The document discusses bearing capacity, which is the ability of soil to safely support the load from a structure without failing. It presents Terzaghi's model of three soil zones under a foundation and his bearing capacity equation. The equation considers cohesion, overburden pressure, footing width and depth factors. Graphs show bearing capacity factors varying with soil friction angle. An example calculates the net allowable bearing capacity of an overconsolidated clay foundation.

1. BEARING CAPACITY
OF SHALLOW
FOUNDATIONS
‫قدرة تحمل التربة‬
‫للساسات الضحلة‬
April 5, 2012 Bearing Capacity 1

2. BEARING CAPACITY OF SOILS
Bearing capacity is the ability of soil to safely carry
the pressure placed on the soil from any engineered
structure without undergoing a shear failure with
accompanying large settlements.
‫قدرة تحمل التربة هى مقدرة التربة على أن تتحمل‬
‫بأمان الضغط الواقع عليها من أى منشأ هندسى بدون‬
.‫حدوث انهيار بالقص مصحوبا بهبوط كبير‬
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3. Terzaghi B/C Assumptions
Three zones do exist:
1- Active zone, just below the foundation.
.‫1- القطاع الفعال: أسفل الساسات مباشرة‬
2- Transition zone, between the active and passive zones.
‫2- القطاع النتقالى: بين القطاع الفعال والقطاع‬
.‫المقاوم‬
3- Passive zone, near the ground surface, just beside the foundation.
‫3- القطاع المقاوم: بالقرب من سطح الرض بجانب‬
.‫الساسات مباشرة‬
passive active
Transition
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4. Terzaghi Bearing Equation for
Strip Footing
qu net = c Nc + γ 1 D (Nq - 1) + 0.5 B γ 2 Nγ
Overburden
‫وزن عمود التربة‬ γ1 D
B
Failure Zone (depth ≈ 2B)
Generalized soil strength : c,φ Soil unit weight : γ 2
‫معاملت القص للتربة‬ ‫كثافة التربة أسفل الساسات‬
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5. Terzaghi Bearing Equation
qult = Cohesion Term
qult = c Nc ‫الجزء الخاص بالتماسك‬
Above F.L.
qult = c Nc + γ 1 D Nq
‫أعلى منسوب التأسيس‬
‫أعلى منسوب التأسيس‬
qult = c Nc + γ 1 D Nq + 0.5B γ 2 Nγ
Below F.L.
April 5, 2012 Bearing Capacity
‫أسفل منسوب التأسيس‬ 5

6. Terzaghi Bearing Equation
Nc, Nq, Nγ are Terzaghi B/C Coefficients, f(φ )
.‫معاملت ترزاجى لقدرة تحمل التربة، دالة فى زاوية الحتكاك الداخلى‬
C, φ are the soil shear strength parameters
‫(.معاملت القص للتربة )التماسك وزاوية الحتكاك الداخلى‬
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7. Bearing Capacity Factors
qult = c Nc + γ 1 D Nq + 0.5 B γ 2 N γ
Nc Nq Nγ
40
Ø – in Degrees
30
20
10
0
70 60 50 40 30 20 10 0 10 20 40 60 80
Nc and Nq 5.7 1.0 Nγ
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8. Terzaghi Bearing Equation
B
L P
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9. Foundation Shape Factors
qult = c.Nc λ c + γ 1 D Nq λ q + 0.5B γ 2 Nγ λ γ
For Rectangular or Square Footing
λ c = 1.0 + 0.30 B/L
λ q = 1.0 Egyptian Code of Practice
λ γ = 1.0 – 0.30 B/L
For Circular Footing
λ c = 1.30
λ q = 1.00 Egyptian Code of Practice
λ γ = 0.70
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10. Bearing Capacity of Clay, φ = 0
qult = c Nc + γ 1 D Nq + 0.50 B γ 2 N γ
For Clay:
Nc = 5.70, Nq = 1.0, Nγ = 0.0
qult = 5.70 cu + γ 1 D
qult net = 5.70 cu qall net = 1.90 cu
cu = qu/2 qu Unconfined compressive strength
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11. Bearing Capacity of Sand, cu = 0
qult = c Nc + γ 1 D Nq + 0.50 B γ 2 N γ
For Sand:
Nc, Nq, Nγ are determined from curve, and cu = 0,
then:
qult = γ 1 D Nq + 0.50 B γ 2 N γ
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12. Gross and Net Bearing Capacity
qult
qall = Gross allowable bearing capacity
F .S .
qult = qult net + γ 1 D Gross ultimate B/C
qult net
qall = + γ1 D Gross allowable B/C
F .S .
qult net
qall net = Net allowable B/C
F .S .
γ 1 D is the overburden pressure
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13. Example
A strip footing of 1.8 m width is located at a depth
of 1.5 m below the ground surface, in an over-
consolidated clay layer. The groundwater level is
10 m below the ground surface. The unconfined
compressive strength of that clay is 120 kPa, γ bulk
= 18 kN/m3, and γ sat = 20 kN/m3. Determine the
net allowable bearing capacity, assuming a factor
of safety of 3.
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14. Solution
qult = c Nc + γ 1 D Nq + 0.5B γ 2 Nγ
For Clay: Nc = 5.7, Nq = 1.0, Nγ = 0.0
qult net = c Nc + γ 1 D (Nq -1)
qu = 120 kPa, cu = 60 kPa
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15. qult net = 60 x 5.7 = 342.00
qult net 342
qall net = = = 114.00 kN/m 2
F .S . 3
qall net = 11.40 t/m2 = 1.14 kg/cm2
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16. . Bearing capacity factors for differentφ
φo Nc Nq Nγ
0 5.0 1.0 0.0
5 6.5 1.50 0.0
10 8.5 2.5 0.50
15 11.0 4.0 1.0
20 15.0 6.50 2.0
22.50 17.50 8.0 3.0
25.0 20.50 10.50 4.50
27.50 25.0 14.0 7.0
30.0 30.0 18.0 10.0
32.50 37.0 25.0 15.0
35.0 46.0 33.0 23.0
37.50 58.0 46.0 34.0
40.0 75.0 64.0 53.0
42.50 99.0 92.0 83.0
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