Sunday, 29 June 2014

Computation of Immediate Settlement

This type of settlement takes place in a short time (about a week) after application of load and is due to elastic distortion of the soil. As the settlement is experienced in a short time, there will not be enough time for soil mass for change in its water content. Hence, Settlement takes place under constant Volume or under undrained conditions. This settlement is computed by elastic theory. Compared to consolidation settlement, particularly in saturated clay, this type of settlement is very small and often neglected unless the structure is very important.


Settlement of Footing in Clay
The total settlement is given by:
s = si + sc + ss
Where s is the total settlement, si is the immediate settlement, sc is the consolidation settlement and ss is the secondary settlement,

Immediate settlement
There are various methods of computing the immediate settlement. The most widely used are the Schleicher’s method and Jambu, Bjerrum and Kjaernsli’s method.
Schleicher’s Method - In this method the settlement at the corner of rectangular loaded area at the surface of a semi-infinite medium of a homogeneous and isotropic soil mass is given by:
si = q×B(1-µ2)Is/E  ———- (1)
Where, si = Immediate settlement
q = Load on foundation
B = Smaller dimension of the loaded area
µ = Poisson’s Ratio
Is = Influence coefficient
E = Modulus of elasticity
To the settlement at the center, the principal of superposition is used. For a rectangular area the settlement at the center is equal to four times the settlement at the corner.
The Value of the influence factor Is for a saturated clay layer of semi-infinite extent can be obtained from Table 1.
Table 1 Values of Influence Factors (Is)
Shape of Loaded Area
Flexible
Rigid
Centre
Corner
Average
Circular
1.00
0.64
0.85
0.80
Rectangular (L/B)

1.0
1.12
0.56
0.95
0.90
1.5
1.36
0.68
1.20
1.09
2.0
1.53
0.77
1.31
1.22
5.0
2.10
1.05
1.83
1.68
10.0
2.52
1.26
2.25
2.02
100.0
3.38
1.69
2.96
2.70

Rigidity Correction - The rigidity correction is done by multiplying the flexible settlement obtained from equation above by a factor, 0.8 called Rigidity Factor.
Alternatively we can write:
sRIGID = 0.8×sFLEXIBLE  ———- (2)
Depth Correction - A foundation placed at the surface will settle more than a foundation placed at a certain depth. To account for this, Fox 1948 has given a chart for depth factor,
Significant Depth – The depth at which the additional stress imposed by the foundation to the sub-soil becomes negligible is called the significant depth. This is generally taken as the zone bounded by 20 % pressure bulb corresponding to which the depth is 1.5 times the width for square foundation and 3 times the width for a strip foundation. For important structures the zone bounded by 10 % contours is taken as the significant depth. Corresponding to this decrease in vertical stress, the significant depth for square foundation is taken as 2 times the width and for strip foundation 6 times the width. For rectangular foundation the shorter dimension should be used to decide upon the significant depth.
Janbu, Bjerrum and Kjaernsli’s Method Janbu, Bjerrum and Kjaernsli (1956) have suggested the equation to compute average immediate settlement under a flexible compressible foundation in saturated undrained clays. The equation is given below:
si = µ0µ1×qB/Eu  ———- (3)
Where, si = Average immediate settlement for flexible footing
 µ0µ1 = Shape factors obtained from the charts shown in Fig.2
Eu = Undrained modulus of elasticity of the soil
q = Load on foundation
B = Smaller dimension of the loaded area


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