Finite Element Analysis y of Elastic Settlement of Spreadfootings Founded in Soil Jae H. Chung, Ph.D. Bridge Software Institute  B id S ft I tit t Un...

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

Jae H. Chung, Ph.D. Bridge Software Institute  B id S ft I tit t University of Florida, Gainesville, FL, USA

UNIVERSITY OF

Civil & Coastal

FLORIDA Engineering

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

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

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Strength vs. Serviceability (2/3) • An ultimate limit state (ULS) corresponds to the maximum  load‐carrying capacity  (either structural or geotechnical  fail re) of the fo ndation The ltimate state is also called the failure) of the foundation. The ultimate state 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. serviceability, and occurs before collapse. • excessive differential or total foundation settlements, • excessive lateral displacements, or • structural deterioration of the foundation. structural deterioration of the foundation UNIVERSITY OF

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Strength vs. Serviceability (3/3) • All relevant limit states must be considered in foundation  design to ensure an adequate degree of safety and   ser iceabilit All fo ndation design in practice is geared serviceability. All foundation design in practice is geared  towards addressing the ULS and the SLS. • Existing design methodology includes: g g gy • the Allowable Stress Design (ASD) • the Ultimate Strength Design (USD) • the Load and Resistance Factor Design (LRFD)  t e oad a d es sta ce acto es g ( )

• Focus is made on ASD for geotechnical design.

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Design concept and procedure (1/4) • The geotechnical design of a spread footing is a two‐part  process.  1 1.

2 2.

EEstimate the allowable soil bearing capacity to ensure stability of the  i h ll bl il b i i bili f h foundation and determine if the proposed structural loads can be  supported on a reasonably sized foundation.  P di Predict an amount of settlement due to the actual structural loads and  f l d h l ll d d the time of occurrence estimated. Experience has shown that  settlement is usually the controlling factor in design.  • Thi This is not surprising since structural considerations usually limit tolerable  i t ii i t t l id ti ll li it t l bl settlements to values that can be achieved only on competent soils not  prone to a bearing capacity failure.

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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 results in a specified amount of settlement; this is a  Th li d t th t lt i ifi d t f ttl t thi i 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 (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 within the influence depth.

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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 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 ) UNIVERSITY OF (source: Geotechnical Engineering: Shallow Foundations by  Zhou, Y., FHWA NHI‐06‐089

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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 1997 UBC and in most concrete design seismic forces in the 1997 UBC, 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  g p determine a size of the footing to the USD procedures to  design the footing.

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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.

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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: y Newmark, Griffiths, Janbu et al., Mayne and Poulos Schmertmann, Meyerhof, Burland and Burbidge

Local shear failure

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Theory vs. Reality (2/2) A h At the present time, various methods are available to calculate the elastic  i i h d il bl l l h l i settlement. They are, in general, in two categories;  (1) methods based on observed settlement of prototypes that are correlated  with in situ tests such as the Standard Penetration Test (SPT) the Cone with in situ tests such as the Standard Penetration Test (SPT), the Cone  Penetration Test (CPT),  Penetration Test (CPT), Pressuremeter Pressuremeter Test (PMT), and the flat dilatometer  test; and  Schemertmann’ss influence line method Schemertmann influence line method (2) methods based on the theory of elasticity such as the Stress Influence  Method (Newmark’s Method ( Newmark’s solution of Boussinesq solution of Boussinesq Eqn.) and the Strain  ((displacement) Influence Method  p ) 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  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),  b but also there is the difficulty of evaluating the in situ stress‐ but also there is the difficulty of evaluating the in situ stress t l th i th diffi lt f l ti th i it t ‐strain properties.  t i ti Reliability‐‐based method is on the horizon. Reliability based method is on the horizon. UNIVERSITY OF

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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  The theory of elasticity : the basis for establishing approximate methods for predicting settlements for practical design where a computationally‐ efficient numerical procedure to estimate “representative” soil properties  based on in situ tests answers to the all important question of selecting a  p q g soil stiffness (modulus) for use in these approximated results.  • Goal: simulate the soil‐structure interaction in the field conditions where a  p p proposed model would allow the engineer to easily calibrate and modify  g y y the modeling parameters by capturing the soil nonlinearity within a  reasonable margin of conservative errors.

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Winkler model Overview of model components

Schematic diagram of primary model components

Euler beam theory

Application of Euler Beam Theory  UNIVERSITY OF

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Linear Finite Element Analysis of Winkler problem Linear Finite Element Analysis  of Winkler problem Discrete element approach

Concept of discretization UNIVERSITY OF

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Coefficient of subgrade 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). ti l ) This Thi is i because b th value the l off subgrade b d modulus d l is i nott constant t t for f a given soil but depends on length, width, and embedment depth of the foundation under consideration.

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FEA model of  FEA model of a combined footing 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 UNIVERSITY OF

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FB‐‐MultiPier Nonlinear Finite Element Analysis  FB Shallow foundation system is modeled using finite shell elements  and soil springs.

A schematic sketch of FEA model of spreadfooting

Spring stiffness

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FB‐‐MultiPier Nonlinear FEA vs. linear (Winkler) FEA FB Soil nonlinear behavior significantly affects the load‐displacement behavior of  the strip footing. Qu is about 38150 kN for a friction angle of 30 deg.

Variation of elastic settlement prediction UNIVERSITY OF

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FB‐‐MultiPier Nonlinear FEA vs. Linear FEA FB 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. l d l / f ) d bl

Concept of safety factor

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FB‐‐MultiPier Nonlinear FEA vs. linear FEA FB 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 of 13500 kN (3000 kips).  Recall a total applied load of 13500 kN (3000 kips)

Application of serviceability limit

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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  l l l l interaction phenomena.

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Parametric study (weak  Parametric study (weak soil) soil) Loose sand with k=1000 kN/m^3 and  Internal friction angle = 30 deg.

Deformation of a strip footing founded on soft soil UNIVERSITY OF

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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 UNIVERSITY OF

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

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2. FB 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. shallow foundation model development is provided in the following.

SSpreadfooting df ti (from FHWA NHI‐06‐089, Dec./2006) UNIVERSITY OF

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Example of FB‐‐MultiPier FEA model development Example of FB • A single, rigid square foundation (118 in X 118 in) is to be constructed to support a column load. Assume that the s pporting soil is a medium supporting medi m dense sand whose hose angle of internal friction, total unit weight, and subgrade modulus are equal to 32 degrees,109 pcf, and 150 pci, respectively.

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Step 1 : Select a problem type

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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.

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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.

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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

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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 elevation g Footing dimensions

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Step 5 : Choose “Bearing Resistance” option S Step 6 : Specify material properties of footing 6 S if i l i ff i

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“Bearing Resistance” option

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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 UNIVERSITY OF

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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., 0.001 psf and 0 001 kips By doing so the axial resistance of the pile becomes negligible At and 0.001 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) UNIVERSITY OF

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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 0.1076 in. With an applied load greater than 1000 kips, convergence  fails for a tolerance of 0 1 kip as the theoretical ultimate bearing capacity of the fails for a tolerance of 0.1 kip as the theoretical ultimate bearing capacity of the  foundation is computed as 0.0720 ksi, which is equivalent to an applied load of 1002.5  kips to a square shallow foundation with a size of 118 in X 118 in.

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Step 9 : Validation of the results

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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) m (or kips per in).

Moment (My) contour

FB‐MultiPier 3‐D results window UNIVERSITY OF

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3. Theoretical basis of FB‐ 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 3.2 Constitutive relationship: Hyperbolic model by Duncan and Chang 3.3 Homogenezation of heterogeity: Averaging methods

Three‐dimensional view of variation of  Three‐dimensional view of variation of stress in elastic medium UNIVERSITY OF

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

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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)

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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 UNIVERSITY OF

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3.2 Constitutive relationship: hyperbolic model

Kondner’s original model (1963)

Hyperbolic  stress‐strain relationship Duncan and Chang model (1970)

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

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3.3 Homogenezation 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 q (predicts very comparable  results to Texas A&M load test) • Anisotropy  averaging method Anisotropy averaging method (great for strain influence  method; compatible for strain  energy approach) energy approach)

Schematic sketch of soil layers and the  influence depth (H) influence depth ( H) UNIVERSITY OF

Civil & Coastal

FLORIDA Engineering

On‐‐going efforts at BSI On • Goal • Develop a versatile, easy‐to‐use computational tool for design  Develop a versatile easy to use computational tool for design engineers • Objectives • Schemertmann’s S h t ’ influence line method is being implemented in FB‐ iinfluence line method is being implemented in FB fl li th d i b i i l t d i FB‐MultiPier  M ltiPi – MultiPier – expected release date: May/2012 expected release date:  May/2012 • Make both stress and strain influence methods available for engineers to  minimize uncertainty in characterization of soil stiffness minimize uncertainty 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 – g continual efforts.

UNIVERSITY OF

Civil & Coastal

FLORIDA Engineering