Elastic Settlement Research Articles

Semi-Analytical Study of Settlement of Two Interfering Foundations Placed on a Slope

In many engineering constructions, the foundations should be built adjacent to each other. Therefore, the effect of interfering of close foundations should be considered in the design stage. In this research work, the effect of interference of closely separated foundations resting on a slope on the elastic settlement is investigated by considering a semi-analytical solution. The distribution of stress due to the footing pressure in the slope is computed by a proposed Airy stress function, and then by employing the finite difference scheme, the displacement of the footings is calculated. The results obtained show that by increasing the distance between the foundations, the interference influence on the ratio of settlement will be diminished. However, this behavior is highly linked to the slope characteristics. For a slope with a height of 10 times of footing width, beyond an S/B ratio larger than 10, the effect of interference is not tangible, and the footings behave like an isolated foundation. By decreasing the slope height, this behavior will occur at a lower S/B.

Comparative Analysis of Kazakhstani and European Design Specifications: Raft Foundation, Pile Foundation, and Piled Raft Foundation

The introduction of Eurocode in Kazakhstan allows for the application of modern technological innovations and the elimination of technical barriers for the realization of international projects. It is significant to study the international standards and design requirements provided in Eurocode. This study presents a comparative analysis of Kazakhstani and European approaches for the geotechnical design of foundations and provides the design methods in the considered codes of practice. Three different types of foundations (i.e., raft, pile, and piled raft foundations) were designed following SP RK 5.01-102-2013—Foundations of buildings and structures, SP RK 5.01-103-2013—Pile foundations, and Eurocode 7: Geotechnical design for the Nur-Sultan soil profile. For all three types of foundations, the calculated results of bearing resistance and elastic settlement showed the conservativeness of Eurocode over SNiP-based Kazakhstani building regulations, as the values of bearing resistance and elastic settlement adhering to Kazakhstani code exceeded the Eurocode values. The difference between the obtained results can be explained by the application of higher values of partial safety factors by Eurocode 7. Sensitivity analysis of the bearing resistance on foundation parameters (i.e., raft foundation width and pile length) for the Kazakhstani and European approaches was performed to support the conclusions of the study.

Empirical Relationships Between the Elastic Settlement of Rigid Rectangular Foundations and the Settlement of the Respective Flexible Foundations

The problem of settlement of shallow foundations is among the most important ones in classical soil mechanics. And while for the settlement of flexible foundations elastic solutions are widely used, for rigid rectangular foundations where the actual contact pressure distribution is still unknown, the problem is approximated either analytically assuming a contact pressure distribution or semi‐empirically combining the theory of elasticity with experimental and/or numerical results. A third and often attractive choice is the use of simple empirical relationships or relevant tabulated values relating the elastic settlement of rigid foundations (ρR) with the settlement of the respective flexible foundations (e.g. at the center, ρCe). Reviewing the relathionships of this third approach, the author revealed serious lack of consesous between the various sources; for example, according to the literature, ρR ranges between 68 and 125% of ρCe, the time when it is well-known that ρR < ρCe. In this paper, comparison of the settlement of 210 rigid foundation cases derived from 3D elastic finite element analysis, with the settlement of the respective flexible foundations derived from the theory of elasticity, led to simple empirical relationships between ρR and ρCe as well as between ρR and ρAv (ρAv = average settlement of the flexible foundation) with coefficient of determination (R2) almost unity. The analysis showed that these relationships are largely independent of the aspect ratio of foundations and the thickness and Poisson’s ratio (ν) of the compressible medium, although separate relationships are given for ν = 0.5, slightly increasing R2. Finally, a correction factor for foundation rigidity is given exploting the known linear relationship that exists between the relative stiffness factor of foundations and settlement.

Climate‐adaptive design approach for embedded footing under extreme climate event

AbstractRecent records indicate that extreme climate events adversely affect the performance of earthen structures and superstructures supported on them by varying the strength and deformation properties of subsurface soil. To better design such structures, the effects of climate events must be well understood, and the conventional design procedures must be improved by incorporating the knowledge of climatology in geotechnical engineering. In this study, a new climate‐adaptive design method is developed to investigate the impact of extreme climate events on the safety and serviceability performances of embedded footing through incorporating the site‐specific hydrological loads such as precipitation, evapotranspiration, and water table depth to geotechnical parameters. The proposed method was applied to two arid climate sites in the United States, Austin, TX, and Albuquerque, NM. The site‐specific extreme hydrological cycle was determined based on historical records. The mathematical model was solved for temporal and spatial variations of the degree of saturation and matric suction considering the hydrological loads as the upper and lower boundary conditions, respectively. The results showed that the worst performance (higher elastic settlement and lower ultimate bearing capacity) was observed during the period when the degree of saturation in the influence zone was the highest. The critical design parameters including ultimate bearing capacity and settlement obtained from the proposed method increased by 28% and 35%, respectively, in Austin, compared to those calculated from conventional approaches where the soil is assumed to be fully saturated. In Albuquerque, the increase in ultimate bearing capacity and settlement were 61% and 45%, respectively.

A new approach for estimating the vertical elastic settlement of a single pile based on the fictitious soil pile model

The development of settlement at pile heads due to vertical loads is one of the most important factors in pile design. For large-scale pile-supported infrastructure and elevated roads, the cumulative plastic deformation caused by cyclic loads could be so dangerous that only elastic deformation is permitted. However, existing methods rely heavily on measurements from field tests, while only a few analytical approaches have been developed based on the Winkler model or load transfer functions, which are mostly empirical. Moreover, present theories can hardly unify the computation of end-bearing piles and floating piles, since the classification between these two types of piles is often ambiguous. In this study, a new approach based on the fictitious soil pile model is proposed, and a semi-analytical is derived. The efficacy of the solution is demonstrated via comparisons against measured curves in the field and rigorous numerical results. Finally, a parametric study is performed to investigate the influence of pile and soil properties and the existence of a strong or weak soil interlayer on the vertical settlement of a single pile. On this basis, a new pile design factor referred as ‘optimal aspect ratio’ is proposed to acquire suitable pile dimensions.

Construction of elastic viscoplastic constitutive model and settlement control of over-consolidated soil using finite element software ABAQUS

To study the settlement process of high-filled embankment before and after construction, an elastic viscoplastic constitutive model of over-consolidated soil is designed based on finite element analysis. The model is used to predict the settlement of subgrade before and after construction. First, the lower load surface is used as the reference yield surface of strain rate. Based on the principle of relative over stress, two rate sensitive parameters are established through the measurement of triaxial compression test with different strain rates. Second, the relative over stress function, stress function, and dynamic yield criterion function are established. Finally, two kinds of over-consolidated soils with over-consolidation ratios of 16 and 8 are tested for triaxial shear creep, and the finite element software is used for simulation analysis. The results show that the ultimate axial strain decreases with the decrease of deviatoric stress. When the creep time exceeds 3000min, the model has good prediction effect. The finite element calculation results of different backfill layers in inversion parameters show that the maximum settlement layer of high-filled embankment may not occur at the top or bottom, so attention should be paid in the construction process of high-filled embankment. This exploration provides a reference for the study of long-term deformation and strength of high-filled embankment.

An Investigation on the Settlement of Shallow Foundations Resting on Cross-Anisotropic Soil Deposits

Natural soil deposition process results in formation of anisotropic planes with different properties along different directions, and hence, such natural deposits possess inherent anisotropy. On the other hand, an estimate of the elastic settlement of surface foundations placed on such anisotropic deposits is very important. In this research, the effect of anisotropy (in fact, cross-anisotropy) on the elastic settlement of shallow foundations resting on anisotropic granular soils, often sands, has been investigated. The most important properties in this work, in addition to the geometry of the footing, are the soil modulus of elasticity, Poisson’s ratio and the ratio of these moduli along anisotropic planes in a cross-anisotropic medium. The governing equations of deformation in such media are first presented. Then, the elastic settlement of shallow foundations resting on such media has been estimated using the finite difference method, and then, some influence factors are presented. The factors are useful in estimating the elastic settlement of shallow foundations on cross-anisotropic soils, when the soil properties along two perpendicular directions are known. A series of design charts are provided in non-dimensional form so as to avail their practical use in a general form.

Assessment of ultimate load of drilled shaft socketed in rocks based on pile load tests

To investigate the settlement characteristics of drilled shaft socketed into igneous, metamorphic, or sedimentary rock, experimental results of the pile load tests were thoroughly collected in 20 different locations, clearly tabulated, and extensively compared with the standards for assessment of ultimate load. Total and elastic settlement patterns of drill shaft were completely dependent on the socketed pile length, the imposed load, the pile diameter, and the shear stress in bedrock, whereas residual settlement did not depend on the factors. It was also observed that the trends of total, residual, and elastic settlements were independent on bedrock types. Comparison between the experimental data and the standards shows that the total and residual settlements of large drilled shaft socketed in bedrock were too high to determine the ultimate load, and the reasonable amount of total or residual settlement measured from pile load test is proposed to assess the ultimate load capacity of drilled shaft socketed in bedrock.

Numerical Analysis of Settlement Response of Shallow Footing Subjected to Heavy Rainfall and Flood Events

The US and many parts around the world have experienced prolonged periods of heavy rainfall, severe floods, and droughts over the past 50 years. This study investigates the impacts of extreme hydrological events such as heavy rainfall and flood on the settlement behavior of continuous footing installed in unsaturated soil using a coupled Geotechnical-Hydrological finite element software, PLAXIS 2D. Initially, the effect of different degrees of saturation on the settlement behavior of the continuous footing of widths 1.5 m, 3.0 m, and 4.5 m was analyzed by applying a mechanical load. Then the settlement behavior of the footing was analyzed by applying heavy rainfall of intensity 102 mm/day for six days. Finally, the settlement behavior of the footing was analyzed by applying a flood head of 2.5 meters for seven days. The results indicated that the wetting front movement during heavy rainfall and flooding led to the weakening of soil strength and stiffness and induced additional settlements. The additional settlement induced by the flood was significantly higher than the heavy rainfall. The differential settlement was higher when the rainfall was applied on one side of the footing. The rebound of the elastic settlement was uniquely noticed when the flood head receded with time. The results indicated that not all the settlements were induced by the soil saturation but also due to the hydrostatic loading due to the flood head. The settlements induced by the flooding exceeded the allowable settlement of 25 mm, resulting in failure. These additional settlements caused by heavy rainfall and flood will lead to poor serviceability of the structures and cause the failure of the footing.

Elastic Settlement Analysis of Rigid Rectangular Footings on Sands and Clays

In this paper an elastic settlement analysis method for rigid rectangular footings applicable to both clays and sands is proposed. The proposed method is based on the concept of equivalent shape, where any rectangular footing is suitably replaced by a footing of elliptical shape; the conditions of equal area and equal perimeter are satisfied simultaneously. The case of clay is differentiated from the case of sand using different contact pressure distribution, whilst, additionally, for the sands, the modulus of elasticity increases linearly with depth. The method can conveniently be calibrated against any set of settlement data obtained analytically, experimentally, or numerically; in this respect the authors used values which have been derived analytically from third parties. Among the most interesting findings is that sands produce “settlement x soil modulus/applied pressure” values approximately 10% greater than the respective ones corresponding to clays. Moreover, for large Poisson’s ratio (v) values, the settlement of rigid footings is closer to the settlement corresponding to the corner of the respective flexible footings. As v decreases, the derived settlement of the rigid footing approaches the settlement value corresponding to the characteristic point of the respective flexible footing. Finally, corrections for the net applied pressure, footing rigidity, and non-elastic response of soil under loading are also proposed.

Experimental investigation of the behavior of soil reinforced with waste plastic bottles under cyclic loads

The low natural degradation rate of plastic products makes the recycling or disposal of increasing post-consumer plastic materials, including Plastic Polyethylene Terephthalate (PET) bottles, a global concern. The current capacity of recycling programs for absorbing annual waste PET materials in environmentally friendly ways is limited. As a novel beneficial option, the cellular form of post-consumer bottles might act to provide sufficient confinement for infill soil and hence provide a technique by which the behavior of foundation beds under applied loads could be improved. In this study, a series of full-scale tests were conducted on unreinforced and PET (Plastic Polyethylene Terephthalate) bottle reinforced beds. For each test 100 cycles of 400 kPa load followed by 400 cycles of 800 kPa load was applied to the pavement through loading plate. Experiments were performed in a 2200 × 2200 × 1000 mm test pit on a 300 mm diameter circular loading plate. Three different sizes (i.e., different external diameters and heights) of waste plastic (PET) bottles filled with soil were tested as a reinforcing element. In some tests, a single layer of HDPE (high-density polyethylene) geogrid layer over bottles reinforced zone was examined. The results showed improvement in all reinforcing arrangement, although improvement was slightly higher for smaller bottles. For the reinforced case, a lower settlement accumulation rate and a higher resilient (elastic) settlement was observed compared to the unreinforced condition. In the case of lower cyclic loading (400 kPa amplitude), an average 42% improvement occurred for the three bottle-reinforced scenarios, however this value was 179% for higher cyclic loading (800 kPa), indicating more benefits of bottle-reinforcement in the case of critically loaded conditions. An extra layer of geogrid over the bottle-reinforced zone increases load distribution area and prevents distortion of bottles, leading to as much as 82% more reduction in soil settlement compared to the case without geogrid. The combined use of bottles and single geogrid layer eliminates the need to multilayer geosynthetic reinforcement usage, helps the economy of the project besides avoiding the high cost of waste bottle disposal.

Strain Influence Factor Charts for Settlement Evaluation of Spread Foundations based on the Stress–Strain Method

In this paper, the stress–strain method for the elastic settlement analysis of shallow foundations is revisited, offering a great number of strain influence factor charts covering the most common cases met in civil engineering practice. The calculation of settlement based on strain influence factors has the advantage of considering soil elastic moduli values rapidly varying with depth, such as those often obtained in practice using continuous probing tests, e.g., the Cone Penetration Test (CPT) and Standard Penetration Test (SPT). It also offers the advantage of the convenient calculation of the correction factor for future water table rise into the influence depth of footing. As is known, when the water table rises into the influence zone of footing, it reduces the soil stiffness and thus additional settlement is induced. The proposed strain influence factors refer to flexible circular footings (at distances 0, R/3, 2R/3 and R from the center; R is the radius of footing), rigid circular footings, flexible rectangular footings (at the center and corner), triangular embankment loading of width B and length L (L/B = 1, 2, 3, 4, 5 and 10) and trapezoidal embankment loading of infinite length and various widths. The strain influence factor values are given for Poisson’s ratio value of soil, ranging from 0 to 0.5 with 0.1 interval. The compatibility of the so-called “characteristic point” of flexible footings with the stress–strain method is also investigated; the settlement under this point is considered to be the same as the uniform settlement of the respective rigid footing. The analysis showed that, despite the effectiveness of the “characteristic point” concept in homogenous soils, the method in question is not suitable for non-homogenous soils, as it largely overestimates settlement at shallow depths (for z/B &lt; 0.35) and underestimates it at greater depths (for z/B &gt; 0.35; z is the depth below the footing and B is the footing width).

Experimental study for elastic deformation under isolated footing

The results of field studies of elastic deformations in the footing base, composed of loses soils. Elastic deformation is the result of compression partially bound water at the contacts between the mineral particles, the value of which depends on the wetness soil environment. It was found that deformation depends on the molecular moisture capacity of the soil while elastic settlement increases in proportion to pressure

Evaluation on full-scale testbed performance of cement asphalt mortar for ballasted track stabilization

This study focuses on the full-scale testbed performance of two types of ballasted railway track systems, with and without cement asphalt mortar (CAM) stabilizing material. This method develops a strong membrane between the fouled ballast particles which provides bonding and strengthening effects to the entire ballast layer, thus reinforcing the structural regularity of the track-bed. The feasibility of the proposed solution (CAM) is evaluated through static and dynamic wheel load application which simulate the actual operation of running trains. To compare the effectiveness of the new solution from the conventional maintenance strategy, the roadbed pressure, plastic/elastic deformation, load distribution, and track stiffness analysis are measured. From the full-scale testbed results, the Life Cycle Cost Analysis (LCCA) is conducted to verify the actual cost-effectiveness. In general, it was confirmed that the CAM stabilizing solution improves the performance of ballasted track system at both static and dynamic loading stages. The testbed results also suggest that a significant reduction in elastic and plastic settlement in stabilized track. The LCCA test results reveal a good potential for the sustainable development of ballasted track system stabilized by CAM.

Comparative Analysis of Kazakhstani and European Approaches for the Design of Shallow Foundations

The design of shallow foundations is performed in accordance with different building regulations depending on geotechnical and geological conditions. This paper involves the design calculations applying Kazakhstani and European approaches. The design of shallow foundations in Nur-Sultan city in Kazakhstan was implemented by the calculation of bearing capacity and elastic settlement in accordance with the design procedures provided in SP RK 5.01-102-2013: Foundations of buildings and structures, and Eurocode 7: Geotechnical design. The calculated results of bearing capacity and elastic settlement for two types of shallow foundations, such as pad foundation and strip foundation, adhering to Kazakhstani and European approaches are relatively comparable. However, the European approach provided higher values of bearing capacity and elastic settlement for the designed shallow foundation compared to the Kazakhstani approach. The difference in the results is explained by the application of different values of partial factors of safety for the determination of bearing capacity and different methods for the calculation of the elastic settlement of shallow foundations (i.e., elasticity theory and layer summation method).

Elastic Settlement Analysis for Various Footing Cases Based on Strain Influence Areas

In the present paper, the strain influence area method is introduced, which, technically, is classified between the classical elastic theory and Schmertmann’s semi-empirical method for immediate settlement analysis, exploiting the advantages of both. Strain influence area values are given in chart form for the calculation of elastic settlement at various locations on the plan view of flexible circular and rectangular footings, embankment loadings as well as for circular rigid footings on sands and clays. Among the major advantages of the proposed method is the direct and convenient calculation of the water table correction factor through the same charts; as known when the water table rises into the influence zone, the soil stiffness reduces, thus, additional settlement is induced. Finally, a new correction factor related to the effect of footing load on the modulus of elasticity of sands is proposed, whilst the Terzaghi’s empirical formula giving the effect of footing shape on the modulus of elasticity of soils has been revisited. It is very interesting that this empirical correction seems to cancel out the adverse effect of the second dimension of footing on elastic settlement analysis.

Reducing Statistical Uncertainty in Elastic Settlement Analysis of Shallow Foundations Relying on Targeted Field Investigation: A Random Field Approach

The present paper deals with the practical problem of reducing statistical uncertainty in elastic settlement analysis of shallow foundations by relying on targeted field investigation with the aim of an optimal design. In a targeted field investigation, the optimal number and location of sampling points are known a priori. As samples are taken from the material field (i.e., the ground), which simultaneously is a stress field (stresses caused by the footing), the coexistence of these two fields allows for some points in the ground to better characterize the serviceability state of structure. These points are identified herein through an extensive parametric analysis of the factors controlling the magnitude of settlement; the number of different cases considered was 3318. This is done in an advanced probabilistic framework using the Random Finite Element Method (RFEM) properly considering sampling of soil property values. In this respect, the open source RSETL2D program, which combines elastic finite element analysis with the theory of random fields, has been modified as to include the function of sampling of soil property values from the generated random fields and return the failure probability of footing against excessive settlement. Two sampling strategies are examined: (a) sampling from a single point and (b) sampling a domain (the latter refers to e.g., continuous cone penetration test data). As is shown in this work, by adopting the proper sampling strategy (defined by the number and location of sampling points), the statistical error can be significantly reduced. The error is quantified by the difference in the probability of failure comparing different sampling scenarios. Finally, from the present analysis, it is inferred that the benefit from a targeted field investigation is much greater as compared to the benefit from the use of characteristic values in a limit state design framework.

Coupled geotechnical-climatic design procedure for drilled shaft subjected to axial load

In this paper, a novel procedure is proposed to incorporate the site-specific hydrological/climatic parameters into the geotechnical design of drilled shaft with sample applications in Riverside, CA and Salt Lake City, UT. The variation of degree of the saturation and/or matric suction due to the hydrological/climatic events was modeled using the one-dimensional Richards’ equation considering historical resultant infiltration rate and water table depth as the upper and lower boundary conditions, respectively. The historical rainfall, evapotranspiration, and water table depth were considered in a probabilistic manner to estimate a representative degree of saturation and/or matric suction in the subsurface soil that support the drilled shaft. The results indicate that the ultimate axial capacity of the drilled shaft increases by as much as 40% of the conventional fully saturated method in Salt Lake City, while this is almost 56% for Riverside, CA. In case of the settlement, the total elastic settlement of the drilled shaft decreases by almost 34% and 30% at Salt Lake City and Riverside, respectively. Also, it is observed that the water table depth, intensity, and duration of the rainfall have noticeable impacts on the design parameters of the drilled shaft.

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...

Extracting some soil parameters and estimating elastic settlements from Direct shear box data for a granular C- Ø soil

Direct shear box tests were carried out on some soil samples obtained from some locations around Uyo metropolis in Akwa-Ibom State, Southeastern Nigeria. The dominant geology is the Coastal Plain Sands. From the test results, the C-O properties of the soils were determined. These values were used to compute ultimate and allowable bearing capacities for the soil samples. Elastic, and shear modulus parameters were computed for the different shear values readings for each vertical loading scheme. Poisson ratio was also computed for the same loading scheme applying the elastic relationship between shear modulus and elastic modulus. These parameters were used to compute elastic settlement using the classical elastic theory equation. Two other modified equations of the elastic theory equation and a consolidation equation was also used to compute immediate and consolidation settlements respectively. The values of immediate settlement obtained for the classical elastic equation is less than those computed by the other two modified equations. This is attributed to the fact that the other two equations assumed a constant value of Poisson ratio for the different imposed loads for which computations were made. For the allowable load of 138.54 kPa the classical elastic theory gave an immediate settlement value of 1.02 cm; the other two modified forms of the theory gave values of 2.94 cm and 4.0 cm. Elastic modulus and Poisson ratio obtained from the Direct shear test for the load are 5662.86 kPa and 0.49. These values were used in the elastic equation. The same value of 5662.86 kPa was used in the other two modified elastic formulas, but Poisson ratio values of 0.15 and 0.2 were assumed for all loads. Direct shear box test provides a convenient, but plausible means of determining parameters required to compute immediate settlement for the type of soil investigated.