Settlement

Settlement

Introduction • The allowable settlement of a shallow foundation may control the allowable bearing capacity. The allowable settlement itself may be controlled by local building codes. Thus, the allowable bearing capacity will be the smaller of the following two conditions: qu   qall = min  FS qallowable settlement

• The settlement of a foundation can be divided into two major categories: (a) elastic or immediately settlement (b) consolidation settlement (primary and secondary)

Elastic Settlement 1. Elastic Settlement under on Saturated Clay Janbu et al. (1956) proposed an equation q0 B Se = A1 A2 Es

where A1 is a function of H/B and L/B and A2 is a function of Df /B. Christian and Carrier (1978) modified the values of A1 and A2 to some extent as presented in Figure 5.14.

The modulus of elasticity (Es) for clays can, in general, be given as

Es = β cu where cu undrained shear strength

Example

2. Elastic or Immediate Settlement, Se In Granular Soil 1 − µ s2 Se = q0 (α B′ ) Is I f Es

where q0 = net applied pressure on the foundation

µ s = Poisson's ratio of soil Es = average modulus of elasticity of the soil under the foundation, measured from z 0= to about z 5 B = B′ = B 2 for center of foundation = B for corner of foundation

2. Elastic or Immediate Settlement, Se In Granular Soil

I s = shape factor (Steinbrenner, 1934) 1 − 2µs I= F1 + F2 s 1 − µs where = F1

1

π

( A0 + A1 )

n′ tan −1 A2 F2 = 2π

• Due to the nonhomogeneous nature of soil deposits, the magnitude of Es may vary with depth. For that reason, Bowles (1987) recommended using a weighted average of Es in Eq. below in

Example

Example

Figure 5.16 Elastic settlement of flexible and rigid foundations

Solution

Consolidation Settlement

Primary Consolidation Settlement Relationships

• Normally Consolidated Clays

• Over Consolidated Clays

′ > σ c′ , For σ 0′ + ∆σ av Sc ( p )

 σ 0′ + ∆σ av ′  Cs H c = log   ′ σ0 1 + e0  

′ For σ 0′ < σ c′ < σ 0′ + ∆σ av  σ 0′ + ∆σ av ′  Cs H c σ c′ Cc H c = + log log  Sc ( p )  1 + e0 σ 0′ 1 + e0 σ c′  

where

σ’0 ∆σ’av σ’c e0 Cc Cs Hc

= average effective pressure on the clay layer before the construction of the foundation = average increase in effective pressure on the clay layer caused by the construction of the foundation = preconsolidation pressure = initial void ratio of the clay layer = compression index = swelling index = thickness of the clay layer

Compression Index (Cc) and Swell Index (Cs) • Skempton (1944) suggested empirical expressions for the compression index. • For undisturbed clays:

= Cc 0.009 ( LL − 10 ) • For remolded clays:

= Cc 0.007 ( LL − 10 ) where LL liquid limit (%).

Compression Index (Cc) and Swell Index (Cs)

Compression Index (Cc) and Swell Index (Cs) From Table 7.2, it can be seen that

Cs ≈ 0.2  0.3Cc

Based on the modified Cam clay model, Kulhawy and Mayne (1990) have shown that

PI Cs ≈ 370

Example • A plan of a foundation 1m × 2m is shown in Figure 5.32. Estimate the consolidation settlement of the foundation

Settlement Due to Secondary Consolidation

Figure 5.33 Variation of e with log t under a given load increment, and definition of secondary compression index

• Mesri (1973) suggested

• For inorganic clays and silts

• For organic clays and silts:

• For peats:

Bearing capacity of mat foundation • The gross ultimate bearing capacity of a mat foundation can be determined by the same equation used for shallow foundation. • A suitable factor of safety should be used to calculate the net allowable bearing capacity.For rafts on clay, the factor of safety should not be less than 3 under dead load and maximum live load.However, under the most extreme conditions,the factor of safety should be at least 1.75 to 2. For rafts constructed over sand,a factor of safety of 3 should normally be used.

Ultimate bearing capacity equation for mat foundation on saturated clay

qnet (u )

Df 0.195B = 5.14Cu (1 + )(1 + 0.4 ) L B

Effect of Soil Compressibility • The change of failure mode is due to soil compressibility, to account for which Vesic (1973) proposed the following modification of Meyerhof’s equation:

In this equation, Fcc, Fqc and Fγc are soil compressibility factors.

Effect of Soil Compressibility • The change of failure mode is due to soil compressibility, to account for which Vesic (1973) proposed the following modification of Meyerhof’s equation:

In this equation, Fcc, Fqc and Fγc are soil compressibility factors.