Bearing capacity of strip and circular footings in sand using finite elements

Design of shallow foundations relies on bearing capacity values calculated using procedures that are based in part on solutions obtained using the method of characteristics, which assumes a soil following an associated flow rule. In this paper, we use the finite element method to determine the vertical bearing capacity of strip and circular footings resting on a sand layer. Analyses were performed using an elastic–perfectly plastic Mohr–Coulomb constitutive model. To investigate the effect of dilatancy angle on the footing bearing capacity, two series of analyses were performed, one using an associated flow rule and one using a non-associated flow rule. The study focuses on the values of the bearing capacity factors N_q and N_γ and of the shape factors s_q and s_γ for circular footings. Relationships for these factors that are valid for realistic pairs of friction angle and dilatancy angle values are also proposed.     

Empirical modeling of plate load test moduli of soil via gene expression programming

New empirical models were developed to predict the soil deformation moduli using gene expression programming (GEP). The principal soil deformation parameters formulated were secant (E_s) and reloading (E_r) moduli. The proposed models relate E_s and E_r obtained from plate load-settlement curves to the basic soil physical properties. The best GEP models were selected after developing and controlling several models with different combinations of the influencing parameters. The experimental database used for developing the models was established upon a series of plate load tests conducted on different soil types at depths of 1–24 m. To verify the applicability of the derived models, they were employed to estimate the soil moduli of a part of test results that were not included in the analysis. The external validation of the models was further verified using several statistical criteria recommended by researchers. A sensitivity analysis was carried out to determine the contributions of the parameters affecting E_s and E_r. The proposed models give precise estimates of the soil deformation moduli. The E_s prediction model provides considerably better results in comparison with the model developed for E_r. The simplified formulation for E_s significantly outperforms the empirical equations found in the literature. The derived models can reliably be employed for pre-design purposes.     

Predicting standard penetration test N-value from cone penetration test data using artificial neural networks

Standard Penetration Test(SPT) and Cone Penetration Test(CPT) are the most frequently used field tests to estimate soil parameters for geotechnical analysis and design.Numerous soil parameters are related to the SPT N-value.In contrast,CPT is becoming more popular for site investigation and geotechnical design.Correlation of CPT data with SPT N-value is very beneficial since most of the field parameters are related to SPT N-values.A back-propagation artificial neural network(ANN) model was developed to predict the N6o-value from CPT data.Data used in this study consisted of 109 CPT-SPT pairs for sand,sandy silt,and silty sand soils.The ANN model input variables are:CPT tip resistance(q_c),effective vertical stress(σ'_v),and CPT sleeve friction(f_s).A different set of SPT-CPT data was used to check the reliability of the developed ANN model.It was shown that ANN model either under-predicted the N_(60)-value by 7-16%or over-predicted it by 7-20%.It is concluded that back-propagation neural networks is a good tool to predict N_(60)-value from CPT data with acceptable accuracy.     

Modelling of the effect of scale on the compressibility parameters of fine-grained soils

ABSTRACT

The effect of sample scale represents a challenge when obtaining engineering parameters in the laboratory compared to those obtained in the field. This study aimed at contributing to existing knowledge numerically using the finite element software PLAXIS 2D. The investigations were analysed in terms of height scale (HS) and diameter scale (DS) through a series of laboratory tests. Its effect on compressibility parameters such as coefficient of consolidation (c_v) was noted experimentally and showed that the sample scale greatly influences soil parameters most particularly at DS. The soil behaviour was found to be dependent on both DS and HS with a correlation factor of 0.650 and 0.062, respectively. The experimental data were validated in PLAXIS and a new proposed model was developed in PLAXIS 2D under the DS. The new proposed model developed was found to show no significant difference with the laboratory data.     

Lanthanide-humic substances complexation. I. Experimental evidence for a lanthanide contraction effect

The interaction of the lanthanides (Ln) with humic substances (HS) was investigated with a novel chemical speciation tool, Capillary Electrophoresis-Inductively Coupled Plasma Mass Spectrometry (CE-ICP-MS). By using an EDTA-ligand competition method, a bi-modal species distribution of LnEDTA and LnHS is attained, separated by CE, and detected online by sector field ICP-MS. We quantified the binding of all 14 rare earth elements (REEs), Sc and Y with Suwannee river fulvic acid, Leonardite coal humic acid, and Elliot soil humic acid under environmental conditions (pH 6-9, 0.001-0.1 mol L⁻¹ NaNO₃, 1-1000 nmol L⁻¹ Ln, 10-20 mg L⁻¹ HS). Conditional binding constants for REE-HS interaction (K_c) ranged from 8.9 < log K_c < 16.5 under all experimental conditions, and display a lanthanide contraction effect, Δ_LK_c: a gradual increase in K_c from La to Lu by 2-3 orders of magnitude as a function of decreasing ionic radius. HS polyelectrolyte effects cause K_c to increase with increasing pH and decreasing ionic strength. Δ_LK_c increases significantly with increasing pH, and likely with decreasing ionic strength. Based on a strong correlation between Δ_LK_c values and denticity for organic acids, we suggest that HS form a range of tri- to tetra-dentate complexes under environmental conditions. These results confirm HS to be a strong complexing agent for Ln, and show rigorous experimental evidence for potential REE fractionation by HS complexation.     

Pull-out behaviour of steel grid soil reinforcement embedded in silty sand

This paper investigates the pull-out behaviour (particularly the bearing resistance) of a steel grid reinforcement embedded in silty sand using laboratory tests and numerical analyses. It is demonstrated that the various common analytical equations for calculating the bearing component of pull-out resistance give a wide range of calculated values, up to about 200% disparity. The disparity will increase further if the issue of whether to use the peak or critical state friction angle is brought in. Furthermore, these equations suggest that the bearing resistance factor, N_q, is only a function of soil friction angle which is not consistent with some design guidelines. In this investigation, a series of large scale laboratory pull-out tests under different test pressures were conducted. The test results unambiguously confirmed that the N_q factor is a function of test pressure. A modified equation for calculating N_q is also proposed. To have more in-depth understanding of the pull-out behaviour, the tests were modelled numerically. The input parameters for the numerical analysis were obtained from laboratory triaxial tests. The analysis results were compared with the experimental results. Good agreement between experimental and numerical results was achieved if the strain-softening behaviour from peak strength to critical state condition was captured by the soil model used.     

Geosynthetic-reinforced and jet grout column-supported embankments on soft soils: Numerical analysis and parametric study

Using a computer code based on the finite element method, a study is conducted to analyse the time-dependent behaviour of a geosynthetic-reinforced and jet grout column-supported embankment on soft soils, as well as the influence of three factors: the embankment height, the elastic modulus of column and the column spacing. The cylindrical unit cell formulation is used. The numerical model incorporates the Biot consolidation theory with soil constitutive relations simulated by the p–q–θ critical state model. Special emphasis is given to the analysis of several parameters: settlement, excess pore pressure, effective stress, stress level, tension in the geosynthetic, soil arching effect and overall efficiency coefficient.     

Improving a thermal conductivity model of unsaturated soils based on multivariate distribution analysis

Soil thermal conductivity (k) is a key parameter for the design of energy geo-structures, and it depends on many soil properties such as saturation degree, porosity, mineralogical composition, soil type and others. Capturing these diversified influencing factors in a soil thermal conductivity model is a challenging task for engineers due to the nonlinear dependencies. In this study, a multivariate distribution approach was utilized to improve an existing soil thermal conductivity model, Cote and Konrad model, by quantitatively considering the impacts of dry density (ρ_d), porosity (n), saturation degree (S_r), quartz content (m_q), sand content (m_s) and clay content (m_c) on thermal conductivity of unsaturated soils. A large database containing these seven soil parameters was compiled from the literature to support the multivariate analysis. Simplified bivariate and multivariate correlations for improving the Cote and Konrad model were derived analytically and numerically to consider different influencing factors. By incorporating these simplified correlations, the predicted k values were more concentrated around the measured values with the coefficient of determination (R²) increased from 0.83 to 0.95. It is concluded that the developed correlations with the information of different soil properties provide an efficient, rational and simple way to predict soil thermal conductivity more accurately. Moreover, the quartz content is a more important factor than the porosity that shall be considered in the establishment of thermal conductivity models for unsaturated soils with high quartz content.

     

Numerical analysis under seismic loads of soils improvement with floating stone columns

Geotechnical Engineering has developed many methods for soil improvement so far. One of these methods is the stone column method. The structure of a stone column generally refers to partial change of suitable subsurface ground through a vertical column, poor stone layers which are completely pressed. In general terms, to improve bearing capacity of problematic soft and loose soil is implemented for the resolution of many problems such as consolidation and grounding problems, to ensure filling and splitting slope stability and liquefaction that results from a dynamic load such as earthquake. In this study, stone columns method is preferred as an improvement method, and especially load transfer mechanisms and bearing capacity of floating stone column are focused. The soil model, 32 m in width and 8 m in depth, used in this study is made through Plaxis 2D finite element program. The clay having 5° internal friction angle with different cohesion coefficients (c 10, c 15, c 20 kN/m²) are used in models. In addition, stone columns used for soil improvement are modeled at different internal friction angles (? 35°, ? 40°, ? 45°) and in different s/D ranges (s/D 2, s/D 3), stone column depths (B, 2B, 3B) and diameters (D 600 mm, D 800 mm, D 1000 mm). In the study, maximum acceleration (a _max = 1.785 m/s²) was used in order to determine the seismic coefficient used. In these soil models, as maximum acceleration, maximum east–west directional acceleration value of Van Muradiye earthquake that took place in October 23, 2011 was used. As a result, it was determined that the stone column increased the bearing capacity of the soil. In addition, it is observed that the bearing capacity of soft clay soil which has been improved through stone column with both static and earthquake load effect increases as a result of increase in the diameter and depth of the stone column and decreases as a result of the increase in the ranges of stone column. In the conducted study, the bearing capacity of the soil models, which were improved with stone column without earthquake force effect, was calculated as 1.01–3.5 times more on the average, compared to the bearing capacity of the soil models without stone column. On the other hand, the bearing capacity of the soil models with stone columns, which are under the effect of earthquake force, was calculated as 1.02–3.7 times more compared to the bearing capacity of the soil models without stone column.     

A Novel Methodology to Classify Soil Liquefaction Using Deep Learning

In this research, deep learning (DL) model is proposed to classify the soil reliability for liquefaction. The applicability of the DL model is tested in comparison with emotional backpropagation neural network (EmBP). The database encompassing cone penetration test of Chi–Chi earthquake. This study uses cone resistance (q_c) and peck ground acceleration as inputs for prediction of liquefaction susceptibility of soil. The performance of developed models has been assessed by using various parameters (receiver operating characteristic, sensitivity, specificity, Phi correlation coefficient, Precision–Recall F measure). The performance of DL is excellent. Consistent results obtained from the proposed deep learning model, compared to the EmBP, indicate the robustness of the methodology used in this study. In addition, both the developed model was also tested on global earthquake data. During validation on global data, both the models shows good results based on fitness parameters. The developed classification models a simple, but also efficient decision-making tool in engineering design to quantitatively assess the liquefaction potential. The finding of this paper can be further used to capture the relationship between soil and earthquake parameters.

     

Intelligent modelling of clay compressibility using hybrid meta-heuristic and machine learning algorithms

Compression index Ccis an essential parameter in geotechnical design for which the effectiveness of correlation is still a challenge.This paper suggests a novel modelling approach using machine learning(ML)technique.The performance of five commonly used machine learning(ML)algorithms,i.e.back-propagation neural network(BPNN),extreme learning machine(ELM),support vector machine(SVM),random forest(RF)and evolutionary polynomial regression(EPR)in predicting Cc is comprehensively investigated.A database with a total number of 311 datasets including three input variables,i.e.initial void ratio e0,liquid limit water content wL,plasticity index Ip,and one output variable Cc is first established.Genetic algorithm(GA)is used to optimize the hyper-parameters in five ML algorithms,and the average prediction error for the 10-fold cross-validation(CV)sets is set as thefitness function in the GA for enhancing the robustness of ML models.The results indicate that ML models outperform empirical prediction formulations with lower prediction error.RF yields the lowest error followed by BPNN,ELM,EPR and SVM.If the ranges of input variables in the database are large enough,BPNN and RF models are recommended to predict Cc.Furthermore,if the distribution of input variables is continuous,RF model is the best one.Otherwise,EPR model is recommended if the ranges of input variables are small.The predicted correlations between input and output variables using five ML models show great agreement with the physical explanation.     

Application of statistical learning algorithms to ultimate bearing capacity of shallow foundation on cohesionless soil

This study employs two statistical learning algorithms (Support Vector Machine (SVM) and Relevance Vector Machine (RVM)) for the determination of ultimate bearing capacity (q_u) of shallow foundation on cohesionless soil. SVM is firmly based on the theory of statistical learning, uses regression technique by introducing varepsilon‐insensitive loss function. RVM is based on a Bayesian formulation of a linear model with an appropriate prior that results in a sparse representation. It also gives variance of predicted data. The inputs of models are width of footing (B), depth of footing (D), footing geometry (L/B), unit weight of sand (γ) and angle of shearing resistance (?). Equations have been developed for the determination of q_u of shallow foundation on cohesionless soil based on the SVM and RVM models. Sensitivity analysis has also been carried out to determine the effect of each input parameter. This study shows that the developed SVM and RVM are robust models for the prediction of q_u of shallow foundation on cohesionless soil. Copyright © 2010 John Wiley & Sons, Ltd.     

A case study on the behaviour of a deep excavation in sand

A complete case record of an excavation in sand is explored in this study. Numerical analyses were conducted to evaluate the influences of soil elasticity, creep and soil–wall interface. Back-analyses indicate small strain parameters should be used if an elastic–perfect plastic model is selected. In addition, excavation-induced seepage has only a limited effect on vertical displacements. Delayed installation of 3rd level struts and base slab construction caused significant time-dependent (creep) movements during the excavation. Back-analyses show that the dynamic viscosity (D_v) used in the visco-elastic model for creep simulation is in the range of 1.5 × 10¹⁵–2.0 × 10¹⁵ Pa, but there are still inconsistencies in movements both near to and far from the excavation. Interpreting from observation data, the creep rate of wall movement caused in the non-supported stage of the excavation varies between 0.14 and 0.38 mm/day. Finally, parametric studies of interface elements indicate that the most sensitive parameters are the normal (K_n) and shear stiffness (K_s) of the interface. Back-analyses using an elastic–perfect plastic model indicate that using 3 × 10⁶ Pa for K_n and K_s produces more acceptable results.     

Bearing capacity of foundations on slopes

By applying the lower bound finite element limit analysis in conjunction with non-linear optimisation, the bearing capacity factors, N_c, N_q and N_γ, due to the components of cohesion, surcharge and unit weight, respectively, have been estimated for a horizontal strip footing placed along a sloping ground surface. The variation of N_c, N_q and N_γ with changes in slope angle (β) for different soil friction angle (φ) have been computed for smooth as well as rough strip footings. The analysis reveals that along a sloping ground surface, in addition to N_γ, the factors N_c and N_q also vary considerably with changes in footing roughness. Compared to the smooth footing, the extent of the plastic zone around the footing becomes greater for the rough footing. The results obtained from the analysis are found to compare well with those previously reported in literature.     

Piles shaft capacity from CPT and CPTu data by polynomial neural networks and genetic algorithms

Cone penetration test (CPT) is one of the most common in situ tests which is used for pile design because it can be realized as a model pile. The measured cone resistance (q_c) and sleeve friction (f_s) usually are employed for estimation of pile unit toe and shaft resistances, respectively. Thirty three pile case histories have been compiled including static loading tests performed in uplift, or in push with separation of shaft and toe resistances at sites which comprise CPT or CPTu sounding. Group method of data handling (GMDH) type neural networks optimized using genetic algorithms (GAs) are used to model the effects of effective cone point resistance (q_E) and cone sleeve friction (f_s) as input parameters on pile unit shaft resistance, applying some experimentally obtained training and test data. Sensitivity analysis of the obtained model has been carried out to study the influence of input parameters on model output. Some graphs have been derived from sensitivity analysis to estimate pile unit shaft resistance based on q_E and f_s. The performance of the proposed method has been compared with the other CPT and CPTu direct methods and referenced to measured piles shaft capacity. The results demonstrate that appreciable improvement in prediction of pile shaft capacity has been achieved.     

Soil geochemical parameters influencing the spatial distribution of anthrax in Northwest Minnesota,USA

Bacillus anthracis is the pathogenic bacterium that causes anthrax, which dwells in soils as highly resilient endospores. B. anthracis spore viability in soil is dependent upon environmental conditions, but the soil properties necessary for spore survival are unclear. In this study we used a range of soil geochemical and physical parameters to predict the spatial distribution of B. anthracis in northwest Minnesota, where 64 cases of anthrax in livestock were reported from 2000 to 2013. Two modeling approaches at different spatial scales were used to identify the soil conditions most correlated to known anthrax cases using both statewide and locally collected soil data. Ecological niche models were constructed using the Maximum Entropy (Maxent) approach and included 11 soil parameters as environmental inputs and recorded anthrax cases as known presences. One ecological niche model used soil data and anthrax presences for the entire state while a second model used locally sampled soil data (n = 125) and a subset of anthrax presences, providing a test of spatial scale. In addition, simple logistic regression models using the localized soil data served as an independent measure of variable importance. Maxent model results indicate that at a statewide level, soil calcium and magnesium concentrations, soil pH, and sand content are the most important properties for predicting soil suitability for B. anthracis while at the local level, clay and sand content along with phosphorous and strontium concentrations are most important. These results also show that the spatial scale of analysis is important when considering soil parameters most important for B. anthracis spores. For example, at a broad scale, B. anthracis spores may require Ca-rich soils and an alkaline pH, but may also concentrate in microenvironments with high Sr concentrations. The study is also one of the first ecological niche models that demonstrates the major importance of soil texture for defining the ecological niche of B. anthracis. These results will help improve our understanding of the soil geochemical conditions most suitable for B. anthracis as well as more reliably identify areas where anthrax may be found to focus prevention and remediation efforts.     

A hybrid computational approach to formulate soil deformation moduli obtained from PLT

In this study, new empirical equations were developed to predict the soil deformation moduli utilizing a hybrid method coupling genetic programming and simulated annealing, called GP/SA. The proposed models relate secant (E_s), unloading (E_u) and reloading (E_r) moduli obtained from plate load–settlement curves to the basic soil physical properties. Several models with different combinations of the influencing parameters were developed and checked to select the best GP/SA models. The database used for developing the models was established upon a series of plate load tests (PLT) conducted on different soil types at various depths. The validity of the models was tested using parts of the test results that were not included in the analysis. The validation of the models was further verified using several statistical criteria. A traditional GP analysis was performed to benchmark the GP/SA models. The contributions of the parameters affecting E_s, E_u and E_r were analyzed through a sensitivity analysis. The proposed models are able to estimate the soil deformation moduli with an acceptable degree of accuracy. The E_s prediction model has a remarkably better performance than the models developed for predicting E_u and E_r. The simplified formulations for E_s, E_u and E_r provide significantly better results than the GP-based models and empirical models found in the literature.     

Determination of the conditional interaction constant between colloidal technetium(IV) and Gorleben humic substances

Varying pertechnetate (Tc(VII)) doses were reduced to Tc(IV) in the presence and absence of Gorleben humic substances with the aid of magnetite, a reducing Fe(II)-containing surface. In absence of humic substances dissolved Tc(IV) concentrations are over-saturated with respect to the known TcO₂ · nH₂O solubility and increase with increasing Tc(VII) dose due to the formation of a range of mononuclear to colloidal Tc(IV) species. In presence of dissolved humic substances, the Tc solubility is enhanced due to the additional interaction of dissolved Tc(IV) species with humic substances. Both in the absence and the presence of dissolved humic substances a sorption mechanism controls the distribution of the range of mononuclear to colloidal Tc(IV) species between the solid and the liquid phase. The proposed reaction mechanism between Tc(IV) and HS is represented by Σ[TcO(OH)₂]_n+HS = [TcO(OH)₂]_n − HS in which Σ[TcO(OH)₂]_n stands for the sum of monomeric and polynuclear (colloidal) Tc(IV) species present in the equilibrium solution. A log K-value of 2.9 (±0.3) was quantified from a modified Schubert approach which is based on the competition of HS and magnetite for all dissolved Tc(IV) species and was found independent of Tc–HS loading, Tc–magnetite loading and pH.     

Estimation of Pullout Capacity of Vertical Plate Anchors in Cohesionless Soil Using MARS

Vertical plate anchors provide an economical solution to safely resist the large horizontal forces experienced by the foundation of different structures such as bulkheads, sheet piles, retaining walls and so forth. This paper develops a multivariate adaptive regression spline (MARS) model-based approach for the determination of horizontal pullout capacity (P _u ) of vertical plate anchors buried in cohesionless soil by utilizing experimental results reported by different researchers. Based on the collection of forty different pullout experimental test results reported in the literature for anchors buried in loose to dense cohesionless soil with an embedment ratio ranges from 1 to 5, a predictive approach for P _u of vertical plate anchors has been developed in terms of non-dimensional pullout coefficient (M _γq ). The capability of the proposed MARS model for estimating the values of M _γq is examined by comparing the results obtained in the present study with those methods available in the literature. Using different statistical error measure criteria, this study indicates that the present approach is efficient in estimating the horizontal pullout capacity of vertical plate anchors as compared to other methods. The sensitivity analysis indicates that the embedment ratio (H/h, where H = embedment depth of anchor, and h = height of anchor) and internal friction angle (?) of soil mass are the two most important parameters for the evaluation of non-dimensional pullout coefficient (M _γq ) using the proposed MARS model.     

Experimental and theoretical investigation on the compression behavior of sand-marine clay mixtures within homogenization framework

In this paper, the compression behavior of sand-marine clay mixtures was investigated, both experimentally and theoretically. The test data reveal that the Normal Compression Line of a sand-clay mixture depends on both the sand fraction and the initial water content of the clay matrix. The local stress in the clay matrix σ′_c is approximately close to the overall stress of the sand-clay mixture σ′ for a sand mass fraction of 20%. The stress ratio, σ′_c/σ′, falls significantly with increasing overall stress for a sand fraction of 60%, which may be attributed to the formation of clay bridges between adjacent sand particles. A compression model was formulated within the homogenization framework. First, a homogenization equation was proposed, which gives a relationship between the overall stiffness E and that of the clay matrix Ec. Then, a model parameter ξ was incorporated considering the sensitivity of the structure parameter on the volume fraction of the clay matrix. Finally, a simple compression model with three model parameters was formulated using the tangent stiffness. Comparisons between the experimental data and simulations reveal that the proposed model can well represent the compression curves of the sand-marine clay mixtures observed in the laboratory.