# Finite Element Analysis of Elastic Settlement of Spreadfootings Founded in Soil

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1 Finite Element Analysis of Elastic Settlement of Spreadfootings Founded in Soil Jae H. Chung, Ph.D. Bid Bridge Software Institute t University of Florida, Gainesville, FL, USA

2 Content 1. Background 2. FB MultiPier FEA model development 3. Theoretical basis of FB MultiPier FEA model 3.1 Computation of soil resistance (Newmark s solution of Boussinesq s equation) 3.2 Constitutive relationship 3.3 Homogenezation of heterogeity 3.4 Soil stiffness 3.5 Averaging methods

3 Strength vs. Serviceability (1/3) Foundations should be proportioned to withstand all anticipated loads safely including the permanent loads of the structure re and transient loads. Most design codes specify the types of loads and load combinations to be considered in foundation design, e.g., g, AASHTO. These load combinations can be used to identify the limit states tt for the foundation types bi being considered. d A limit it state tt is reached when the structure no longer fulfills its performance requirements.

4 Strength vs. Serviceability (2/3) An ultimate limit state (ULS) corresponds to the maximum load carrying capacity (either structural or geotechnical failure) of the foundation. The ultimate ltimatestate is also called the strength limit state. bearing capacity of soil exceeded, excessive loss of contact, i.e., eccentricity, sliding at the base of footing, loss of overall stability, i.e.,, global stability, or exceedance of structural capacity 1997 UBC or ACI 318 A serviceability limit state (SLS) corresponds to loss of serviceability, and occurs before collapse. excessive differential or total foundation settlements, excessive lateral displacements, or structuraldeterioration of the foundation.

5 Strength vs. Serviceability (3/3) All relevant limit states must be considered in foundation design to ensure an adequate degree of safety and serviceability. All foundation design in practice isgeared towards addressing the ULS and the SLS. Existing design methodology includes: the Allowable Stress Design (ASD) the Ultimate Strength Design (USD) the Load and Resistance sta Factor Design (LRFD) Focus is made on ASD for geotechnical design.

6 Design concept and procedure (1/4) The geotechnical design of a spread footing is a two part process. 1. Estimate the allowable soil bearing capacity to ensure stability of the foundation and determine if the proposed structural loads can be supported on a reasonably sized foundation. 2. Predict an amount of settlement due to the actual structural loads and the time of occurrence estimated. Experience has shown that settlement is usually the controlling factor in design. This is not surprising ii since structural t considerations usually limit it tolerable settlements to values that can be achieved only on competent soils not prone to a bearing capacity failure.

7 Geotechnical design concept and procedure (1/2) The allowable bearing capacity of a spread footing is the lesser of The applied stress that results in a shear failure divided by a suitable factor of safety (FS); this is a criterion based on ULS; or The applied stress that t results in a specified amount of settlement; t this is a criterion based on SLS. Factor of Safety (FS) = Mean value of Resistance (Material Strength)/Design Load (the maximum load the footing should ever withstand in service); a typical value of FS ranges from 2.5 to 3 The concept of decreasing allowable bearing capacity with increasing footing width for the settlement controlled cases is an important concept to understand. As the footing width increases, the stress increase felt by the soil may decrease but the effect of the applied stress will extend more deeply below the footing base. Settlements may increase as the width increases depending on the type of soils within the influence depth.

8 Geotechnical design concept and procedure (2/2) In such cases, the only way to limit the settlements to a certain desired value is by reducing the applied stress; the allowable bearing capacity is the value of the applied stress at the footing base that will result in a given settlement. The more stringent the settlement criterion the less the stress that can be applied to the footing which in turn means that the allowable bearing capacity is correspondingly reduced. In allowable bearing capacity estimation, a total safety factor of 2.5~3.0 is mostly used. Allowable bearing capacity (shear failure vs. settlement ) (source: Geotechnical Engineering: Shallow Foundations by Zhou, Y., FHWA UNIVERSITY NHI OF

9 Structural design concept and procedure Foundation design procedures typically provide soil bearing pressures on an allowable stress design (ASD) basis while seismic forces in the 1997UBC, and in most concrete design under ACI 318, are on an ultimate strength design (USD) basis. The designer makes a transition from the ASD procedure to determine a size of the footing to the USD procedures to design the footing.

10 Example of a combined footing They are used primarily when the column spacing is non uniform (Bowles, 1996) or when isolated spreadfootings become so closely spaced that a combination footing is simpler to form and construct. Spill through

11 Theory vs. Reality (1/2) There are various theories to predict (1) shear failure and (2) load deformation behavior of soil. Why: semi empirical nature and uncertainty General shear failure Variation of frictional shear strength factor Elastic settlement analysis methods: Newmark, Griffiths, Janbu et al., Mayne and Poulos Schmertmann, Meyerhof, Burland and Burbidge Local shear failure

12 Theory vs. Reality (2/2) At the present time, various methods are available to calculate l the elastic settlement. They are, in general, in two categories; (1) methods based on observed settlement of prototypes that are correlated within in situ tests such asthe Standard Penetration Test (SPT), the Cone Penetration Test (CPT), Pressuremeter Test (PMT), and the flat dilatometer test; and Schemertmann s influence line method (2) methods based on the theory of elasticity such as the Stress Influence Method (Newmark s solution of Boussinesq Eqn.) and the Strain (displacement) Influence Method Despite all the extensive library of methods, uncertainties always exist in predicting settlements of the shallow foundation in soil due to highly erratic density and compressibility variation. If soil were elastic, homogeneous, and isotropic, there would be no difficulty in the settlement prediction using the theory of elasticity. In reality, not only are actual soils nonhomogeneous (e.g., strata formation) and anisotropic (e.g., the elastic modulus varying with depth), but also there is the difficulty of evaluating the in situ stress strain strain properties. Reliability based based method is on the horizon.

13 Necessity of a numerical analysis tool For practical application in design practice, a reliable standardized procedure has to be a combination of these two methods. The theory of elasticity : the basis for establishing approximate methods for predicting settlements for practical design where a computationallyefficient numerical procedure to estimate representative soil properties based on in situ tests answers to the all important question of selecting a soil stiffness (modulus) for use in these approximated results. Goal: simulate the soil structure interaction in the field conditions where a proposed p model would allow the engineer to easily calibrate and modify the modeling parameters by capturing the soil nonlinearity within a reasonable margin of conservative errors.

14 Winkler model Overview of model components Euler beam theory Schematic diagram of primary model components Application of Euler Beam Theory

15 Linear Finite Element Analysis of Winkler problem Discrete element approach Concept of discretization

16 Coefficient of subgrade reaction If a flexible foundation is to be analyzed, then it is recommended that Subgrade Modulus, i.e., the coefficient of subgrade reaction, be selected in consideration of geometry (B or L) and embedment depth (Terzaghi 1955 and Vesic 1961, respectively). This is because the value of subgrade modulus is not constant t for a given soil but depends on length, width, andembedment depth of the foundation under consideration.

17 FEA model of a combined footing A combined footing that supports a three column façade is subjected to service loads. Dimensions of the column is 1 m x 1m. The bearing soil is a 10 m thick medium dense sand. Compute an immediate settlement due to service loads only. Linear FEA model of Winkler problem A schematic sketch of a combined footing

18 FB MultiPier Nonlinear Finite Element Analysis Shallow foundation system is modeled using finite shell elements and soil springs. A schematic sketch of FEA model of spreadfooting Spring stiffness

19 FB MultiPier Nonlinear FEA vs. linear (Winkler) FEA Soil nonlinear behavior significantly affects the load displacement behavior of the strip footing. Qu is about kn for a friction angle of 30 deg. Variation of elastic settlement prediction

20 FB MultiPier Nonlinear FEA vs. Linear FEA What if a factor of safety of 3 is used in design, i.e., a maximum service load is limited to Qu/3=12716 kn. That s about a total applied load. But settlement is still too excessive (linear analysis predicts about 12 in settlement whereas nonlinear FEA predicts 18 in. settlement at 1/3 of Qu) and not acceptable. Concept of safety factor

21 FB MultiPier Nonlinear FEA vs. linear FEA Even with a factor of safety of 3, the predicted settlement is too excessive. If the settlement is limited to 2 in., an allowable load is 2086 kn (459 kips). Recall a total applied load of13500kn (3000 kips). Application of serviceability limit

22 Interpretation of the numerical results Limitation of linear elastic analysis Stiffness of soil is constant and independent of applied loads The footing behaves almost like a rigid body (relatively speaking) Deflection of the footing is predicted to be 0.33 m (13 in.) The current footing design (size) is inadequate for serviceability Considering an excessive deformation, reliability of the results is in question Soil could be in near failure stages; what would be the ultimate bearing capacity of the footing? Membrane stiffness of footing may be a contributing factor to flexure and, thus, deflection. FB MultiPier solution captures nonlinear soil structure interaction phenomena.

23 Parametric study (weak soil) Loose sand with k=1000 kn/m^3 and Internal friction angle = 30 deg. Deformation of a strip footing founded on soft soil

24 Parametric study (stiff soil) Dense sand with k=12000 kn/m^3 and Internal friction angle = 38 deg. Deformation of a strip footing founded on stiff soil

25 Parametric study (stiff soil) FB MultiPier nonlinear FEA results

26 2. FB MultiPier FEA model development FB MultiPier is a 3 D nonlinear FEA software program for use in bridge pier application. With a proven record of the validity, FB MultiPier is widely used in analysis of bridge subfoundations both in U.S. and world wide. A step by step procedure of FB MultiPier shallow foundation model development is provided in the following. Spreadfooting (from FHWA NHI , Dec./2006)

27 Example of FB MultiPier FEA model development A single, rigid square foundation (118 in X 118 in) is to be constructed to support a column load. Assume that the supportingsoil is a mediumm dense sand whose angle of internal friction, total unit weight, and subgrade modulus are equal to 32 degrees,109 pcf, and 150 pci, respectively.

28 Step 1 : Select a problem type

29 Step 2 : Select global parameters Go to Analysis page and specify a maximum number of iteration and the tolerance for a degree of accuracy of numerical solution. User must be familiar with the numerical solution procedure of FB MultiPier in nonlinear analysis and choose an appropriate tolerance for problem of interest.

30 Step 3 : Discretization of footing Change a pile cap grid spacing in Pile Edit and locate a pile at the center of the pile cap. NOTE: At least one pile must be assigned. In Step 8, it will be explained how to make the axial resistance of this pseudo pile negligible and thus, its contribution to the bearing capacity of the foundation can be minimal.

31 Step 3 : Discretization of footing Change a pile cap grid spacing in Pile Edit and locate a pile at the center of the pile cap. NOTE: At least one pile must be assigned. In Step 8, it will be explained how to make the axial resistance of this pseudo pile negligible and thus, its contribution to the bearing capacity of the foundation can be minimal. Mesh generation Grid spacing table

32 Step 4 : Specify a footing elevation Change the cap (footing) elevation accordingly to the ground surface. NOTE: The pile cap is modeled using finite thin shell elements. The centerline elevation of the cap (the shell elements) must be properly located to include the half of the cap thickness. The length of a pseudo pile have to be at least equal to the pile cap thickness: by default, the program expects to have at least one pile embedded in the soil. Footing dimensions Footing elevation

33 Step 5 : Choose Bearing Resistance option Step 6 : Specify material ilproperties of footing

34 Bearing Resistance option

35 Step 7 : Specify soil material properties Select a lateral py model of medium dense sand of interest. The bearing stiffness in the soil cap interaction is controlled by the lateral py model of the FB MultiPier program; internal friction angle and subgrade modulus are the key parameters in order to compute the bearing stiffness of cohesionless soil whereas undrained shear strength (= cohesion) is used as to compute the bearing stiffness for cohesive soil. Soil page Soil properties

36 Step 8 : Modify the axial soil models A pile length of 5 ft is chosen in the model. Set values for ultimate skin friction of the soil axial model (tz curve) and axial bearing failure load of the soil tip model (qz curve) equal to a small magnitude, e.g., psf and kips. By doing so, the axial resistance of the pile becomes negligible. At minimum, one pile must be included in the model. Tip properties (Q z curve) Axial properties (T z curve)

37 Step 9 : Validation of the results For this particular example, FB MultiPier solution process can converge with a tolerance of 0.01 kip of which the foundation is subjected to an axial load of 200 kips and resulting displacement is in. With an applied load greater than 1000 kips, convergence fails for a tolerance of kip as the theoretical ultimate bearing capacity of the foundation is computed as ksi, which is equivalent to an applied load of kips to a square shallow foundation with a size of 118 in X 118 in.

38 Step 9 : Validation of the results

39 Step 10 : Interpretation of the data The data from all shell elements consist of shear and moment. It is important to note that the moments and shear results are per unit length of plate. For example, unit of moment is kn m per m (or kip in per in in US customary unit) and unit of shear is kn per m (or kips per in). Moment (My) contour FB MultiPier 3 D results window

40 3. Theoretical basis of FB MultiPier FEA model Theory and Implementation of nonlinear soil structure interaction 3.1 Computation of soil resistance: Newmark s solution of Boussinesq s equation 3.2 Constitutive relationship: Hyperbolic model by Duncan and Chang 3.3 Homogenezation of heterogeity: Averaging methods Three dimensional view of variation of stress in elastic medium

41 3.1 Computation of soil resistance (1/3) Newmark s load characterization: stress under a rectangular area of uniform contact pressure by Boussinesq (1885)

42 3.1 Computation of soil resistance (2/3) Stress superposition method is applied to analytical solution of Boussinesq s equation by Newman (1935) Superposition technique Variation of the influence factors beneath the corner (red) and the center (blue)

43 3.1 Computation of soil resistance (3/3) Variation of induced vertical compressive stresses beneath a rectangular shallow foundation Three dimensional view of variation of stress in elastic medium

44 3.2 Constitutive relationship: hyperbolic model Kondner s original model (1963) Duncan and Chang model (1970) Hyperbolic stress strain relationship

45 3.2 Constitutive relationship Duncan and Chang (1970) model is conceptually simple and computationally robust The two parameters of this nonlinear stress strain relationship can be directly obtained from drained triaxial compression test of both cohesive and cohesionless soil whereas the model parameters are also abundantly available in the literature Limitation Numerical instability may occur when stress approaches shear failure No volume change due to shear stress is considered, d i.e. shear dilatancy Input parameters must be selected appropriately for soil conditions; what if Non homogeneous soil condition exists Quasi static static analysis only

46 3.3 Homogenezation of heterogeneity Averaging techniques of the elastic modulus of the soil is evaluated over a depth of the shallow foundation Bowles weighted averaging method (shown in the right) Equivalent thickness method (predicts very comparable results to Texas A&M load test) Anisotropy averaging method (great for strain influence method; compatible for strain energy approach) Schematic sketch of soil layers and the influence depth (H)

47 On going efforts at BSI Goal Develop a versatile, easy to use computational tool for design engineers Objectives Sh Schemertmann s influence line method is being bi implemented di in FB MultiPier expected release date: May/2012 Make both stress and strain influence methods available for engineers to minimizeuncertainty in characterization of soil stiffness Provide engineers with a well documented validation using relevant in situ and load test results, i.e., a degree of the validity of the numerical model Refine the tool based on feedback from the engineers continual efforts.

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