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This set of slides provides a comprehensive overview of vertical stress increases in soil, focusing on various loading types and analysis methods. It delves into the boussinesq and westergaard methods, exploring their assumptions and applications. The slides also include detailed explanations of point, line, strip, circular, and rectangular loading, accompanied by illustrative figures and tables. This resource is valuable for students and professionals in civil engineering and geotechnical engineering, offering a solid foundation in understanding soil behavior under load.
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14.330 SOIL MECHANICS Soil Stresses
ERTICAL
TRESS
NCREASES IN
OIL
YPES OF
OADING Point Loads (P) Figure 6.11. Das FGE (2005). Examples:
14.330 SOIL MECHANICS Soil Stresses Examples:
ERTICAL
TRESS
NCREASES IN
OIL
YPES OF
OADING
14.330 SOIL MECHANICS Soil Stresses Based on the assumption that the soil on which load is applied is reinforcedby closely spaced horizontal layers which prevent horizontal displacement.The effect of the Westergaard assumption is to reduce the stresses substantially below those obtained by the Boussinesq equations . An approximate stress distribution assumes that the total applied load onthe surface of the soil is distributed over an area of the same shape as theloaded area on the surface, but with dimensions that increase by an amount equal to the depth below the surface. Vertical stresses calculated 2V:1H method agree reasonably well withthe Boussinesq method for depths between B and 4B below thefoundation.
ERTICAL
TRESS
NCREASES IN
OIL
NALYSIS
ETHODS
ESTERGAARD
ERTICAL
TRESS
NCREASES IN
OIL
NALYSIS
ETHODS
ETHOD
Slide 5 of 24 14.330 SOIL MECHANICS Soil Stresses (^2) / 5 2 2 3 (^35) ) ( 3 2 3 2 z r z P z L P z^
∆ π π σ ( ) [ ]^ 1 2 2 / 5 2 2 1 / 1 2 3 I P z z r P z z^ =
= ∆ π σ Stresses in an Elastic Medium Caused by Point Loading Figure 6.11. Das FGE (2005). Where: ∆σ z = Change in Vertical Stress P = Point Load I 1 = 3 2 π 1 r / z ( ) 2
1 5/ *Based on homogeneous, elastic, isotropic infinitely large half-space
ERTICAL
TRESS
NCREASE
∆σ∆σ∆σ∆σ Z
IN
OIL P OINT
OADING
OUSSINESQ
14.330 SOIL MECHANICS Soil Stresses 2 2 2 2 2 3 1 2 ) / ( ) ( 2
= ∆
= ∆ x z z q z x qz π σ π σ Where: ∆σ = Change in Vertical Stress q = Load per Unit Length z = Depth x = Distance from Line Load *Based on flexible line load of infinite length on a homogeneous, elastic, isotropic semi-infinite half-space or Dimensionless Form Line Load over the Surface of a Semi-infinite Soil Mass^ Figure 6.12. Das FGE (2005). V ERTICAL
TRESS
NCREASE
∆σ∆σ∆σ∆σ Z
IN
OIL L INE
OADING
OUSSINESQ
Revised 02/ 14.330 SOIL MECHANICS Soil Stresses Table 6. Variation of ∆σ /(q/z) with x/z (Das, FGE 2006). V ERTICAL
TRESS
NCREASE
∆σ∆σ∆σ∆σ Z
IN
OIL L INE
OADING
OUSSINESQ
14.330 SOIL MECHANICS Soil Stresses Table 6. Variation of ∆σ /q with 2z /B and 2x/B (Das, FGE 2006). V ERTICAL
TRESS
NCREASE
∆σ∆σ∆σ∆σ Z
IN
OIL S TRIP
OADING
OUSSINESQ
14.330 SOIL MECHANICS Soil Stresses ∆ σ = q 1 − 1 ( R / z ) 2
1 3/ Vertical Stress Below Center of Uniformly Loaded Flexible Circular Area Figure 6.15. Das FGE (2005). Where: ∆σ = Change in Vertical Stress q = Load per Unit Area z = Depth R = Radius V ERTICAL
TRESS
NCREASE
∆σ∆σ∆σ∆σ Z
IN
OIL C IRCULAR
OADING
OUSSINESQ
Slide 13 of 24 14.330 SOIL MECHANICS Soil Stresses
−
= − 1 1 2 tan 2 1 1 1 2 (^14) 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 n m n m n m mn n m n m n m n m n m mn I π
= = + + = = ∆ B y L x qI z y x dxdy qz d 0 0 2 2 / 5 2 2 2 3 ) ( 2 ) ( 3 π σ σ Vertical Stress Below Corner of Uniformly Loaded Flexible Rectangular Area Figure 6.16. Das FGE ( ). Where: ∆σ = Change in Vertical Stress q = Load per Unit Area z = Depth L^ z n B^ z m = = ; V ERTICAL
TRESS
NCREASE
∆σ∆σ∆σ∆σ Z
IN
OIL R ECTANGULAR
OADING
OUSSINESQ
14.330 SOIL MECHANICS Soil Stresses Variation of I 2 with m and n . Figure 6.17. Das FGE (2005). V ERTICAL
TRESS I NCREASE
∆σ∆σ∆σ∆σ Z
IN S OIL R ECTANGULAR
OADING (B OUSSINESQ
Slide 16 of 24 14.330 SOIL MECHANICS Soil Stresses ∆ σ = q I 2(1)
I 2(2)
I 2(3)
I 2(4) ∆ σ c = qI c I c = f ( m 1 , n 1 ) m 1 = L B ; n 1 = z B 2 Within a Rectangular Loaded Area: Under Center of Footing: Figure 6.18. Das FGE (2005). V ERTICAL
TRESS
NCREASE
∆σ∆σ∆σ∆σ Z
IN
OIL R ECTANGULAR
OADED
REA
Revised 02/ 14.330 SOIL MECHANICS Soil Stresses Table 6. Variation of Ic with m 1 and n 1 (Das, FGE 2006). V ERTICAL
TRESS
NCREASE
∆σ∆σ∆σ∆σ Z
IN
OIL C ENTER OF
ECTANGULAR
OADED
REA
14.330 SOIL MECHANICS Soil Stresses
OUSSINESQ
OLUTIONS
UMMARY (EM 1110-1-1904 T ABLE C-1)
14.330 SOIL MECHANICS Soil Stresses
OUSSINESQ
OLUTIONS
UMMARY (EM 1110-1-1904 T ABLE C-1)
