New design equations for estimation of ultimate bearing capacity of shallow foundations resting on rock masses

Rock masses are commonly used as the underlying layer of important structures such as bridges, dams and transportation constructions. The success of a foundation design for such structures mainly depends on the accuracy of estimating the bearing capacity of rock beneath them. Several traditional numerical approaches are proposed for the estimation of the bearing capacity of foundations resting on rock masses to avoid performing elaborate and expensive experimental studies. Despite this fact, there still exists a serious need to develop more robust predictive models. This paper proposes new nonlinear prediction models for the ultimate bearing capacity of shallow foundations resting on non-fractured rock masses using a novel evolutionary computational approach, called linear genetic programming. A comprehensive set of rock socket, centrifuge rock socket, plate load and large-scaled footing load test results is used to develop the models. In order to verify the validity of the models, the sensitivity analysis is conducted and discussed. The results indicate that the proposed models accurately characterize the bearing capacity of shallow foundations. The correlation coefficients between the experimental and predicted bearing capacity values are equal to 0.95 and 0.96 for the best LGP models. Moreover, the derived models reach a notably better prediction performance than the traditional equations.

Numerical Analysis and Centrifuge Modeling of Shallow Foundations

The influence of non-coaxial constitutive model on predictions of dense sand behavior is investigated in this paper. The non-coaxial model with strain softening plasticity is applied into finite-element program ABAQUS, which is first used to predict the stress-strain behavior and the non-coaxial characteristic between the orientations of the principal stress and principal plastic strain rate in simple shear tests. The model is also used to predict load settlement responses and bearing capacity factors of shallow foundations. A series of centrifuge tests for shallow foundations on saturated dense sand are performed under drained conditions and the test results are compared with the corresponding numerical results. Various footing dimensions, depths of embedment, and footing shapes are considered in these tests. In view of the load settlement relationships, the stiffness of the load-displacement curves is significantly affected by the non-coaxial model compared with those predicted by the coaxial model, and a lower value of non-coaxial modulus gives a softer response. Considering the soil behavior at failure, the coaxial model predictions of bearing capacity factors are more advanced than those of centrifuge test results and the non-coaxial model results;besides, the non-coaxial model gives better predictions. The non-coaxial model predictions are closer to those of the centrifuge results when a proper non-coaxial plastic modulus is chosen.

Assessing foundation behaviour under complex loading near tunnels

The stability of strip footings subjected to eccentrically inclined loads is critical for reliable foundation design.This study investigates the effect of a circular unlined tunnel in a rock mass on the ultimate bearing capacity(UBC)of a foundation with width B under inclined and eccentric loads.Adaptive finite element limit analysis was employed to evaluate the reduction in UBC of the footing resting above a tunnel.The examined critical parameters include normalized load eccentricity(e/B),load inclination(β),and horizontal and vertical distances of the tunnel from the foundation(P/B and Q/B,respectively),along with rock mass properties.The results reveal that for e/B≥0.25 and β≤60°,the reduction coefficient,R_(c)≥0.90,suggesting that the presence of a tunnel has a minimal impact on the load-bearing capacity of the footing,with failure primarily governed by load eccentricity and inclination.Additionally,potential failure mechanisms are explored,showing that at lower e/B,higher β,and lower Q/B,the tunnel significantly affects footing's failure envelope.Conversely,at higher e/B and lower β,failure is due to rotational effects of footing,regardless of the tunnel's position.To predict the Rc more accurately,due to the time-consuming nature of direct calculations,both MLR and ANN models were developed.The MLR model provided a baseline for comparison,while the ANN model,with a coefficient of determination(R2)of 0.98,demonstrated superior accuracy compared to the R2=0.96 of MLR.Using both approaches ensured robust and efficient predictions of Rc.Since Rc does not directly provide the reduced UBC of footing due to presence of tunnel,the study introduced bearing capacity factor(Nc)to enable direct calculation of the reduced UBC of footing.These findings offer theoretical guidelines for preliminary design and provide practitioners with an effective tool for evaluating UBC reduction in complex loading scenarios involving tunnels.

Shallow foundation response variability due to soil and model parameter uncertainty

Geotechnical uncertainties may play crucial role in response prediction of a structure with substantial soil-foundation-structure-interaction （SFSI） effects. Since the behavior of a soil-foundation system may significantly alter the response of the structure supported by it, and consequently several design decisions, it is extremely important to identify and characterize the relevant parameters. Moreover, the modeling approach and the parameters required for the modeling are also critically important for the response prediction. The present work intends to investigate the effect of soil and model parameter uncertainty on the response of shallow foundation-structure systems resting on dry dense sand. The SFSI is modeled using a beam-on-nonlinear-winkler-foundation （BNWF） concept, where soil beneath the foundation is assumed to be an assembly of discrete, nonlinear elements composed of springs, dashpots and gap elements. The sensitivity of both soil and model input parameters on shallow foundation responses are investigated using first-order second-moment （FOSM） analysis and Monte Carlo simulation through Latin hypercube sampling technique. It has been observed that the degree of accuracy in predicting the responses of the shallow foundation is highly sensitive soil parameters, such as friction angle, Poisson＇s ratio and shear modulus, rather than model parameters, such as stiffness intensity ratio and spring spacing; indicating the importance of proper characterization of soil parameters for reliable soil- foundation response analysis.

Elastoplastic numerical analysis of layered soil foundation under the rectangular shallow footing subjected to vertical load

Finite and infinite coupled element method was used to analyze the strength and deformation in layered soil foundation which was under the rectangular shallow footing subjected to vertical loads. In the numerical analysis, the footing was assumed to be elastic; the soil was assumed to be elastoplastic and the Drucker-Prager constitutive model was applied to describe its mechanic behavior. Corresponding program was employed to compute six kinds of layered soil foundations constituted by different soil layers. The conclusions which are useful in the theory and practice were made according to the analysis of the computation results.

Numerical Analysis of the Interaction between Shallow （Square, Circular and Strip） Foundations and Subsoil

In this paper, the effects of the stiffness of circular, square and strip foundation structures and bonding effects were analyzed. Presented analysis was oriented on the influence of stiffness system ＂foundation--subsoil＂ and bonds （bi-directional bond and one-directional bond with and without friction）. The results of numerical calculations have proved that the relative stiffness of system ＂foundation--subsoil＂ affect considerably the value and the distribution of contact stresses （vertical normal and shear stresses） in the foundation gap and value of the displacements （settlement, deflection and relative deformations） of foundation. From the numerical point of view, this problem was solved by deformation variant of the FEM （finite element method）. The numerically obtained results were presented in the graphical and tabular forms. Obtained results were qualitative and quantitative compared with one another. From the calculation results it is obvious that relative stiffness of the system ＂foundation structure--subsoil＂ substantially affects distribution of contact stresses in the foundation subsoil and displacements （settlement, deflection and relative deformations, flexibility） of foundation. In the case of flexible foundations, the bond on the contact surfaces must be considered during the calculation. On the other hand, the effects of friction on the contact surface between the foundation and subsoil affect the distribution of contact stresses and deformations only to smaller extent.

Reliability Analysis for Retaining Pile in Foundation Pit Based on Bayesian Principle

Moso bamboo has the advantages of high short-term strength and reproducibility,appropriating for temporary supporting structure of shallow foundation pit.According to the displacement of the pile top from an indoor model test,the reliability of the supporting effect of the moso bamboo pile was analyzed.First,the calculation formula of reliability index was deduced based on themean-value first-order second-moment(MVFOSM)method and probability theory under ultimate limit state and serviceability limit state.Then,the dimensionless bias factor(the ratio of the measured value to the calculated value)was introduced to normalize the displacement.The mathematical characteristics of the displacement were estimated and optimized based on Bayesian theory.Finally,taking 2.5 as the design reliability index,the effect of safety factor,tolerable limit displacement,and the ratio of the ultimate limit displacement to the tolerable on reliability index was analyzed.The results show that the safety level of the supporting pile can be increased by 1–2 levels when the safety factor increases by 0.5.When the coefficient of variation of tolerable limit displacement is less than 0.3,the safety factor can be 2–2.5.And the ratio of the ultimate limit displacement to the tolerable has a great influence on the reliability index,when the soil conditions is well,the ratio can be 1.2–1.3.

Spatially variable soils affecting geotechnical strip foundation design

Natural soil variability is a well-known issue in geotechnical design,although not frequently managed in practice.When subsoil must be characterized in terms of mechanical properties for infrastructure design,random finite element method(RFEM)can be effectively adopted for shallow foundation design to gain a twofold purpose:(1)understanding how much the bearing capacity is affected by the spatial variability structure of soils,and(2)optimisation of the foundation dimension(i.e.width B).The present study focuses on calculating the bearing capacity of shallow foundations by RFEM in terms of undrained and drained conditions.The spatial variability structure of soil is characterized by the autocorrelation function and the scale of fluctuation(δ).The latter has been derived by geostatistical tools such as the ordinary Kriging(OK)approach based on 182 cone penetration tests(CPTs)performed in the alluvial plain in Bologna Province,Italy.Results show that the increase of the B/δratio not only reduces the bearing capacity uncertainty but also increases its mean value under drained conditions.Conversely,under the undrained condition,the autocorrelation function strongly affects the mean values of bearing capacity.Therefore,the authors advise caution when selecting the autocorrelation function model for describing the soil spatial variability structure and point out that undrained conditions are more affected by soil variability compared to the drained ones.

Bearing capacity of surface circular footings on granular material under low gravity fields

Low gravity fields have been simulated through magnetic acceleration to conduct experimental study on bearing capacity of circular footings on a type of crushable planetary regolith simulant,which has comparable density and particle size distribution of lunar soil.The loadesettlement responses of surface spread footings are obtained by investigating the relative density,footing size and gravity effects.Applying the hyperbolic asymptote method,normalised foundation stiffness and ultimate bearing capacity are obtained by curve fitting and predicted by power functions using multivariate nonlinear regression.The results show that the nonlinear gravity effect is not negligible,related to stress condition,soil dilatancy and mobilised friction angle.A cone penetration test(CPT)-based method for prediction of bearing capacity is proposed with correlations between ultimate bearing capacity of footings and shallow penetration stiffness of CPTs,avoiding the uncertainties of soil property estimations.Analyses of allowable bearing capacity and footing influence zone in consideration of footing size and gravity effects could therefore improve the design of shallow foundations on the Moon and Mars,and provide new understandings and potential implications to the bearing capacity of shallow foundations on crushable granular material in both terrestrial and extraterrestrial geotechnical engineering.

Slip-line field solution for ultimate bearing capacity of a pipeline on clayey soils

A slip-line field solution is presented for the ultimate bearing capacity of the pipeline on a purely-cohesive clay soil, taking into account the circular configuration of the pipe, the pipe embedment, and the pipe-soil interfacial cohesion. The derived bearing capacity factors for a smooth rigid pipe limit to those for the conventional rectangular strip footing while the pipe embedment approaches zero. Parametric studies indicate that, the pipe-soil interfacial properties have much influence on the bearing capacity for the pipe foundation on clayedy soils.

A Refined Formula for the Allowable Soil Pressure Using Shear Wave Velocities

Based on a variety of case histories of site investigations, including extensive bore hole data, laboratory testing and geophysical prospecting at more than 550 construction sites, an empirical formulation is proposed for the rapid determination of allowable bearing pressure of shallow foundations in soils and rocks. The proposed expression corroborates consistently with the results of the classical theory and is proven to be rapid, and reliable. Plate load tests have been also carried out at three different sites, in order to further confirm the validity of the proposed method. It consists of only two soil parameters, namely, the in situ measured shear wave velocity and the unit weight. The unit weight may be also determined with sufficient accuracy, by means of other empirical expressions proposed, using P or S -- wave velocities. It is indicated that once the shear and P-wave velocities are measured in situ by an appropriate geophysical survey, the allowable bearing pressure as well as the coefficient of subgrade reaction and many other elasticity parameters may be determined rapidly and reliably.

Assessment of glass fiber-reinforced polyester pipe powder in soil improvement

This study investigates the use of glass fiber-reinforced polyester(GRP)pipe powder(PP)for improving the bearing capacity of sandy soils.After a series of direct share tests,the optimum PP addition for improving the bearing capacity of soils was found to be 12%.Then,using the optimum PP addition,the bearing capacity of the soil was estimated through a series of loading tests on a shallow foundation model placed in a test box.The bearing capacity of sandy soil was improved by up to 30.7%.The ratio of the depth of the PP-reinforced soil to the diameter of the foundation model(H/D)of 1.25 could sufficiently strengthen sandy soil when the optimum PP ratio was used.Microstructural analyses showed that the increase in the bearing capacity can be attributed to the chopped fibers in the PP and their multiaxial distribution in the soil.Besides improving the engineering properties of soils,using PP as an additive in soils would reduce the accumulation of the industrial waste,thus providing a twofold benefit.