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.
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Bearing 2
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
April 5, 2012 Bearing Capacity 2
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
April 5, 2012 Bearing Capacity 3
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
April 5, 2012 Bearing Capacity 4
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
April 5, 2012 Bearing Capacity 6
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
April 5, 2012 Bearing Capacity 7
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
April 5, 2012 Bearing Capacity 9
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
April 5, 2012 Bearing Capacity 10
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
April 5, 2012 Bearing Capacity 11
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
April 5, 2012 Bearing Capacity 12
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.
April 5, 2012 Bearing Capacity 13
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
April 5, 2012 Bearing Capacity 14
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
April 5, 2012 Bearing Capacity 15