Geotechnical Engineering

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UNIVERSITI MALAYSIA PAHANG Department of Civil
and Environmental Engineering

• Geotechnical Engineering
• BAA 3513
• Chapter 3 Shallow Foundation Part 2 3

Muzamir bin Hasan, M.Eng. Lecturer
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Shallow Foundation

• In designing shallow foundation, certain criteria
  are to be considered
• The factor of safety against shear failure must
  be adequate (FS 2.5 3.0)
• Settlement must not be more than structures
  limits
• For cohesionless soil ? 50 mm
• For cohesive soil - ? 75 mm

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Terzaghis Theory of Bearing Capacity

• There is no method in obtaining the ultimate
  bearing capacity of the foundation other than
  estimation
• The most popular Terzaghi equations
• Assumption made
• - only consider shallow foundations
• - consider rough base
• There are frictions and cohesions exist between
  the base and the soil
• These frictions and cohesions prevent failure
  wedge from occurring underneath the foundation

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Terzaghis Theory of Bearing Capacity

• Bearing Capacity Failure

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Terzaghis Theory of Bearing Capacity

• Bearing Capacity Failure
• How do we estimate the maximum bearing pressure
  that the soil can withstand before failure
  occurs?

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Terzaghis Theory of Bearing Capacity
The ultimate bearing capacity
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Terzaghis Theory of Bearing Capacity
The allowable load
The gross allowable load
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Terzaghis Theory of Bearing Capacity
The net ultimate bearing capacity
The net allowable bearing capacity
The net gross allowable load
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Terzaghis Theory of Bearing Capacity

• Bearing Capacity Failure
• Types/Modes of Failure
• general shear failure
• local shear failure
• punching shear failure

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Terzaghis Theory of Bearing Capacity

• General Shear Failure
• Continues failure surface develop between edges
  of the footing and the ground surface
• State plastic equilibrium fully developed
  throughout the soil above the failure surface.
• Therefore heave occurs on both sides of the
  footing although the final slip movement would
  occur only on one side accompanied by tilting of
  the footing
• Typical failure mode for soil of low
  compressibility (dense/silt soil)
• Well defined the qu from the area

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Terzaghis Theory of Bearing Capacity

• General Shear Failure

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Terzaghis Theory of Bearing Capacity

• Local Shear Failure
• Significant compression of the soil under the
  footing and only partial development of the state
  of plastic equilibrium.
• Slight heaving occurs
• Tiling of the foundation is not expected
• Associated with high compressibility soils (very
  soft, soft soil, very loose, loose)
• Characterized by the occurrence of relatively
  large settlement, qu not clearly defined

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Terzaghis Theory of Bearing Capacity

• Local Shear Failure

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Terzaghis Theory of Bearing Capacity

• Punching Shear Failure
• Occurs when there is relatively high compression
  of soil under footing, accompanied by shearing in
  the vertical direction around the edges of the
  footing
• No heaving of the ground surface and no tilting
  of the footing
• Large settlement with no failure plane and cause
  vertical movement
• Qu is not well defined
• Depends on the compressibility of the soil and
  depth of foundation

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Terzaghis Theory of Bearing Capacity
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Terzaghis Theory of Bearing Capacity
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Terzaghis Theory of Bearing Capacity

• Factor of Safety
• Type of soil
• Level of Uncertainty in Soil Strength
• Importance of structure and consequences of
  failure
• Likelihood of design load occurrence

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Terzaghis Theory of Bearing Capacity

• Minimum Factor of Safety

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Terzaghis Theory of Bearing Capacity
L

• Bearing Capacity Analysis square base
• GENERAL SHEAR FAILURE
• L/B 1
• Where
• qu Gross ultimate bearing capacity
• Nc N? Nq bearing capacity factor (Terzaghi,
  Meyerhof, Hansen, etc. which are dimensionless
  and function of ?) Table 9.7 for General Shear
  Failure.

B
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Terzaghis Theory of Bearing Capacity
L

• Bearing Capacity Analysis square base
• LOCAL SHEAR FAILURE
• L/B 1
• Where
• qu Gross ultimate bearing capacity
• Nc N? Nq bearing capacity factor
  (Terzaghi, Meyerhof, Hansen, etc. which are
  dimensionless and function of ?) Table 9.8 for
  Local Shear Failure.

B
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Terzaghis Theory of Bearing Capacity

• Bearing Capacity Analysis circular base
• GENERAL SHEAR FAILURE
• Where
• qu Gross ultimate bearing capacity
• Nc N? Nq bearing capacity factor (Terzaghi,
  Meyerhof, Hansen, etc. which are dimensionless
  and function of ?) Table 9.7 for General Shear
  Failure.

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Terzaghis Theory of Bearing Capacity

• Bearing Capacity Analysis circular base
• LOCAL SHEAR FAILURE
• Where
• qu Gross ultimate bearing capacity
• Nc N? Nq bearing capacity factor
  (Terzaghi, Meyerhof, Hansen, etc. which are
  dimensionless and function of ?) Table 9.8 for
  Local Shear Failure.

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Terzaghis Theory of Bearing Capacity
L

• Bearing Capacity Analysis - strip footing
• GENERAL SHEAR FAILURE
• L/B gt 5
• Where
• qu Gross ultimate bearing capacity
• Nc N? Nq bearing capacity factor (Terzaghi,
  Meyerhof, Hansen, etc. which are dimensionless
  and function of ?) Table 9.7 for General Shear
  Failure.

B
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Terzaghis Theory of Bearing Capacity

• Bearing Capacity Analysis - strip footing
• LOCAL SHEAR FAILURE
• L/B gt 5
• Where
• qu Gross ultimate bearing capacity
• Nc N? Nq bearing capacity factor
  (Terzaghi, Meyerhof, Hansen, etc. which are
  dimensionless and function of ?) Table 9.8 for
  Local Shear Failure.

L

B
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Terzaghis Theory of Bearing Capacity
L

• Bearing Capacity Analysis - strip footing
• If ? increases N? Nq decreases
• If ? 0 (clay) N? 0 and Nq 1
• qu
  (clay) C Nc ?
• The 1st term contribution due to constant
  component of shear strength (wedge)
• The 2nd term contribution of the self weight of
  the soil
• The 3rd term contribution due to surcharge
  (overburden pressure)

B
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Terzaghis Theory of Bearing Capacity

• Bearing Capacity Analysis

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Factor of Safety
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Factor of Safety
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Factor of Safety
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Example 9.1

• The plan of a 1.25 m square footing is shown in
  Figure 9.11. Determine the gross allowable load,
  Qall (Qall qall x area of the footing) that the
  footing can carry. A factor of safety of 3 is
  needed.

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Example 9.1
1m
? 15kN/m3 F20º c9.6kN/m2
1.25m
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Solution
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Solution
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Example 9.2

• Redo Example 9.1 assuming local shear failure

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Solution
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Solution
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Example 9.3

• A square footing is shown in Figure 9.12. The
  footing will carry a gross mass of 30,000 kg.
  Using a factor of safety of 3, determine the size
  of the footing - that is, the size of B.

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Example 9.3
30,000kg
? 1850kg/m3 F35º c0
1m
B
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Solution
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Solution
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Example 9.4

• Refer to Example 9.1. Determine the net allowable
  load, Qall(net) with an Fs3 against the net
  ultimate bearing capacity.

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Solution
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Example 9.5

• Refer to Example 9.1. Determine the gross
  allowable load with a factor of safety of 3
  against shear failure.

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Solution
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Solution
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Terzaghis Theory of Bearing Capacity
Effect of Groundwater Table
If ground water table is close to the footing,
some changes are required
Case 1 If the G.W.T. is located at a distance D
above the bottom of the foundation, -and ? in
bearing capacity equation should be replaced by
?.
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Terzaghis Theory of Bearing Capacity

• Case I

?
Groundwater table
Df
D
?sat
B
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Terzaghis Theory of Bearing Capacity
Effect of Groundwater Table
Case II If the G.W.T. coincides with the bottom
of the foundation, the magnitude of q is equal to
?Df
-and ? in bearing capacity equation should be
replaced by ?.
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Terzaghis Theory of Bearing Capacity

• Case II

?
Df
Groundwater table
?sat
B
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Terzaghis Theory of Bearing Capacity
Effect of Groundwater Table
Case III When the G.W.T. is at depth D below the
bottom of the foundation,
-and ? in bearing capacity equation should be
replaced by ?av. (for D lt B) (for D gt B)
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Terzaghis Theory of Bearing Capacity

• Case III

Df
?
D
B
Groundwater table
?sat
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Example A

• A square footing is shown in figure below. For
  the following case, determine the safe gross
  allowable load, Qall, that the footing can carry.
  Use Terzaghis equation for general shear
  failure. (Fs3). Given ? 1800 kg/m3, ?sat
  1980 kg/m3, c 23.94 kN/m2, f 20º, B 1.8 m,
  Df 1.2 m, h 0.6 m.

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Example A
?
h
Groundwater table
Df
?sat
B
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Solution
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Solution
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Example B

• A square footing is shown in figure below. For
  the following case, determine the safe gross
  allowable load, Qall, that the footing can carry.
  Use Terzaghis equation for general shear
  failure. (Fs3). Given ? 1800 kg/m3, ?sat
  1980 kg/m3, c 23.94 kN/m2, f 20º, B 1.8 m,
  Df 1.2 m.

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Example B
?
Df
Groundwater table
?sat
B
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Solution
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Solution