Spread Footings in Sand: Load Settlement Curve Approach

A study of the assumptions involved in the ultimate bearing capacity equation indicates the shortcomings of that equation and load test data confirm these shortcomings. A new approach using a normalized load settlement curve is proposed to alleviate these shortcomings and to obtain the complete load settlement curve for a footing in sand. The normalization consists of plotting the mean footing pressure divided by a measure of the soil strength within the depth of influence of the footing versus the settlement divided by the footing width. It is shown that the normalized load settlement curve for a footing is independent of footing size and embedment. It is proposed to obtain the normalized curve point-by-point from a soil test. Because the deformation of the soil observed under full-scale footings during loading indicates a barreling effect similar to the soil deformation around a pressuremeter probe, the preboring pressuremeter curve is used to obtain the footing curve. The new method consists of transforming the preboring pressuremeter curve point-by-point into the footing load settlement curve. Load tests and numerical simulations are used to propose a method for a rectangular footing near a slope subjected to an eccentric and inclined load. The new method gives the complete load settlement curve for the footing and alleviates the problems identified with the bearing capacity equation.     

Bond-Slip Analytical Formulation toward Optimal Embedment of Concrete-Filled Circular FRP Tubes into Concrete Footings

This paper presents a robust analytical model for a moment connection of concrete-filled fiber reinforced-polymer (FRP) tubes (CFFTs) to concrete footings. The CFFT connection is based on a simple approach of direct embedment into the footing, thereby eliminating the need for connection rebar or mechanical devices. The CFFT is externally subjected to lateral and axial loads, resembling practical applications such as piles affixed to pile caps, bridge columns, or utility poles. The model adopts the concepts of equilibrium, deformations compatibility, and nonlinear concrete stress-strain behavior. It also employs a “bond stress-slip” relation that can be obtained from simple push-through tests on some of the commercially used tubes. The model can predict the critical embedment length Xcr, which is the minimum length required to achieve material failure of the CFFT outside the footing, and bond failure inside the footing, simultaneously. If the actual embedment length is less than Xcr, bond failure occurs prematurely at a lower strength that can also be predicted by the model. The model was verified using experimental data and showed that Xcr was only 0.7 of the diameter for that case. A sensitivity parametric analysis was carried out that led to some approximations. Based on which, a simple closed-form expression was established for Xcr in the case of lateral loading only.     

Experimental Investigations of the Response of Suction Caissons to Transient Combined Loading

Combined loading of foundations is a fundamental problem in civil engineering, particularly in the offshore industry where harsh environmental conditions occur. Large moment and horizontal loads may be applied to the foundation as well as vertical loads. Also, as the waves pass a structure, there can be rapid changes in the loads, so that transient effects need to be considered. When designing shallow foundations, such as suction caissons, there is uncertainty in the current understanding of how the foundation responds to these loads. This paper presents experiments, performed on model suction caisson foundations, where typical cyclic loading conditions are applied. The footing is embedded in oil-saturated sand so that dimensionless drainage times are comparable with the typical offshore conditions. Most of the testing was carried out with the vertical load held constant, to mimic the structural dead weight, while realistic “pseudorandom” moment and horizontal cyclic loads were applied. Experiments were carried out at different vertical loads, showing that the response depends on the vertical load level. Nondimensional relationships were established which accounted for this dependency. Surprisingly, the rate of loading had little impact on the load–displacement behavior for the experiments undertaken.     

Contact Interface Model for Shallow Foundations Subjected to Combined Cyclic Loading

It has been recognized that the ductility demands on a superstructure might be reduced by allowing rocking behavior and mobilization of the ultimate capacity of shallow foundations during seismic loading. However, the absence of practical reliable foundation modeling techniques to accurately design foundations with the desired capacity and energy dissipation characteristics and concerns about permanent deformations have hindered the use of nonlinear soil–foundation–structure interaction as a designed mechanism for improving performance of structural systems. This paper presents a new “contact interface model” that has been developed to provide nonlinear relations between cyclic loads and displacements of the footing–soil system during combined cyclic loading (vertical, shear, and moment). The rigid footing and the soil beneath the footing in the zone of influence, considered as a macroelement, are modeled by keeping track of the geometry of the soil surface beneath the footing, along with the kinematics of the footing–soil system, interaction diagrams in vertical, shear, and moment space, and the introduction of a parameter, critical contact area ratio (A/Ac); the ratio of footing area (A) to the footing contact area required to support vertical and shear loads (Ac). Several contact interface model simulations were carried out and the model simulations are compared with centrifuge model test results. Using only six user-defined model input parameters, the contact interface model is capable of capturing the essential features (load capacities, stiffness degradation, energy dissipation, and deformations) of shallow foundations subjected to combined cyclic loading.     

Axial Compression of Footings in Cohesionless Soils. II: Bearing Capacity

An extensive database of full-scale field load tests was used to examine the bearing capacity for footings in cohesionless soils. Each load test curve was evaluated consistently to determine the interpreted failure load (i.e., bearing capacity) using the L1-L2 method. This test value then was compared with the theoretical bearing capacity, computed primarily using the basic Vesi? model. The comparisons show that, for footing widths B>1?m, the field results agree very well with the Vesi? predictions. However, for B<1?m, the results indicated a relationship between B and the predicted-to-measured bearing capacity ratio. Accordingly, a simple modification was made to the bearing capacity equation, and the resulting predictions are very good.     

Load Transfer Curves along Bored Piles Considering Modulus Degradation

The load-transfer (or t-z) curve, which reflects the interaction between a pile and the surrounding soil, is important for evaluating the load-settlement response of a pile subjected to an axial load using the load-transfer method. Preferably, the nonlinear stress-strain behavior of the soil should be incorporated into the t-z curve. This paper presents a practical approach for the estimation of t-z curves along bored piles by considering the nonlinear elastic properties and modulus degradation characteristics of the soil. A method for evaluating the modulus degradation curve from the results of a pressuremeter test is proposed. The results of load tests on one instrumented bored pile in Piedmont residual soil in Atlanta and another in the residual soil of the Jurong Formation in Singapore provide verification of the validity of the proposed approach.     

Settlement of Footing on Compacted Ash Bed

Compacted coal ash fills exhibit capillary stress due to contact moisture and preconsolidation stress due to the compaction process. As such, the conventional methods of estimating settlement of footing on cohesionless soils based on penetration tests become inapplicable in the case of footings on coal ash fills, although coal ash is also a cohesionless material. Therefore, a method of estimating load-settlement behavior of footings resting on coal ash fills accounting for the effect of capillary and preconsolidation stresses is presented here. The proposed method has been validated by conducting plate load tests on laboratory prepared compacted ash beds and comparing the observed and predicted load-settlement behavior. Overestimation of settlement greater than 100% occurs when capillary and preconsolidation stresses are not accounted for, as is the case in conventional methods.     

Experimental and Theoretical Studies for the Behavior of Strip Footing on Oil-Contaminated Sand

This paper presents the results of a series of plain-strain model tests carried out on both clean sand and oil-contaminated sand loaded with a rigid strip footing. The objectives of this study are to determine the influence of oil-contaminated sand on the bearing capacity characteristics and the settlement of the footing. Contaminated sand layers were prepared by mixing the sand with an oil content of 0–5% with respect to dry soil to match the field conditions. The investigations are carried out by varying the depth and the length of the contaminated sand layer and the type of oil contamination. A plain-strain elastoplastic theoretical model with an interface gap element between footing and the soil is carried out to verify the test results of the model. It is shown that the load-settlement behavior and ultimate bearing capacity of the footing can be drastically reduced by oil contamination. The bearing capacity is decreased and the settlement of the footing is increased with increasing the depth and the length of the contaminated sand layer. The agreement between observed and computed results is found to be reasonably good in terms of load-settlement behavior and effect of oil contamination on the bearing capacity ratio. A comparison between the model results and the prototype scale (B = 1.0?m) results are also studied.     

Effects of Moment-to-Shear Ratio on Combined Cyclic Load-Displacement Behavior of Shallow Foundations from Centrifuge Experiments

Current design guidelines for shallow foundations supporting building and bridge structures discourage footing rocking or sliding during seismic loading. Recent research indicates that footing rocking has the potential to reduce ductility demands on structures by dissipating earthquake energy at the footing-soil interface. Concerns over cyclic and permanent displacements of the foundation during rocking and sliding along with the dependence of foundation capacity on uncertain soil properties hinder the use of footing rocking in practice. This paper presents the findings of a series of centrifuge experiments conducted on shear wall-footing structures supported by dry dense to medium dense sand foundations that are subjected to lateral cyclic loading. Two key parameters, static vertical factor of safety (FSV), and the applied normalized moment-to-shear ratio (M/(H?L)) at the footing-soil interface, along with other parameters, were varied systematically and the effects of these parameters on footing-soil system behavior are presented. As expected, the ratio of moment to the horizontal load affects the relative magnitude of rotational and sliding displacement of the footing. Results also show that, for a particular FSV, footings with a large moment to shear ratio dissipate considerably more energy through rocking and suffer less permanent settlement than footings with a low moment to shear ratio. The ratio of actual footing area (A) to the area required to support the vertical and shear loads (Ac), called the critical contact area ratio (A/Ac), is used to correlate results from tests with different moment to shear ratio. It is found that footings with similar A/Ac display similar relationships between cyclic moment-rotation and cumulative settlement, irrespective of the moment-to-shear ratio. It is suggested that shallow foundations with a sufficiently large A/Ac suffer small permanent settlements and have a well defined moment capacity; hence they may be used as effective energy dissipation devices that limit loads transmitted to the superstructure.     

Modeling Permanent Deformation of Unbound Granular Materials under Repeated Loads

Finite-element analysis on a pavement structure under traffic loads has been a viable option for researchers and designers in highway pavement design and analysis. Most of the constitutive drivers used were nonlinear elastic models defined by empirical resilient modulus equations. Few isotropic/kinematic hardening elastoplastic models were used but applying thousands of repeated load cycles became computationally expensive. In this paper, a cyclic plasticity model based on fuzzy plasticity theory is presented to model the long-term behavior of unbound granular materials under repeated loads. The discussion focuses on the model parameters that control long-term behavior such as elastic shakedown. The performance of the constitutive model is presented by comparing modeled and measured permanent strain at various numbers of load cycles. Calculated resilient modulus from the complete stress-strain curve is also discussed.     

Static Stability of Beam-Columns under Combined Conservative and Nonconservative End Forces: Effects of Semirigid Connections

Stability criteria that evaluate the effects of combined conservative and nonconservative end axial forces on the elastic divergence buckling load of prismatic beam-columns with semirigid connections is presented using the classic static equilibrium method. The proposed method and stability equations follow the same format and classification of ideal beam-columns under gravity loads presented previously by Aristizabal-Ochoa in 1996 and 1997. Criterion is also given to determine the minimum lateral bracing required by beam-columns with semirigid connections to achieve “braced” buckling (i.e., with sidesway inhibited). Analytical results obtained from three cases of cantilever columns presented in this paper indicate that: (1) the proposed method captures the limit on the range of applicability of the Euler’s method in the stability analysis of beam-columns subjected to simultaneous combinations of conservative and nonconservative loads. The static method as proposed herein can give the correct solution to the stability of beam-columns within a wide range of combinations of conservative and nonconservative axial loads without the need to investigate their small oscillation behavior about the equilibrium position; and (2) dynamic instability or flutter starts to take place when the static critical loads corresponding to the first and second mode of buckling of the column become identical to each other. “Flutter” in these examples is caused by the presence of nonconservative axial forces (tension or compression) and the softening of both the flexural restraints and the lateral bracing. In addition, the “transition” from static instability (with sidesway and critical zero frequency) to dynamic instability (with no sidesway or purely imaginary sidesway frequencies) was determined using static equilibrium. It was found also that the static critical load under braced conditions (i.e., with sidesway inhibited) is the upper bound of the dynamic buckling load of a cantilever column under nonconservative compressive forces. Analytical studies indicate the buckling load of a beam-column is not only a function of the degrees of fixity (ρa and ρb), but also of the types and relative intensities of the applied end forces (Pci and Pfj), their application parameters (ci, ηj, and ξj), and the lateral bracing provided by other members (SΔ).     

Case History Evaluation of Laterally Loaded Piles

This paper examines seven case histories of load tests on piles or drilled shafts under lateral load. Since the current design software to estimate lateral load resistance of deep foundations requires p-y curves. The first approach used was correlative whereby soil parameters determined from in situ tests [standard penetration test (SPT) and cone penetration test (CPT)] were used as input values for standard p-y curves. In the second approach p-y curves were calculated directly from the stress deformation data measured in dilatometer (DMT) and cone pressuremeter tests. The correlative evaluation revealed that, on the average, predictions based upon the SPT were conservative for all loading levels, and using parameters from the CPT best predicted field behavior. Typically, predictions were conservative, except at the maximum load. Since traditionally SPT and CPT correlation-based p-y curves are for “sands” or “clays,” this study suggests that silts, silty sands, and clayey sands should use cohesive p-y curves. For the directly calculated curves, DMT derived p-y curves predict well at low lateral loads, but at higher load levels the predictions become unconservative. p-y curves derived from pressuremeter tests predicted well for both “sands” and “clays” where pore pressures are not anticipated.     

Behavior of Rigid Footings on Gravel under Axial Load and Moment

A laboratory testing program was conducted to study the settlement and rotation response of rigid square footings under combined axial load and moment. A total of 17 tests were performed in which the size of the footing, footing embedment, axial load, and load eccentricity were changed. The test soil consisted of a fine and well-graded gravel contained in a box with dimensions: 1.52×1.52?m (5×5?ft) cross section and 0.91?m (3?ft) deep. The soil was compacted in layers 150?mm (6?in.) thick to an approximate relative density of 84%. In each test, the axial load, moment, settlement at the center of the footing, and footing rotation were measured. Concentrically loaded footings with different sizes exhibited a similar behavior in terms of the applied stress-normalized settlement (settlement divided by size of footing) response. The analytical model proposed was based on such normalized response as an input, and it was calibrated to account for the change in soil stiffness with confinement. The formulation captures the inherent nonlinear deformations of the soil with load and the coupled nature of settlements and rotations of footings under axial load and moment. The model was tested by comparing calculated values with laboratory measurements from tests not included in its calibration. The comparisons showed a satisfactory agreement between calculations and measurements, bringing confidence in the analytical formulation proposed and the methodology used.     

Probabilistic Construction Load Model for Multistory Reinforced-Concrete Buildings

This paper develops a probabilistic construction load process model for multistory reinforced-concrete building construction. This model considers loads causing peak structural actions on floor slabs for two widely used shoring procedures and includes probability distributions and temporal characteristics of slab self-weight, sustained construction live loads, “material stacking” loads, and “move-in” loads. Construction load statistics derived from Monte Carlo simulation show that the mean of maximum construction loads exceeds nominal (design) service (occupancy) loads whenever the nominal live-to-dead load ratio is less than approximately 1.0. A Type I extreme value distribution provided the best fit to the inferred distributions of construction live loads.     

Characterization of Model Uncertainty in the Static Pile Design Formula

Level 1 reliability methods have been internationally accepted as the basis for development of the new generation of geotechnical design codes. A key requirement of this design approach is the identification and quantification of uncertainties associated with the geotechnical design under consideration. This paper presents four load test databases from South Africa for driven piles in noncohesive soils (29 tests), bored piles in noncohesive soils (33 tests), driven piles in cohesive soils (59 tests), and bored piles in cohesive soils (53 tests). The capacity model factor is defined as the ratio of the interpreted capacity (Chin-Davisson approach) and the predicted capacity (static pile design formula). The uncertainty in the capacity model factor is modeled as a lognormal random variable. The model factor statistics reported in this study are required for reliability-based ultimate limit state design. The uncertainty in the load-settlement behavior is characterized by fitting measured load-settlement data to a hyperbolic equation and then normalizing the hyperbolic curve with the interpreted capacity. The resulting exercise reduces uncertainties in a set of nonlinear continuous curves to uncertainties in two hyperbolic curve-fitting parameters. This approach is practical and grounded realistically on the load test database with minimal assumptions. The hyperbolic parameter statistics reported in this study are required for reliability-based serviceability limit state design.     

Energy Capacity Criterion for the Design of Columns against Collapse

Current practice in buckling design is based on the ultimate strength of a member such that excessive lateral deflections do not occur. This ultimate strength is often dictated by empirically derived formulae which correspond to postulated element imperfections including residual stresses. In this paper, the postbuckling behavior of columns is considered, and the limit state is considered to be total collapse. The load versus end displacement relationship is derived for a simplified elastic–perfectly plastic column model. Using this curve, the energy absorbed and released in going from one load/deflection state to another can be easily quantified. With this, the energy absorption capacity of an already loaded column is considered to be the critical performance metric. This “energy capacity criterion” is then used to develop alternative design curves for different levels of energy absorption capacity.     

Thermal Effect on the Postbuckling Behavior of an Elastic or Elastoplastic Truss

Temperature rise may lead to strength degradation and stiffness deterioration of structures under fire conditions. The purpose of this paper is to theoretically study the thermal effect on the postbuckling behavior of an elastic or elastoplastic two-member truss, based on large-deformation elasticity considerations. Two kinds of loadings are considered, i.e., trusses under constant temperature but increasing loads, and trusses under constant loads but rising temperature. For the case with constant temperature, the critical load of an elastic truss will be greatly reduced if the effect of yielding is taken into account. Moreover, yielding of material can cause the truss to bifurcate from the original elastic path. For the case with constant loads, a critical temperature that occurs as the limit point of the temperature–deflection curve can always be found. Besides, the presence of yielding can drastically reduce the critical temperature of an elastic truss, causing it to collapse in an abrupt manner. The solutions presented herein can be used as benchmarks for calibration of the accuracy of general finite-element procedures in analyzing structures under fire conditions.     

Simple Formulas for the Response of Shallow Foundations on Compressible Sands

The engineering design of shallow foundations on sand is almost universally based on one of the variants of the classical bearing capacity formula. However, this formula is suitable only where the sand exhibits dilative behavior and a clear rupture mechanism forms at failure. The main challenge then is choosing a suitable friction angle, taking into account the soil density and the high stresses beneath the footing. When other conditions apply, in particular when the footing is large or founded on compressible materials, alternative approaches need more focus on soil compressibility. Two simple semianalytical formulas are proposed and explored in this paper: (1) an analysis using a one-dimensional (1D) compression equation; and (2) an analysis using the concept of “bearing modulus.” It is argued that the bearing modulus approach may be used for conditions that reflect moderate design parameters (i.e., moderate foundation size and sand compressibility), but for very large foundations or highly compressible soils the 1D compression method is found more suitable. It is shown that the bearing modulus analysis can be approached in terms of the compression response of the soil, suggesting a possible route to link the bearing modulus directly to the compression model parameters of the soil.     

Brittle Failure and Bond Development Length of CFRP-Concrete Beams

The performance of a series of 1.5 m-long reinforced concrete beams with CFRP plates bonded to the soffit is presented. Effects of the plate length, the reinforcing steel ratio, and the thickness of the concrete cover on behavior of the beams are discussed with particular emphasis on the brittle failure mode of the concrete ripping. It was found that before the brittle failure, the composite action of the beam could be divided into three distinct zones based on the distribution of the strains along the CFRP plate: (1) The “destressed” zone, (2) the “bond development” zone; and (3) the “fully composite” zone. Concrete ripping may be prevented by limiting the strain at the transition point of the composite zone of the plate. An analytical formulation to predict the failure load corresponding to the concrete ripping failure mode is proposed based on composite theory in combination with a strain limiting criterion. The strain limit can be determined based on simple bond tests with various bond lengths for a given CFRP and adhesive combination.     

Analytical Method for Load-Transfer Characteristics of Rock-Socketed Drilled Shafts

The load-settlement behavior of rock-socketed drilled shafts under axial loading is investigated by a load-transfer approach. Special attention is given to the shear load-transfer function and an analytical method for estimating load-transfer characteristics of rock-socketed drilled shafts. A nonlinear triple curve is employed to determine the shear load-transfer function of rock-socketed drilled shafts based on the constant normal stiffness direct shear tests and the Hoek-Brown failure criterion. An analytical method that takes into account the soil coupling effect was developed using a modified Mindlin’s point load solution. Through comparisons with field case studies, it is found that the proposed methodology in the present study is in good agreement with the general trend observed by in situ measurements and, thus, represents a significant improvement in the prediction of drilled shaft shear behavior.