GLE/CEE 330: Soil Mechanics Settlement of Shallow Footings Geological Engineering University of Wisconsin-Madison

Learning Objectives Discuss service limit state Learn approach for estimating consolidation settlement Learn approach for estimating elastic settlement Learn approaches for estimating settlement from results of field tests (SPT & CPT)

Foundation Design Philosophy Limit State = “condition beyond which a component/member of a foundation or other structure ceases to satisfy the provisions for which the component/member was designed” Strength Limit State (bearing capacity analysis) Service Limit State (settlement analysis) Extreme Event Limit State Fatigue Limit State

Settlement of Shallow Footings Total Settlement (d) d Differential Settlement (dD) dD S Angular Distortion(q) dD q=dD/S

Serviceability Requirements Total Settlement (d) Typical Values Type of Structure dmax (in) dmax (mm) Office Building 0.5 – 2.0 12-50 Heavy Industrial 1.0 – 3.0 25 - 77 Bridges 2.0 50 Need to consider: Connections (other structures) Utilities (gas, electric, hydraulic) Surface Drainage Access Aesthetics

Serviceability Requirements Differential Settlement (dD) q = angular distortion S = span (e.g., column spacing, footing width) Typical Values Type of Structure q Steel Tanks 1/25 Bridges (simple supp.) 1/125 Commercial Buildings 1/500 Machinery Foundations 1/1500

Types of Settlement Analysis Primary Consolidation Settlement (Time Dependent) Elastic Settlement (Immediate)

Primary Consolidation Settlement Similar to 1D consolidation analysis (Cr, Cc, s’p) Must consider how induced load varies with depth and rigidity of footing s’zf = final vertical effective stress beneath center of footing s’z0= initial vertical effective stress beneath center of footing (sz)induced= induced vertical total stress beneath center of footing Initial effective stress and induced stress vary with depth break into sublayers and calculate settlement of each do analysis at middle of each layer the more layers, the more accurate

Generally 3 layers is sufficient for manual calculations… (e.g., square footing) Df B B/2 B 2B

B B/2 2B zf P q = P/A Df Circular Footings: Square Footings:

B B/2 2B zf P q = P/A Df Strip Footings: Rectangular Footings:

P Calculate d for each layer… q = P/A Normally Consolidated Clay (s’z0 = s’p) r = “rigidity factor” (r = 0.85 for reinforced concrete, r = 1.0 for flexible footing) Log s’ e Cc Df B B/2 zf B Overconsolidated Clay – Case I (s’zf < s’p) Log s’ e Cr 2B Overconsolidated Clay – Case II (s’z0 < s’p < s’zf ) Log s’ e Cr Cc

Elastic Settlement (Clay) Arbitrarily shaped footing Settlement: Undrained Elastic Parameters (UU Triaxial Tests): Eu = Undrained elastic modulus vu = Undrained Poisson’s ratio Shape, Embedment, and Side-Wall Factors:

Settlement Based on Field Tests Most applicable for coarse-grained soils (difficult to obtain high quality lab samples) Standard Penetration Test (SPT) Cone Penetration Test (CPT) Plate Load Test (PLT)

Elastic Settlement Based on SPT Normally Consolidated Sand: (Burland and Burbridge, 1985) r = mm sa = vert. stress applied by footing N = uncorrected blow count See Budhu, Section 9.11.1

What N value do we use???? Boring 1 Boring 2 15 16 18 20 17 23 B N = ? Use some average in the heavily loaded zone (z = Df + B) Pick a conservative value (lowest N) Use engineering judgment!

Elastic Settlement Based on CPT Sands: (Schmertmann, 1970) See Budhu, Section 9.11.2