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
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)
• 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)
• N60 = Corrected blow count to a “reference hammer” which is 60% efficient and other
factors
• N = blow count from field test
6
.
0
60
h
d
s
b
C
C
C
E
N
=
N
Note max. value
( )
kPa) Units, (SI 2 100 ksf) Units, (U.S. 2 2 60 60 1 ≤ ′ = ≤ ′ = = vo N vo N N C C N C N σ σEffect of Soil
Compressibility
• Vesić Compressibility Factor
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
• 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
φ
tan
o rp
c
G
I
+
=
r r rrI
I
I
Δ
+
=
1
(
+
μ
)
=
1
2
E
G
Values of Young’s Modulus
and Poisson’s Ratio
Inclusion of Soil
Compressibility Factors
( )
⎭ ⎬ ⎫ ⎩ ⎨ ⎧ + + ⎥⎦ ⎤ ⎢⎣ ⎡ −=
φ φ φ sin 1 2 log sin 07 . 3 tan 25 11 5 3 Ir L B qe
C
φ
tan 1 q q q c N C C C = − − c C γ C Cq =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
Meyerhof Slope Factors
Top 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
7'
4.5 kips/ft wall length
Clay (φ = 0) γ = 100 pcf c = 1 ksf 2' 20' 60º
Example of Footings on
Slopes
• 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 B FS 2 0.2 10 4.4 4.6 10.22 2.5 0.28 9 4.5 4.7 9.4 3 0.38 8 4.6 4.8 8.53 3.5 0.5 7 4.9 5.1 7.93 4 0.67 6 5 5.2 6.93 4.5 0.9 5 5.3 5.5 6.11 5 1.25 4 5.7 5.9 5.24 5.5 1.83 3 6.2 6.4 4.27 6 3 2 6.9 7.1 3.16 6.5 6.5 1 7 7.2 1.6 Ncq qult • 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
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