Calculation of Heave of Deep Pier Foundations By John D. Nelson, Ph.D., P.E., Hon. M. SEAGS, F. ASCE, Kuo-Chieh (Geoff) Chao, Ph.D., P.E., M. SEAGS, M. ASCE, Daniel D. Overton, M.S., P.E., F. ASCE, and Robert W. Schaut, M.S., P.E., M. ASCE August

DAMAGE FROM EXPANSIVE SOILS Photo of Shear Failure in South Side of Pier at N7

Outline of Presentation Introduction Free-Field Heave Prediction Pier Heave Prediction Validation of APEX Pier Design Curves Example Foundation Design Conclusions

INTRODUCTION Pier and grade beam foundations are a commonly used foundation type in highly expansive soils. Existing pier design methods consider relatively uniform soil profiles, and piers with length to diameter ratios of about 20 or less. Fundamental parameter on which foundation design is based is the “Free-Field Heave“ (i.e. the heave of the ground surface with no applied loads) A finite element method of analysis (APEX) was developed to compute pier movement in expansive soils having: Variable Soil Profiles, Complex Wetting Profiles, Large Length-to-Diameter Ratios, and Complex Pier Configurations and Materials

FREE-FIELD HEAVE PREDICTION

FREE-FIELD HEAVE PREDICTION by Oedometer Method Terminology and notation for oedometer tests

FREE-FIELD HEAVE PREDICTION Determination of Heave Index, C H Vertical stress states in soil profile

FREE-FIELD HEAVE PREDICTION Stress Paths Under Different Loading Conditions C S S%S% A CcCc LOG h M E K B LOG  ’  ’ CS  ’ CV  ’ i2  ’ i1 ’i’i 0’ 0 J H P N F G L hoho h C1 D CHCH CSCS

FREE-FIELD HEAVE PREDICTION Determination of Heave Index, C H

FREE-FIELD HEAVE PREDICTION Calculations of Design Heave σ‘ vo (S % ) z

FREE-FIELD HEAVE PREDICTION Determination of Heave Index, C H

Data from Method A of the ASTM D Standard

FREE-FIELD HEAVE PREDICTION Determination of Heave Index, C H Method A data from the Standard plotted in semi-log form

FREE-FIELD HEAVE PREDICTION Determination of Heave Index, C H Method A data from the Standard plotted in semi-log form

Data collected from Porter, 1977; Reichler, 1997; Feng et al., 1998; Bonner, 1998; Fredlund, 2004; Thompson et al. 2006; and Al-Mhaidib, 2006 The types of the soils consist of claystone, weathered claystone, clay, clay fill, and sand-bentonite  = 0.36 to 0.90 (avg = 0.62) for claystone = 0.36 to 0.97 (avg = 0.59) for all soil types FREE-FIELD HEAVE PREDICTION Relationship between  ′ cv and  ′ cs Logarithmic Form:

FREE-FIELD HEAVE PREDICTION Relationship between  ′ cv and  ′ cs Histograms of the λ values determined using the logarithmic form

PIER HEAVE PREDICTION Typical pier and grade beam foundation system

DAMAGE FROM EXPANSIVE SOILS Pier Diagonal Crack

PIER HEAVE PREDICTION Rigid Pier Analysis Rigid Pier Analysis P dl U D

PIER HEAVE PREDICTION Elastic Pier Analysis Normalized Pier Heave vs. L/Z AD Ref: Poulos & Davis (1980) Nelson & Miller (1992) Nelson, Chao & Overton (2007) Straight Shaft Belled Pier

PIER HEAVE PREDICTION Elastic Pier Analysis Straight Shaft Belled Pier Normalized Force vs. L/Z AD Ref: Poulos & Davis (1980) Nelson & Miller (1992) Nelson, Chao & Overton (2007)

PIER HEAVE PREDICTION APEX Method A nalysis of P iers in EX pansive soils

PIER HEAVE PREDICTION APEX Method The field equations with soil swelling where:  iso = isotropic swelling strain,  rr,  qq,  zz = components of stress and strain in cylindrical coordinates, and E = modulus of elasticity of the soil

PIER HEAVE PREDICTION APEX Method Interface Conditions soil boundary conditions pier-soil boundary conditions where: F t = the nodal force tangent to pier, H p = the pier heave, U t = the nodal displacement tangent to pier, and k = the parameter used to adjust shear stress

PIER HEAVE PREDICTION APEX Method Adjustment in pier heave initial-no force on pier soil heave-upward force on pier

PIER HEAVE PREDICTION APEX Method Soil failure and shear strain Strength envelopes for slip and soil failure modes

PIER HEAVE PREDICTION APEX Method APEX Input E = modulus of elasticity  = coeff. of adhesion ρ i = cumulative free-field heave Z AD = design active zone d = diameter of pier P dl = dead load

PIER HEAVE PREDICTION APEX Method Variation of Slip Along Pier Typical APEX results Shear Stress Distribution Along Pier

PIER HEAVE PREDICTION APEX Method Typical APEX results Axial Tensile Force (KN) (d) Axial Force Distribution

VALIDATION OF APEX Case I Manufacturing Building in Colorado, USA Case II Colorado State University (CSU) Expansive Soil Test Site

VALIDATION OF APEX Soil heave distribution for Cases I and II Case I Manufacturing Building Case II CSU Expansive Soil Test Site

VALIDATION OF APEX Elevation survey data in hyperbolic form compared with heave computed by APEX for Manufacturing Building

Measured versus predicted axial force in the concrete pier for the CSU Test Site VALIDATION OF APEX

PIER DESIGN CURVES Pier heave - linear free-field heave distribution

PIER DESIGN CURVES Pier heave - linear free-field heave distribution

PIER DESIGN CURVES Pier heave - nonlinear free-field heave distribution

EXAMPLE FOUNDATION DESIGN Weathered Claystone Claystone Sandy Claystone 0 m 5 m 10 m Z AD = 10 m D = 300mm Free-field heave = 192 mm Tolerable pier heave = 25 mm  = 0.4 w = 12 %  = 1.9 Mg/m3  E s = 9,400 kPa  S % = 2.0 %   ’ cs = 350 kPa w = 9 %  = 1.8 Mg/m3 E s = 11,200 kPa S % = 3.5 %  ’ cs = 550 kPa w = 8 %  = 1.8 Mg/m3 E s = 120,000 kPa S % = 1.86 %  ’ cs = 305 kPa

EXAMPLE FOUNDATION DESIGN Cumulative heave profile for example calculation Weathered Claystone Claystone Sandy Claystone

EXAMPLE FOUNDATION DESIGN Example pier heave computed from APEX program

EXAMPLE FOUNDATION DESIGN 0 m 5 m 10 m 15 m 20 m 25 m Weathered Claystone Claystone Sandy Claystone L = 15.3 m APEX (Uncased) L = 18.0 m Elastic Pier 0 m 5 m 10 m 15 m 20 m 25 m Rigid Pier L = 18.7 m Tolerable pier heave = 25 mm L = 11.4 m APEX (Cased)

CONCLUSIONS The rigid pier method assumes equilibrium of the pier, and hence, no pier movement, providing an overly conservative design. The elastic pier method allows for some tolerable amount of pier heave. However, it is limited to use in simplified soil profiles and uniform piers. The APEX program is a versatile and robust method of analysis. APEX allows for pier analysis within complex soil profiles where soil properties and/or water contents vary with depth. APEX generally predicts lower pier heave values, and shorter design lengths than other methods.

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