Settlement Of Footings Research Articles

Development of Two Novel Hybrid Prediction Models Estimating Ultimate Bearing Capacity of the Shallow Circular Footing

In the present work, we employed artificial neural network (ANN) that is optimized with two hybrid models, namely imperialist competition algorithm (ICA) as well as particle swarm optimization (PSO) in the case of the problem of bearing capacity of shallow circular footing systems. Many types of research have shown that ANNs are valuable techniques for estimating the bearing capacity of the soils. However, most ANN training models have some drawbacks. This study aimed to focus on the application of two well-known hybrid ICA–ANN and PSO–ANN models to the estimation of bearing capacity of the circular footing lied in layered soils. In order to provide the training and testing datasets for the predictive network models, extensive finite element (FE) modelling (a database includes 2810 training datasets and 703 testing datasets) are performed on 16 soil layer sets (weaker soil rested on stronger soil and vice versa). Note that all the independent variables of ICA and PSO algorithms are optimized utilizing a trial and error method. The input includes upper layer thickness/foundation width (h/B) ratio, footing width (B), top and bottom soil layer properties (e.g., six of the most critical soil characteristics), vertical settlement of circular footing (s), where the output was taken ultimate bearing capacity of the circular footing (Fult). Based on coefficient of determination (R2) and Root Mean Square Error (RMSE), amounts of (0.979, 0.076) and (0.984, 0.066) predicted for training dataset and amounts of (0.978, 0.075) and (0.983, 0.066) indicated in the case of the testing dataset of proposed PSO–ANN and ICA–ANN models of prediction network, respectively. It demonstrates a higher reliability of the presented PSO–ANN model for predicting ultimate bearing capacity of circular footing located on double sandy layer soils.

Implementation of Fuzzy Reliability Analysis for Elastic Settlement of Strip Footing on Sand Considering Spatial Variability

AbstractThis paper deals with the reliability analysis for the elastic settlement of the surface strip footing resting on cohesionless soil using the concept of fuzzy set theory in conjunction with...

Centrifuge model study on settlement of strip footing subject to rising water table in loess

Owing to man-made activities and natural conditions, the groundwater table experiences considerable changes in Lanzhou. Centrifugal model tests were performed to investigate the settlement of strip footings on loess subject to rising water table under different foundation pressures. The air-fall method was employed to reconstitute the artificial loess samples. The applicability of the air-fall prepared samples was evaluated against the parameters of the undisturbed loess samples obtained from the same location. The results of centrifuge tests reveal that the footing settlement increases significantly with increasing foundation loading pressure or increasing rising water table. However, the rate of increase in ultimate footing settlement under combined rising water level and footing pressure is established to be more intriguing. A simplified method for predicting the ultimate footing settlement on collapsible loess due to rising water table height is proposed. The proposed formulation is verified, as there is a good agreement between the test results under various loading pressures and rising water heights and the predicted ultimate footing settlements. A discussion on the ultimate settlement of strip footings subjected to rising water table against conventional bearing capacity safety factors is presented to provide some basis for the foundation design consideration under rising water scenario.

Bearing capacity and settlement of shallow footings on liquefiable soil subjected to seismic loading

In liquefying soils, Shallow foundations may experience a reduction in bearing capacity and increase in settlement and tilt due to seismic loading. Therefore, the buildings on shallow footings may settle and tilt excessively. In this paper, the bearing capacity and settlement of shallow foundation on liquefiable deposits has studied. The study includes a shaking table test, reviewing of theoretical equations (available in literature), which estimating settlement of shallow footings due to seismic loading, calibration, and verification of these equations with data from the shaking table test for improved soil by grouting and unimproved soil. It is important to note that the grouting materials used in this study are the CKD and Bentonite slurries. A modification to the seismic bearing capacity and settlement equations had been done to account for the liquefaction state. Good convergence has been gotten between predicted and measured settlement.

Stochastic analysis of foundation immediate settlement on heterogeneous spatially random soil considering mechanical anisotropy

The study presents a probabilistic immediate settlement analysis of shallow foundations resting on an anisotropic soil layer of spatially random properties. To this end, a rigid foundation of quite negligible slippage has been considered. Stochastic finite element method along with the numerous Monte Carlo simulations is implemented to explore the potential influence of mechanical anisotropy on the elastic settlement of a single spread footing. The analysis is also performed for the differential undrained settlement response of a pair of shallow foundations. Exploiting variable stochastic properties for the soil elastic modulus, including covariance, scale of fluctuation and cross-anisotropy ratios, several realizations of the respective soil stiffness measure are adopted, leading to the consequential corresponding realizations of the shallow foundation settlement. The results of the numerical simulations show that the increase in the elastic modulus anisotropy ratios leads to a dramatic reduction in the induced foundation settlement. Furthermore, it was observed that with the increase in the auto-correlation distance for the soil elastic modulus, the discrepancies between the evaluated settlements using deterministic and stochastic analyses grow more phenomenal. The computed settlements of the footings, considering the substantial effect of soil anisotropy, are also observed to be greater when a stochastic analysis is employed.

Effect of geocell-reinforced sand base on bearing capacity of twin circular footings

The presence of a rigid layer underlying a soil bed layer supporting twin footings affects the footing bearing capacity and settlement. In this study, the bearing capacity and settlement of twin large-scale circular footings on unreinforced and geocell-reinforced sand layers with various thicknesses are investigated. The role of layer thickness, distance between two adjacent footings, and footing diameter indicates that the rigid base substantially influences the footing bearing pressure, settlement and tilt. The results show that the maximum bearing capacity is achieved when two footings are in contact and the rigid base is at shallow depth. The influence of the footing interference on settlement and tilting of closely spaced footings at a given load decreases with decreasing depth of rigid base and reinforcing the sand with geocells. This is observed for rigid bases located at less than about 2B, where B is the footing diameter.

Settlement of deep footings in reconstituted sand

The paper examines methods for predicting the settlement of deep footings in reconstituted sand. Results from vertical load tests on deep circular plates within a laboratory pressure chamber are interpreted using data from triaxial tests, cone penetration tests (CPTs), and pressuremeter tests obtained for the same reconstituted sand. A simple nonlinear CPT-based relationship is shown to match the response observed in the plate tests and be consistent with finite element analyses as well as other comparable physical tests. The relationships between foundation stiffness and the sand’s small-strain stiffness, its stiffness at 50% mobilized strength, and its response to pressuremeter loading are also explored. Comparisons with full-scale tests in the field reveal a strong effect of ageing on foundation stiffness, which appears to be better captured by small-strain stiffness than CPT end resistance. Measurements confirm that vertical loading of a deep plate is analogous to the expansion of a spherical cavity.

Long-Term Behavior of a Geosynthetic Reinforced Soil Integrated Bridge System in Hawaii

A 109.5-Ft-long Geosynthetic Reinforced Soil Integrated Bridge System (GRS-IBS) in Hawaii was instrumented to measure superstructure strains, vertical pressures below the footing, lateral pressures behind the end wall and modular block facing, and lateral displacements of the facing. Field surveys were also performed to measure the bridge footing settlement. The field data showed that: (1) with time the superstructure compressive concrete strains gradually increased and the end wall lateral pressures gradually decreased, evidence of superstructure concrete creep and shrinkage; (2) three years after construction, the total footing settlement was ≈ 1.2 in.; and (3) the bridge superstructure undergoes daily and seasonal thermal expansion and contraction cycles. Also seasonally, the vertical pressures beneath the footing, lateral pressures behind the end walls, and superstructure strains fluctuate cyclically. The vertical footing pressure closest to the stream experienced the greatest daily pressure fluctuation (≈ 2500−3000 psf), while the one nearest the end wall experienced the least. Based on the results of cyclic triaxial tests on a basalt aggregate similar to the GRS backfill to estimate permanent deformation of the abutment due to daily pressure fluctuations, it was estimated that the permanent strain ≈ 1%, comparable to what was observed in the bridge footing. After three years, the total settlement is about 1.6% of the GRS abutment height; ≈ 0.7% of this is due to the structure dead weight and the remaining 0.9% is due to cyclic loading, consistent with the 1% cyclic strain from laboratory permanent deformation tests.

Footing settlement formula based on multi-variable regression analyses

The formulas offered so far on the settlement of raft footings provide only a rough estimate of the actual settlement. One of the best ways to make an accurate estimation is to conduct 3-dimensional finite element analyses. However, the required procedure for these analyses is comparatively cumbersome and expensive and needs a bit more expertise. In order to address this issue, in this study, a raft footing settlement formula was developed based on ninety finite element model configurations. The formula was derived using multi-parameter exponential regression analyses. The settlement formula incorporates the dimensions and the elastic modulus of a rectangular raft, vertical uniform pressure and soil moduli and Poisson\'s ratios up to 5 layers. In addition to this, an equation was offered for the estimation of average deflection of the raft. The proposed formula was checked against 3 well-documented case studies. The formula that is derived from 3D finite element analyses is useful in optimising the raft properties.

Reliability Analysis of Differential Settlement of Strip Footings by Stochastic Response Surface Method

The differential settlement of structures which are founded on soil is occurred due to heterogeneity of the soil, and it would not be beneficial to the serviceability of the structures. The heterogeneity of the soil can be implemented by qualified probabilistic analysis. This paper studies the reliability of differential settlement between two strip footings by stochastic finite element method (SFEM). For this purpose, stochastic response surface method (SRSM) as a non-intrusive formulation of SFEM is used. The linear-elastic model is used to represent the soil behavior. The Young’s modulus (E) is considered as spatially random variable and modeled as lognormal random field. The well-known Karhunen–Loeve expansion is used for discretization of the random field. The results of proposed SRSM are compared with those of the Monte Carlo simulation. The results show that the horizontal and vertical autocorrelation lengths are important parameters in reliability analysis of differential settlement. Furthermore, the probability of failure increases with increasing the coefficient of variation of Young’s modulus.

Load-settlement response of shallow square footings on geogrid-reinforced sand under cyclic loading

To study the settlement and dynamic response characteristics of shallow square footings on geogrid-reinforced sand under cyclic loading, 7 sets of large scale laboratory tests are performed on a 0.5 m wide square footing resting on unreinforced and geogrid reinforced sand contained in a 3 m × 1.6 m × 2 m (length × width × height) steel tank. Different reinforcing schemes are considered in the tests: one layer of reinforcement at the depth of 0.3B, 0.6B and 0.9B, where B is the width of the footing; two and three layers of reinforcement at the depth and spacing both at 0.3B. In one of the two double layered reinforcing systems, the reinforcements are wrapped around at the ends. The footings are loaded to 160 kPa under static loading before applying cyclic loading. The cyclic loadings are applied at 40 kPa amplitude increments. Each loading stage lasts for 10 min at the frequency of 2 Hz, or until failure, whichever occurs first. The settlement of the footing, strain in the reinforcement and acceleration rate in the soil have been monitored during the tests. The results showed that the ultimate bearing capacity of the footings was affected by the number and layout of the reinforcements, and the increment of bearing capacity does not always increase with the number of reinforcement layers. The layout of the reinforcement layers affected the failure mechanisms of the footings. Including more layers of reinforcement could greatly reduce the dynamic response of the foundations under cyclic loading. In terms of bearing capacity improvement, including one layer of reinforcement at the depth of 0.6B was the optimum based on the test results. It is found that fracture of geogrid could occur under cyclic loading if the reinforcement is too shallow, i.e. for the cases with the first layer of reinforcement at 0.3B depth.

Reinforcement Effect on the Static Analysis of Circular Footing Resting over Winkler Elastic Foundation

This paper pertains to the development of a lumped parameter model for predicting the flexural response of a circular footing resting on an engineered reinforced soil bed. The bed is constructed by placing a smooth circular geo-mat over the natural loose sand deposit on which a compacted sand fill is placed. The dense and the loose sand strata are idealized with Winkler springs of different stiffness values. Considering the problem to be axi-symmetric the resulting governing differential equations have been derived and solved for appropriate boundary and continuity conditions by using finite difference technique. Effects of the different parameters like the ratio of flexural rigidity and the dimensions of the footing and the reinforcing element, the ratio of stiffness of the upper and the lower sand layers, and the placement depth of the reinforcement on the settlement and flexural response of the footing have been presented.

Settlement of Shallow Foundations on Cohesionless Soils Based on SPT Value Using Multi-Objective Feature Selection

Accurate prediction of settlement for shallow footings on cohesionless soil is a complex geotechnical problem due to large uncertainties associated with soil. Prediction of the settlement of shallow footings on cohesionless soil is based on in situ tests as it is difficult to find out the properties of soil in the laboratory and standard penetration test (SPT) is the most often used in situ test. In data driven modelling, it is very difficult to choose the optimal input parameters, which will govern the model efficiency along with a better generalization. Feature subset selection involves minimization of both prediction error and the number of features, which are in general mutual conflicting objectives. In this study, a multi-objective optimization technique is used, where a non-dominated sorting genetic algorithm (NSGA II) is combined with a learning algorithm (neural network) to develop a prediction model based on SPT data based on the Pareto optimal front. Pareto optimal front gives the user freedom to choose a model in terms of accuracy and model complexity. It is also shown how NSGA II can be effectively applied to select the optimal parameters and besides minimizing the error rate. The developed model is compared with existing models in terms of different statistical criteria and found to be more efficient.

Immediate Settlement of Ring Footings Resting on Inhomogeneous Finite Stratum

This paper describes the immediate settlement of uniformly loaded rough ring footings with any stiffness on an inhomogeneous finite layer overlying a rough rigid base, which is not yet covered in the literature. Numerical solutions for a wide range of geometric and material combinations are obtained by finite element method. The effects of dimensionless parameters related to footing internal opening, compressibility, footing stiffness, finite layer thickness and soil inhomogeneity are examined. Based on the results, design charts are presented in the form of settlement influence factors that can be used to calculate the immediate settlements at the inner and outer points of ring footings.

The use of skirts to improve the performance of a footing in sand

This paper investigates the use of skirts to improve the bearing capacity and to reduce the settlement of a circular footing resting on dune sand. The skirts are fixed to the perimeter of the footings. A series of tests were conducted on model footings in a large tank and the footings were instrumented to measure normal stresses and settlement. The test results indicate that the skirts increase the bearing capacity and reduce the settlement of the footing. The improvement in the bearing capacity is up to about 470% for a surface footing with skirt of a depth of 1.25B. The skirts also reduced the settlement of the footings to as small as 17% of the original settlement of a surface footing without skirts. A modified bearing equation was proposed for circular footings with skirts. The proposed equation agrees quite well with published experimental results.

Stability analysis of transmission tower foundations in permafrost equipped with thermosiphons and vegetation cover on the Qinghai-Tibet Plateau

During the construction of the ±400 kV direct current power transmission line (DCPTL), frozen blocks were backfilled into the foundation pits in permafrost regions because of the lack of backfilling materials and other problems, but this resulted in less compact backfilled soils. To ensure the stability of the tower foundations, a large number of thermosiphons were installed. This study discusses the threat to the stability of tower foundations of water infiltration along the large voids created within the backfilled soils by the use of frozen blocks, and quantifies the efficacy of a combination of thermosiphons and vegetation cover in enhancing tower stability, based on field collected data from January 2011 to April 2017. The results indicate that the cooling effects of thermosiphons caused a large amount of net heat removal from the foundation soils, even during the first operational year of the foundation, while foundation soils without thermosiphons exhibited net heat input during the same period. Ponding in the pits and downward infiltration of water obviously work to warm the foundation soils, and can result in the settlement of the tower footings, threatening the tower stability. The combination of thermosiphons and vegetation cover is shown to effectively cool the foundation soils and to reduce the settlement of the footings, thus ensuring the continued tower stability. This study also shows that the backfilling of frozen blocks should be avoided in the current climate conditions, even though effective cooling measures like thermosiphons are used because the downward infiltration of water along the large voids between the frozen backfilled blocks can’t be totally prevented. If the current degradation of the frozen state of the backfilled soils continues, the infiltrated water, which has been frozen at the bottom of the backfill, will begin to thaw again, threatening the stability of the tower foundations.

Effect of Tie Beam Dimensions on The Behaviors of Isolated Footings Under Eccentric Loading

Background: Foundations may be subjected to eccentric loads. If the load is eccentric the stress distribution underneath the footing will be non-uniform causing differential settlement between the two edges. Objective: In the present study, the finite element program software PLAXIS 3D 2014 has been used to study the effect of tie beam dimensions connecting isolated footings under eccentric loading on settlement and horizontal displacement as well as bending moment and shear force. The investigated program consists of eccentric footings connected with tie beams with different thicknesses and widths. The details and variation of the selected parameters were presented. Results: It was concluded that, the settlement and horizontal displacement values in both directions as well the contact pressure values decrease with increasing the thickness and widths of tie beam. However, the values of bending moment and shear forces along axis decreases with increasing the dimensions of tie beam. In addition, the distribution of stresses under footing along axis's decreases with increasing both of tie beam thickness and width. Conclusion: However, the differential settlements of footings decrease with increasing tie beam dimensions.

Settlement Prediction of Footings Using VS

The shear wave velocity (VS) is a key parameter for estimating the deformation characteristics of soil. In order to predict the settlement of shallow footings in granular soil, the VS and the concept of Schmertmann’s framework were adopted. The VS was utilized to represent soil stiffness instead of cone tip resistance (qc) because the VS can be directly related to the small-strain shear modulus. By combining the VS measured in the field and the modulus reduction curve measured in the laboratory, the deformation characteristics of soil can be reliably estimated. Vertical stress increments were determined using two different profiles of the strain influence factor (Iz) proposed in Schmertmann’s method and that calculated from the theory of elasticity. The corresponding modulus variation was determined by considering the stress level and strain at each depth. This state-dependent stress-strain relationship was utilized to calculate the settlement of footings based on the theory of elasticity. To verify the developed method, geotechnical centrifuge tests were carried out. The VS profiles were measured before each loading test, and the load-settlement curves were obtained during the tests. Comparisons between the measured and estimated load-settlement curves showed that the developed method adequately predicts the settlement of footings, especially for over-consolidated ground conditions.

Applied bearing pressure beneath a reinforced soil foundation used in a geosynthetic reinforced soil integrated bridge system

Geosynthetic reinforced soil integrated bridge system (GRS-IBS) design guidelines recommend the use of a reinforced soil foundation (RSF) to support the dead loads that are applied by the reinforced soil abutment and bridge superstructure, as well as any live loads that are applied by traffic on the bridge or abutment. The RSF is composed of high-quality granular fill material that is compacted and encapsulated within a geotextile fabric. Current GRS-IBS interim implementation design guidelines recommend the use of design methodologies for bearing capacity that are based around rigid foundation behavior, which yield a trapezoidal applied pressure distribution that is converted to a uniform applied pressure that acts over a reduced footing width for purposes of analysis. Recommended methods for determining the applied pressure distribution beneath the RSF for settlement analyses follow conventional methodologies for assessing the settlement of spread footings, which typically assume uniformly applied pressures beneath the base of the foundation that are distributed to the underlying soil layers in a fashion that can reasonably be modeled with an elastic-theory approach. Field data collected from an instrumented GRS-IBS that was constructed over a fine-grained soil foundation indicates that the RSF actually behaves in a fairly flexible way under load, yielding an applied pressure distribution that is not uniform or trapezoidal, and which is significantly different than what conventional GRS-IBS design methodologies assume. This paper consequently presents an empirical approach to determining the applied pressure distribution beneath the RSF in GRS-IBS construction. This empirical approach is a useful first step for researchers, as it draws important attention to this issue, and provides a framework for collecting meaningful field data on future projects which accurately capture real GRS-IBS foundation behavior.

Seismic performance of strip foundations on liquefiable soils with a permeable crust

Modern seismic codes dictate that the use of shallow foundations on liquefiable soils may be considered only after appropriate ground improvement. No further instructions are given regarding the improvement depth, or what changes if the surface layer (crust) does not liquefy. Hence, it is standard practice to improve the entire liquefiable soil layer below the foundation, whatever its depth or thickness. This study examines the seismic performance of strip foundations laying on a two-layered soil profile, consisting of a bottom layer of liquefiable sand and a (manmade or natural) permeable crust on top. Regardless of its origin, this crust does not develop (significant) excess pore pressures during shaking and is stronger and stiffer than the underlying liquefied sand. The problem is investigated numerically, through fully coupled non-linear dynamic finite-difference analyses. Following the identification of the governing response parameters, a set of multi-variable relations is developed for the approximate assessment of the seismic footing settlements and the bearing capacity degradation due to liquefaction appearing below the permeable crust.