Cohesive Soils Research Articles

Root hairs: an underexplored target for sustainable cereal crop production.

To meet the demands of a rising human population, plant breeders will need to develop improved crop varieties that maximize yield in the face of increasing pressure on crop production. Historically, the optimization of crop root architecture has represented a challenging breeding target due to the inaccessibility of the root systems. Root hairs, single cell projections from the root epidermis, are perhaps the most overlooked component of root architecture traits. Root hairs play a central role in facilitating water, nutrient uptake, and soil cohesion. Current root hair architectures may be suboptimal under future agricultural production regimes, coupled with an increasingly variable climate. Here, we review the genetic control of root hair development in the world's three most important crops-rice, maize, and wheat-and highlight conservation of gene function between monocots and the model dicot species Arabidopsis. Advances in genomic techniques including gene editing combined with traditional plant breeding methods have the potential to overcome many inherent issues associated with the design of improved root hair architectures. Ultimately, this will enable detailed characterization of the effects of contrasting root hair morphology strategies on crop yield and resilience, and the development of new varieties better adapted to deliver future food security.

A neural network approach for the reliability analysis on failure of shallow foundations on cohesive soils

A collection of feed forward neural networks (FNN) for estimating the limit pressure load and the according displacements at limit state of a footing settlement is presented. The training procedure is through supervised learning with error loss function the mean squared error norm. The input dataset is originated from Monte Carlo simulations for a variety of loadings and stochastic uncertainty of the material of the clayey soil domain. The material yield function is the Modified Cam Clay model. The accuracy of the FNN’s is in terms of relative error no more than 10-5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^{-5}$$\\end{document} and this applies to all output variables. Furthermore, the epochs of the training of the FNN’s required for construction are found to be small in amount, in the order of magnitude of 90,000, leading to an alleviated data cost and computational expense. The input uncertainty of Karhunen Loeve random field sum appears to provide the most detrimental values for the displacement field of the soil domain. The most unfavorable situation for the displacement field result to limit displacements in the order of magnitude of 0.05 m, that may result to structural collapse if they appear to the founded structure. These series can provide an easy and reliable estimation for the failure of shallow foundation and therefore it can be a useful implement for geotechnical engineering analysis and design.

Effect of shear rate and saturation on shear strength of mineral and anthropogenic soil

The aim of the study was to determine the shear strength of mineral and anthropogenic soil of similar grain size as a function of the applied shear rate and water saturation. Stability calculations using the finite element method of the road embankment model were also carried out to demonstrate the variation in factor of safety values depending on the adopted values of the angle of internal friction and cohesion. The tests were carried out in a direct shear apparatus in a 100 x 100 mm box with a sample height of 20.5 mm. The samples were formed directly in the apparatus box at optimum moisture content until a compaction index of IS = 1.00 was obtained. Tests were carried out under conditions without and with water saturation at shear rates of 0.01, 0.05, 0.1, 0.5 and 1.0 mm•min–1 until 18% horizontal displacement was achieved. The results showed that the effect of shear rate on the strength parameters was not unequivocal and was much smaller than the changes caused by saturation of samples. An increase in shear rate resulted in small changes in the angle of internal friction with a tendency towards a decrease. In contrast, cohesion varied over a much larger range with increasing shear rate, with an apparent initial decrease and subsequent increase. The saturation of the samples resulted in a decrease in the angle of internal friction of the cohesive soil and an increase for the ash-slag mixture. The cohesion of both soils decreased. The results obtained from the road embankment model stability calculations confirmed that soil saturation had a greater influence on the factor of safety values obtained than the shear rate.

Amelioration of High-plasticity Cohesive Soils Using Ground Granulated Blast Furnace Slag for Low-volume Pavement Applications

Amelioration of High-plasticity Cohesive Soils Using Ground Granulated Blast Furnace Slag for Low-volume Pavement Applications

The effectiveness of data pre-processing methods on the performance of machine learning techniques using RF, SVR, Cubist and SGB: a study on undrained shear strength prediction

In the field of data engineering in machine learning (ML), a crucial component is the process of scaling, normalization, and standardization. This process involves transforming data to make it more compatible with modeling techniques. In particular, this transformation is essential to ensure the suitability of the data for subsequent analysis. Despite the application of many conventional and relatively new approaches to ML, there remains a conspicuous lack of research, particularly in the geotechnical discipline. In this study, ML-based prediction models (i.e., RF, SVR, Cubist, and SGB) were developed to estimate the undrained shear strength (UDSS) of cohesive soil from the perspective of a wide range of data-scaling and transformation methods. Therefore, this work presents a novel ML framework based on data engineering approaches and the Cubist regression method to predict the UDSS of cohesive soil. A dataset including six different features and one target variable were used for building prediction models. The performance of ML models was examined considering the impact of the data pre-processing issue. For that purpose, data scaling and transformation methods, namely Range, Z-Score, Log Transformation, Box-Cox, and Yeo-Johnson, were used to generate the models. The results were then systematically compared using different sampling ratios to understand how model performance varies as various data scaling/transformation methods and ML algorithms were combined. It was observed that data transformation or data sampling methods had considerable or limited effects on the UDSS model performance depending on the algorithm type and the sampling ratio. Compared to RF, SVR, and SGB models, Cubist models provided higher performance metrics after applying the data pre-processing steps. The Box-Cox transformed Cubist model yielded the best prediction performance among the other models with an R2 of 0.87 for the 90% training set. Also, the UDSS prediction model generally yielded the best performance metrics when it was used with the transformed-based models (i.e., Box-Cox, Log, and Yeo-Johnson) than that of scaled-based (i.e., Range and Z-Score) models. The results show that the Cubist model has a higher potential for UDSS prediction, and data pre-processing methods have impacts on the predictive capacity of the evaluated regression models.

Performance of industrial fly ash based stabilized mine haul roads under seasonal moisture changes

Mine haul roads play an important role in the mining industry. They are often designed as unsealed roads, which are frequently damaged due to seasonal moisture variation, especially when the subgrade soil is expansive clay. In this study, the performance of mine haul roads built on expansive clay soil is investigated for seasonal moisture variation using experimental and numerical investigations. Shrinkage, swelling, soil water characteristics curve (SWCC) tests, and direct shear testing were first performed to assess the hydraulic and shear performance of the control and municipal solid waste incineration (MSWI) fly ash-treated soils. The swelling reduced from 1.95 to 1.02, while the shrinkage reduced from 3.4% to 1.84% after the addition of 20% MSWI fly ash. SWCC results showed that the MSWI fly ash addition reduces the void spaces and increases residual saturation. The consolidation settlement reduced by 50% after adding 20% MSWI fly ash. The cohesion of both soil and MSWI fly ash-treated samples exhibited a bell-shaped trend with moisture increase, in contrast to friction angles which decreased with increasing saturation levels. 3D numerical models were used to predict the performance of control soil and MSWI stabilized mining haul roads using the experimental test data. The control pavement experienced increased settlement and rutting as saturation levels increased. The behaviour of the stabilized pavement differed, with the model having a 20% degree of saturation showing the least deformation due to increased stiffness from high suction. Overall, this study highlights the benefits of MSWI fly ash-based soil stabilization in improving the performance of mine haul roads under seasonal moisture changes. The findings emphasize the importance of considering the degree of saturation and stabilization techniques in pavement design to mitigate settlement and enhance overall performance.

The three-dimensional stability analysis of piled slopes in unsaturated and inhomogeneous soils with nonlinear failure criterion

Under the nonlinear Mohr-Coulomb (MC) failure criterion, based on the upper-bound limit analysis theorem, the three-dimensional(3D) stability of piled unsaturated inhomogeneous slopes is analyzed. By incorporating the nonlinear strength parameters c t and φ t, the energy balance equation is established, and the explicit expression of slope safety factor (F S) is derived by the gravity increase method (GIM). In addition, a genetic algorithm (GA) is used to calculate the minimum F S. The results obtained were compared with those of existing literature to verify the effectiveness of the method used in this paper. The influence of nonlinear parameters on slope stability was studied through parameter analysis. The results show that the nonlinear parameters of soil have a significant influence on the stability of piled slopes. The F S increases with the increase of nonlinear coefficient and uniaxial tensile strength and decreases with the increase of initial cohesion of soil. In addition, the critical slip surface of the slope becomes shallower with the weakening of soil nonlinearity. Furthermore, ignoring the suction effect will overestimate the slope stability, and the slope stability intensified with decreased soil inhomogeneity.

The effect of different degree of compaction towards electrical resistivity value for cohesive soil

The effect of different degree of compaction towards electrical resistivity value for cohesive soil

Exploring alkali-source, pore-filling and cementation damage effects in cemented clay with typical industrial waste binders

Various industrial waste binders (IWBs) are being recycled in soil stabilization to save cement consumption. However, the coupled effects brought out by combined IWBs on stabilized soils are still unclear. IWBs are categorized into two typical categories (IWB-A and IWB-B) referring to their chemical role in this study. The alkali-source effect, pore-filling effect and cementation damage effect by IWBs in soil stabilization are explored. A series of mechanical and microscopic tests is performed on stabilized clay with different proportions of IWB-A and IWB-B. Moreover, initial water contents and cement contents of cement-stabilized clay are varied to examine the evolution of coupled effect with void ratio and cementation level. The results indicate that the alkali-source effect strengthens the cementation bonds and increases the early strength by 0.5–1.3 times, whereas the pore-filling effect improves the microfabric especially for the specimen with a large void ratio. The alkali-source effect increases soil cohesion cu at the pre-yield stage, and the pore-filling effect increases frictional angle φu at the post-yield stage. The cementation damage effect is remarkable at a low void ratio, which may result in many extruded pores among soil aggregates. The strength evolution with IWB proportions can be well stimulated by considering the coupled alkali-source effect, pore-filling effect and cementation damage effect. The optimal proportion of IWBs corresponds to an optimal combination of coupled effect.

Numerical Approach to Appreciate the Interaction of Two Neighbouring Shallow Foundation on a Cohesive and Partially Cohesive Soil

The program (cast3m) produced for us tables of values of stresses, displacements, images characterising stresses, displacements and deformations with their corresponding graphs. The results were presented as part of this study. It has been found that: two shallow closed foundations seriously affect the soil between them regardless of the soil type. Then, when the foundation is at same level in the different soil type and stress values are extracted in the zone of the cohesive soil (soft clay). A horizontal separation to width of foundation ratio was 0.7 and an influence equation was 0.333 if values of stresses are extracted from the partially cohesive soil (sandy clay). As per the vertical variation of the foundation in the different soil type. Independent of the soil type and the depth variation, a vertical separation to width of foundation ratio of 0.333 was observed. As the cohesion increases, the soil becomes denser which account for the high limit compressive stress compared to inferior values of cohesion. Finally, it is seen as a result of this research that the type of soil has a great rule to play as far as the interaction between two foundations is concern. An interaction led to failure when the foundation had a vertical gap between it that did not meet the above equation.

Utilizing undisturbed soil sampling approach to predict elastic modulus of cohesive soils: a Gaussian process regression model

Utilizing undisturbed soil sampling approach to predict elastic modulus of cohesive soils: a Gaussian process regression model

Lateral load-carrying mechanism of driven battered minipiles

The lateral load-carrying mechanism of vertically installed and battered minipiles is evaluated using 1g-physical and numerical modelling. Single minipiles with batter angles of 0°, ± 25° and ± 45° are tested under lateral load in medium dense and dense sand. The minipiles are instrumented with fibre Bragg grated optic fibres to obtain a strain profile (two-dimensional) along the minipile shaft. A calibrated numerical model is further adopted to produce p–y curves for battered minipiles at various node deflections. The ratio of soil reaction of battered minipiles to vertically installed minipiles is observed to change with both deflection and depth of the minipile. An analytical solution is developed based on the decomposition of lateral load into skin friction and passive pressure for battered minipiles. A reduction factor is proposed that considers a decrease in passive pressure when the minipile is loaded in the opposite direction of the batter. The analytical solution is capable of accounting for soil properties, pile rigidity and the angle of inclination of battered minipiles. The analytical method is subsequently verified for cohesive soils using full-scale field results. The ratio of the ultimate lateral load of battered minipiles to vertical minipiles presented in the literature corroborated the findings of this study.

The impacts of cover crop mixes on the penetration resistance model of an Oxisol under no-tillage

Soil penetration resistance is used as an indicator of mechanical resistance to root growth into the soil matrix. However, penetration resistance measured only under wet soil conditions may not identify the effects of cover crops on soil structure. We aimed to determine the impact of individual and mixes of cover crops on soil penetration resistance as a function of water content and bulk density in an Oxisol under no-tillage in southern Brazil. Six treatments of individual and mixed cover crops were tested: (i) black oat; (ii) ryegrass; (iii) forage radish; (iv) wheat; (v) Fibrous-rooted crop mix: with 80 % fibrous-rooted and 20 % tap-rooted plants; and (vi) Tap-rooted crop mix: 40 % fibrous-rooted and 60 % tap-rooted plants. Soil cores were collected from a depth of 0–0.10 and 0.10–0.20 m and soil penetration resistance was evaluated under four soil water matric potentials (−6, −33, −100, and −500 kPa). Soil penetration resistance (Q) data for each treatment were fitted as a function of bulk density (ρ) and water content (θ) [Q=f(ρ, θ)]. The soil penetration resistance model was a non-linear equation (i.e., a double power function, with a negative exponent for water content and a positive exponent for bulk density). Under a given combination of bulk density and water content values, soil penetration resistance was higher after single crops than crop mixes, indicating a crop-mediated soil strengthening process. The cover crop mixes increased the macroporosity, resulting in an adequate soil physical quality for successional crops such as soybean, although no differences were observed for cover crops at soil water matric potentials of −60 hPa and −330 hPa when soil penetration resistance was used as a static measurement. The modelling of the soil resistance to penetration, as a function of soil bulk density and soil water content, showed that cover crops changed soil cohesion and reduced the impact of drying on soil strength when compared to the single cropping systems, indicating that soil penetration resistance should be modelled under a broad range of water contents, instead of only under a specific soil water content, to quantify the impacts of cover crops on soil strength.

Numerical Investigation of Seismic Behaviour for a Flexible Cantilever Retaining Wall with Cohesive Backfill

In the seismic design of flexible cantilever walls retaining cohesive backfill soil, the common practice is to neglect the cohesion effect. Dynamic lateral earth pressure is typically evaluated based on approaches primarily intended for cohesionless soils or through analytical pseudo-static methods. Nevertheless, both experimental and theoretical evidence has demonstrated significant effects due to soil cohesion that are not accounted for by these methods. This study involved finite element modeling (FE) of a flexible cantilever wall with a height of 5.4m, supporting homogeneous cohesive backfill under initial static and seismic loadings. The calculated active earth thrust was then compared with values obtained experimentally and through conventional analytical methods. The obtained results indicate that the presence of soil cohesion significantly reduces seismic demands on flexible cantilever retaining walls, resulting in a substantial reduction of seismic active earth pressures and total seismic thrust by up to 50% and 52%, respectively. It enhances also the overall stability of the system by shifting the point of application of seismic thrust toward the base of the wall, thereby increasing the safety margin. In addition, it significantly decreases the wall displacement at the stem top, with reductions of up to 104% compared with the case involving cohesionless backfill. It was observed that the conventional methods recommended by some seismic regulations largely underestimate seismic active pressure.

Predictive models for treated clayey soils using waste powdered glass and expanded polystyrene beads using regression analysis and artificial neural network

Waste materials contribute to a wide range of environmental and economic problems. To minimize their effects, a safe strategy for reducing such negative impact is required. Recycling and reusing waste materials have proved to be effective measures in this respect. In this study, an eco-friendly treatment is investigated based on using waste powdered glass (WGP) and EPS beads (EPSb) as mechanical and chemical admixers in soils. For this purpose, Atterberg limit, standard proctor, free swell, and unconfined compression tests are performed on soil samples with different ratios of waste materials at their optimum moisture contents. The obtained test results indicate that adding WGP to cohesive soils increases the unconfined compressive strength (UCS) and reduces free swell (FS). In contrast, using EPSb reduces both FS and UCS of the treated soil samples. An optimum combination of both waste materials is determined for the improvement of the properties of high plasticity clay used in this study. Furthermore, multiple linear regression (MLR) and artificial neural network (ANN) methods are used to predict the FS and UCS of the clayey soils based on the data obtained here and the experimental test results reported in the literature. Once the FS and UCS values of untreated soil and additive percentages are defined as independent variables, both methods are shown to predict the FS and UCS values of the treated soil samples on a satisfactory level with the coefficient of correlation (R2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${R}^{2}$$\\end{document}) values greater than 0.926. Additionally, when only the index properties (liquid limit, plastic limit, and plasticity index) of the soil samples with waste materials are used as dependent variables, the R2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${R}^{2}$$\\end{document} values obtained by the ANN method are 0.968 and 0.974 for FS and UCS, respectively. The results of the untreated soil samples' FS and UCS tests are known, and the linear regression and ANN techniques yield similar results. Lastly, the ANN method is used to predict the FS and UCS of the treated samples in accordance to the limited predictors (e.g., only the Atterberg limits of the soil sample).

Development of Z number-based fuzzy inference system to predict bearing capacity of circular foundations

Precise bearing capacity prediction of circular foundations is essential in civil engineering design and construction. The bearing capacity is affected by factors such as depth, density of soil, internal angle of friction, cohesion of soil, and foundation radius. In this paper, an innovative perspective on a fuzzy inference system (FIS) was proposed to predict bearing capacity. The uncertainty of fuzzy rules is eliminated by using Z-number theory. The effective parameters, i.e., depth, density of soil, internal angle of friction, cohesion of soil, and foundation radius were considered as inputs to the proposed model. To compare regression and FIS model with Z-based FIS, statistical indices such as the coefficient of determination (R2), root mean square error (RMSE), and variance account for (VAF) were employed. For training and testing Z-FIS, the R2 was (0.977 and 0.971), the RMSE was (1.645 and 1.745), and the VAF was (98.549% and 98.138), whereas for the FIS method, the values were (0.912 and 0.904), (5.962 and 6.76), and (90.12% and 88.49%). It should be mentioned that Z theory decreased the computational time by 89.28% (174.04 s to 18.65 s). The comparison of the statistical indicators of the presented models revealed the superiority of the Z-FIS model over the FIS. Notably, sensitivity analysis revealed that the most effective parameters on bearing capacity are internal angle of friction, depth, and soil density.

РІЗНІ ПРАКТИКИ ОЦІНЮВАННЯ МІЦНОСТІ ШАРІВ ҐРУНТОВОЇ ОСНОВИ І ДИСПЕРСНИХ МАТЕРІАЛІВ ЗА РЕЗУЛЬТАТАМИ ДИНАМІЧНОГО ВИПРОБУВАННЯ КОНУСНИМ ПЕНЕТРОМЕТРОМ

Introduction. The introduction to the paper highlights the methods of standard geotechnical tests for in situ measurements of subgrade strength or strength estimation. Problem statement. The issue of the paper concerns the interpretation and the application of the results of testing of the subgrades or granular layers of a road pavement by the dynamic cone penetrometer. Purpose. The goal of the paper consists of the analysis of practices of the subgrade strength evaluation by the conversion of the dynamic cone penetration test (DCPT) results to the nominal values of the California bearing ratio (CBR) or by plotting the subgrade profile and also of practices for the layer thickness evaluation and compaction control. Results. The main principles of DCPT were reviewed with performing the analysis of factors affecting the test results. The equations of the dependence of the nominal CBR values on the penetration index as the main result of DCPT was analyzed. The assumption was made that the difference in such equations may be determined by the differed confinement conditions under testing in accordance with which the calculated values provided by the results of testing under the triaxial confinement are higher. Also the stair-stepping effect appeared when performing DCPT on cohesive soils was reviewed.

A case study on soil slope landslide failure and parameter analysis of influencing factors for safety factor based on strength reduction method and orthogonal experimental design.

In civil engineering, stability analysis of slope is one of the main content of design. By using the finite element limit analysis software OptumG2, a landslide geological model is established to simulate the failure process of the landslide in Huadu District, Guangzhou City, China. The analysis focused on the deformation and failure characteristics, as well as the mechanical mechanism of landslide; the landslide mode of homogeneous soil is circular sliding. Additionally, investigating the influencing factors affecting slope stability is crucial in engineering implementation; in which the five influencing factors are considered as follow: slope height, slope gradient, soil cohesion, soil internal friction angle, and soil unit weight, respectively. A stability calculation model for a soil slope is established under 25 working conditions based on strength reduction method and orthogonal experimental design, in which the relationship between the safety factor and slope height, slope gradient, soil cohesion, soil internal friction angle, and soil unit weight is obtained. As the slope height increases from 5m to 45m, the safety factor of soil slope gradually decreases from 2.21 to 0.94; As the slope gradient increases from 20° to 60°, the safety factor of soil slope decreases approximately linearly from 1.80 to 0.95; As the cohesion of soil increases from 10kpa to 30kpa, the safety factor of soil slope increases approximately linearly from 1.04 to 1.60; As the internal friction angle of soil increases from 10° to 30°, the safety factor of soil slope increases approximately linearly from 1.00 to 1.81; As the unit weight of soil increases from 13kN/m3 to 21kN/m3, the safety factor of soil slope decreases approximately linearly from 1.50 to 1.21. The influencing factors affecting the safety factor of soil slope in descending order are slope height, slope angle, soil internal friction angle, soil cohesion, and soil unit weight. The research has reference significance for studying the stability and failure laws of soil slopes and conducting landslide control on soil slopes.

METHOD OF ACCOUNTING SOIL-AGROCHEMICAL POTENTIAL FOR OPTIMIZING THE STRUCTURE OF LAND USE OF THE VOLOZHINSK DISTRICT OF THE REPUBLIC OF BELARUS

The article discusses one of the ways to assess the condition of soil cover to improve the efficiency of land management using the example of the Volozhin region of the Republic of Belarus. A comprehensive assessment of the agrochemical and natural potential of the soil is proposed by means of typing the soil cover depending on agrochemical indicators (pHKCl, humus content, mobile compounds of phosphorus and potassium) and a quality score reflecting the natural state of the soil. Using geostatistical methods, the values of agrochemical indicators were interpolated from elementary areas into areas of soil varieties of agricultural lands and classified according to the degree of content of agrochemical elements that made up the agrochemical potential (AP). After crossing the AP with the bonitet score, 9 groups of soils were identified according to soil-agrochemical potential (SAP), of which the largest share (58,2 %) is occupied by soils with average potential (61,950 ha). Based on the results of a spatial assessment of the PAP, it was determined that sod-podzolic and sod-podzolic swampy soils developing on light loams and cohesive sandy loams have the greatest potential. It was also revealed that areas with low PAP gravitate towards the most dissected areas of the terrain with sandy and cohesive sandy soils. Based on the typification carried out, the main types of preferred land use in the Volozhin region were determined: more than half of the agricultural land can be used for intensive agricultural use for arable land (52,1 %) and meadows (12,5 %), traditional land use is possible for 29,3 % territories and only 6,2 % of lands require the use of soil protection farming systems, primarily focused on erosion-hazardous areas of the area.

Seismic analysis of a soil-liquid tank system using the two-step method

Seismic analysis of soil-structure interaction (SSI) is a challenge due to the non-linearities of soil-foundation interaction (SFI). The reliability of the design and the analysis results will suffer if SSI is ignored. In this paper, a two-step method based on the superposition theorem is used to perform a seismic analysis of a soil-foundation-tank-liquid system (soil-liquid tank system). The SFI analysis was conducted in the first step using the CyclicTP program's finite-element method. Meanwhile, the liquid tank system was analyzed in the second step using the lumped-parameter method. Numerical simulations conducted in homogeneous strata of sand soil demonstrated that the responses of the liquid tank were 24–70% higher than the results of the fixed-base model. Compared to the sway-rocking model, these responses did not differ by 20%. This study also investigated cohesive soils of homogeneous clays and multiple strata. The paper recommends that future research investigate the experimentation, the geometric nonlinearity of the soil-foundation system, and the stress-strain analysis of the tank wall