Foundation Analysis and Design

ENCE 4610 Foundation Analysis and Design Bearing Capacity Other Topics

Other Topics in Bearing  Capacity • Bearing Capacity from Field Tests o SPT o CPT

• Effect of Soil Compressibility (Local and Punching Shear) • Bearing Capacity for Foundations on Top of a Slope • Foundations on Rock

Use of SPT and CPT Methods to  Determine Bearing Capacity • Approach I: Use SPT and CPT correlations (such as we discussed in 3610) and determine soil properties (γ, φ, c) and then apply to bearing capacity equations • Approach II: Use a “direct” approach such as given in textbook (Murthy, 12.12 and 12.13) • First approach is preferable as it allows more flexibility in soil type and layering structure o Note: in this course (and the vast majority of practice) the reference standard for SPT efficiency is 60%, thus N60 = Ncor are based on this efficiency

SPT Efficiency Correction Factors (without overburden correction)

N 60

E hC d C sC b = N 0 .6

• N60 = Corrected blow count to a “reference hammer” which is 60% efficient and other factors • N = blow count from field test

• Eh = hammer type factor • Cb = borehole diameter factor • Cs = sampler correction factor • Cd = rod length factor • Factors given in Murthy (but Equation 9.6 is wrong)

Note max. value

(N1 )60 = C N N 60 CN =

2 ≤ 2 (U.S. Units, ksf) σ vo′

100 CN = ≤ 2 (SI Units, kPa) ′ σ vo

Effect of Soil  Compressibility • Bearing capacity equations presented until now are directed at the general shear case • We saw that we also had local and punching shear as well • These conditions require some consideration of the compressibility of the soil

• Vesić Compressibility Factor

E G= 2(1 + μ )

G Ir = c + po tan φ o G = shear modulus of soil o c = cohesion of soil o p0 = effective stress (in this case, at a depth of Df + B/2 o φ = friction angle of soil o Δ = volumetric strain in plastic zone

Ir I rr = 1 + ΔI r

Values of Young’s Modulus  and Poisson’s Ratio

Inclusion of Soil  Compressibility Factors Cc

Cc = C q −

1 − Cq N q tan φ

Cq = Cγ

Cq = e

⎧ ⎡ 3 B 11 ⎤ 3.07 sin φ log ( 2 I r ) ⎫ − + tan φ ⎨⎢ ⎬ ⎥ L 1 sin φ + 5 25 ⎦ ⎩⎣ ⎭

Application of Soil  Compressibility Factors • Determine the modulus of elasticity and Poisson’s ratio for the given soil (use values in earlier slide) • Compute Ir using these values and other soil properties (c, φ, γ and compute effective stress) • Determine critical rigidity index Ircrit (Murthy Table 12.4 or Equation 12.35) • Compare your result of Ir with Ircrit o If Ir > Ircrit, then soil is incompressible and ignore compressibility factors o If Ir < Ircrit, then soil is compressible and include compressibility factors in bearing capacity analysis

• Compute bearing capacity equations w/compressibility factors

Bearing Capacity for  Foundation at Top of a Slope • Two Approaches o Use Vesić’s bearing capacity factor for foundations on slopes o Use Meyherhof’s method given in text (Murthy, 12.15)

• Outine of Meyerhof’s Method o Bearing capacity equations are the same as given earlier except for the following: • Do not use Vesić’s bearing capacity factor for foundations on slopes • Replace the main bearing capacity factors (Nc, Nγ, Nq) with factors for slopes (Ncq, Nγq, Nqq) • Ncq, Nγq given in the following slides for two cases: foundation on top of the slope and foundation at the base of the slope (latter not in Murthy) • Nqq = 0 always • Handle water table same way as any other layered foundation

Meyerhof Slope Factors Top of Slope

Meyerhof Slope Factors: Base of Slope

Example of Footings on  Slopes • Given o Bearing wall for warehouse o Located close to slope

• Find o Size of strip footing to be provided, ignore weight

4.5 kips/ft wall length 60º

2'

20' 7'

Clay (φ = 0) γ = 100 pcf c = 1 ksf

Example of Footings on  Slopes Curve used

• For this problem, b = 7 – B/2 < Hs = 20’ • From that, Ns = 0 • We thus use the top, “dashed” portion of the chart

Example of Footings on  Slopes b b/B 2 0.2 2.5 0.28 3 0.38 3.5 0.5 4 0.67 4.5 0.9 5 1.25 5.5 1.83 6 3 6.5 6.5

B Ncq qult FS 10 4.4 4.6 10.22 9 4.5 4.7 9.4 8 4.6 4.8 8.53 7 4.9 5.1 7.93 6 5 5.2 6.93 5 5.3 5.5 6.11 4 5.7 5.9 5.24 3 6.2 6.4 4.27 2 6.9 7.1 3.16 1 7 7.2 1.6

• qult = cNcq + 0.5γBNγq (Murthy Eq. 12.66) • Nγq = 1 (Murthy Eq. 12.67) • From the above, qult = cNcq + 0.5γB (Murthy Eq. 12.68) • FS = B qult / P • From the table, B = 2’

Required Footing  Setbacks For example problem: H/3 = 20/3 = 6.67' from 45 degree line

Other Notes on Bearing  Capacity Factors •

• •

AASHTO (2002) guidelines recommend calculating the shape factors, s, by using the effective footing dimensions, B′f and L′f. However, the original references (e.g., Vesić, 1975) do not specifically recommend using the effective dimensions to calculate the shape factors. Since the geotechnical engineer typically does not have knowledge of the loads causing eccentricity, it is recommended that the full footing dimensions be used to calculate the shape factors for use in computation of ultimate bearing capacity. Bowles (1996) also recommends that the shape and load inclination factors (s and i) should not be combined. In certain loading configurations, the designer should be careful in using inclination factors together with shape factors that have been adjusted for eccentricity (Perloff and Baron, 1976). The effect of the inclined loads may already be reflected in the computation of the eccentricity. Thus an overly conservative design may result.

Bearing Capacity on Rock • Generally, the limit-state approach used with soils is not applied to rock. • Spread footings on rocks are generally designed according to a “presumptive bearing capacity” approach, where a maximum q is determined based on the type and quality of the rock • The Rock Quality Designation (RQD) is commonly used to determine the bearing capacity of foundations in rock • For foundations on unweathered intact rocks, the rock may have greater structural strength than the concrete, and thus bearing capacity determination becomes unnecessary

Bearing Capacity on  Rock: Tables

Questions?