of the study suggest that continuous updating of the observations reduces the uncertainties involved in soil parameters. It is noted that the values of safety factor calculated using updated parameters are consistent with the slope failure observed in the field. Hence, results of the study can be used for the reliability-based design of slopes and the provision of remedial measures.

Stochastic optimization model for determining support system parameters of a subway station

The process of designing the support system of a subway station using a concrete arch pre-supporting system (CAPS) construction method includes an estimation of design variables based on intuition and experience. However, this process may often lead to controversial and economically unfavorable designs. In this regard, developing an optimization model to determine design variables (support system parameters) is necessary. In this study, a stochastic optimization model is developed to determine the support system parameters of a subway station constructed using CAPS. To estimate the risk of uncertainties of the soil properties, the concept of conditional value at risk (CVaR) is used. A Python script is programmed in cooperation with a 2D Finite Element Method (FEM) software to provide the dataset. Then, the results are applied to prepare multi-layer perceptron (MLP) models, which are subsequently used as meta-models and linked to a reference-point-based non-dominated sorting genetic algorithm III (NSGA-III). It should be noted that the selection of the NSGA-III algorithm was based on comparing its performance with a few other meta-heuristic algorithms such as NSGA-II, MOPSO, and MOMBIII considering metrics such as hypervolume (HV), inverted generational distance (IGD), spread, and pure diversity (PD). Finally, all optimal solutions are ranked using the ELECTRE multi-criteria decision-making method. Various weighting scenarios for the objectives are considered to evaluate the importance of the selected design criteria. The results of the numerical modeling confirm that the proposed algorithm can provide worthwhile information for a logical decision about the support system parameters of a subway station. Thus, the outcome of this study is to achieve an appropriate and economical design by minimizing four following objectives: the risk of instability, risk of the maximum surface settlement, risk of the maximum displacement throughout the station structure, and the concreting volume. The presented algorithm could also alter the prioritization of design goals based on the project's sensitivity and the designer's judgment. On the other hand, by considering the uncertainty in soil parameters, the optimal parameters of the support system are determined more accurately in comparison with an assumption of homogenous soil. Therefore, the main contribution of this article to the design of a subway station constructed by the CAPS method is to increase the accuracy of the design of support system parameters by considering the risk of uncertainties in soil parameters, the importance of the project, and goals of the designer. In this way; the overly conservative designs in practice would be avoided.

A semi-analytical random shakedown solution for pavements with spatial variability

ABSTRACT The present paper proposes a step-by-step random shakedown solution, by considering uncertainty in soil parameters explicitly, to meet the safety requirements of road pavement systems design rationally. To this aim, theoretical-based random analysis, called Random Analytical Shakedown Analysis, is established and then validated through comparison of the obtained predictions with the known Random Mesh-free Shakedown Analysis results. It has been shown that the developed theoretical model can effectively capture the effects of soil spatial variability on the pavement shakedown behaviour in a shakedown analysis model. The difference between the deterministic shakedown limit loads obtained by the proposed method and the mesh-free model is within 2%, which shows the comparable accuracy of the suggested theoretical model with the mesh-free method which comprises hundreds of variables and constraints in the optimisation problem. Another advantage of the developed theoretical solution is the prevention of non-convergence situations occurrence in the mesh-free shakedown analysis. Accordingly, the introduced scheme can be efficiently used for rapid evaluation of the shakedown capacity of spatially-varying pavements.

Floor response spectra analysis of a nuclear reactor considering uncertainties in soil parameters

Floor response spectra of the nuclear reactor building are an important part of the seismic analysis and design of the whole reactor system. Uncertainties exist in the calculation of floor response spectra considering soil-structure interaction effect due to uncertainties in soil parameters. Stochastic models of shear wave velocity, shear modulus reduction, and damping ratio were built, and random samples were generated via Monte Carlo simulation, according to the survey data of 2 MW Thorium Molten Salt Reactor-Liquid Fuel 1 by the China Earthquake Administration. Site response analysis carried out using an equivalent linear methodology was performed to study the influence of uncertainties in different soil parameters on surface response spectra. The coefficient of variation (Cv) was calculated via generating and enveloping random samples of low strain shear modulus to count for uncertainties in soil parameters, unlike many studies which take Cv as code’s minimum requirement of 0.5 directly. Floor response spectra considering uncertainties in soil parameters were calculated by the time-domain method using Cv. The results indicate that the uncertainty of shear wave velocity has the most significant influence on the surface response spectra. Floor response spectra have increased significantly after considering uncertainties in soil parameters, and the behavior of taking Cv as 0.5 like other studies is not conservative enough to consider uncertainties in soil parameters. Soil uncertainties have not been considered thoroughly in the calculation of floor response spectra in past studies, and this paper addresses this knowledge gap via Monte Carlo simulation. The findings will be used to perform floor response spectra analysis considering uncertainties in soil parameters.

Brief Literature Review and Classification System of Reliability Methods for Evaluating the Stability of Earth Slopes

The issue of slope stability is one of the most important and yet most difficult geotechnical problems. Assessing slope stability is particularly difficult because of the many uncertainties involved in the process. To take these uncertainties into account, probabilistic methods are used, and the reliability approach is adopted. There are many methods for reliability assessment of earth slope stability. However, there is no system that would organize all of these methods in an unambiguous way. In fact, these methods can be classified in different ways: by assignment to a deterministic classification of methods, by description of uncertainties of soil parameters, by level of reliability according to the theory of reliability, etc. The huge number of articles summarizing the research in this field, but in various “disordered” directions, certainly do not facilitate the understanding or ultimately the practical application of the reliability approach by the engineer. The paper proposes a universal classification system of reliability methods for evaluating the stability of earth slopes. This proposal is preceded by a brief literature review of both historical background and contemporary research on reliability analysis of earth slope stability.

Reliability assessment method for environmental vibrations of a tunnel embedded in layered foundation

This paper proposes a reliability assessment method for environmental vibrations of a tunnel embedded in layered foundation under moving train load. Based on wave functions transformation, a vehicle-track-tunnel-soil model for evaluating system dynamic response can be established. Then combined with the Monte Carlo simulation, the reliability assessment of environmental vibrations is realized. The effect of soil parameter uncertainty on the prediction result of environmental vibrations is analyzed via case studies. The results show that the predictions from the deterministic model tend to be conservative, which is less than the superior limit of 95% confidence interval of the uncertainty model predicted outcome. The soil parameter uncertainty has less influence on the distribution of system dynamic response, which mainly affects the system dynamic response amplitude.