## Hpw

= 3°j)5QQC)75 (°-76 x 50 + °-56 x 50 + 0.64 x 30) = 1.28m

### The effect of depth

Fox (1948) showed that for deep foundations (z > B) the calculated immediate settlements are more than the actual ones, and a reduction may be applied. If z = B the reduction is approximately 25 per cent, increasing to about 50 per cent for infinitely deep foundations.

Most foundations are shallow, however, and although this reduction can be allowed for when a layer of soil is some depth below a foundation, the settlement effects in this case are small so it is not customary practice to reduce them further.

### Determination of E

The modulus of elasticity, E, is usually obtained from the results of a consolidated undrained triaxial test carried out on a representative sample of the soil that is consolidated under a cell pressure approximating to the effective overburden pressure at the level from which the sample was taken. The soil is then sheared undrained to obtain the plot of total deviator stress against strain; this is never a straight line and to determine E a line must be drawn from the origin up to the value of deviator stress that will be experienced in the field when the foundation load is applied. In deep layers there is the problem of assessing which depth represents the average, and ideally the layer should be split into thinner layers with a value of E determined for each.

A certain amount of analysis work is necessary in order to carry out the above procedure. The increments of principal stress Acti and Acr3 must be obtained so that the value of Aui — At73 is known, and a safety factor of 3.0 is generally applied against bearing capacity failure. Skempton (1951) points out that when the factor of safety is 3.0 the maximum shear stress induced in the soil is not greater than 65 per cent of the ultimate shear strength, so that a value of E can be obtained directly from the triaxial test results by simply determining the strain corresponding to 65 per cent of the maximum deviator stress and dividing this value into its corresponding stress. The method produces results that are well within the range of accuracy possible with other techniques.

### 9.2.2 Cohesionless soils

Owing to the high permeabilities of cohesionless soils, both the elastic and the primary effects occur more or less together. The resulting settlement from these factors is termed the immediate settlement.

The chance of bearing capacity failure in a foundation supported on a cohesionless soil is remote, as Exercise 4 at the end of Chapter 8 illustrates numerically. For cohesionless soils it has become standard practice to use settlement as the design criteria, and the allowable bearing pressure, p, is generally defined as the pressure that will cause an average settlement of 25 mm in the foundation.

The determination of p from the results of the standard penetration test has been discussed in Chapter 8. If the actual bearing pressure is not equal to the value of p then the value of settlement is not known and, since it is difficult to obtain this value from laboratory tests, resort must be made to in situ test results. Most methods used required the value of Cr, the penetration resistance of the Dutch cone, which is usually expressed in MN/m2 or kN/m2.

Meyerhof's method

A quick estimate of the settlement, p, of a footing on sand has been proposed by Meyerhof (1974): ApB

where

B = the least dimension of the footing

Cr = the average value of Cr over a depth below the footing equal to B Ap = the net foundation pressure increase which is simply the foundation loading less the value of vertical effective stress at foundation level,

The two other methods commonly in use were proposed by De Beer and Martens (1957) and by Schmertmann (1970). Both methods require a value for Cr and, if either is to be used with standard penetration test results, it is necessary to have the correlation between Cr and N.

Obviously the value of Cr obtained from the Dutch cone penetration test must be related to the number of recorded blows, N, obtained from the standard penetration test. Various workers have attempted to find this relationship but, so far, the results have not been encouraging. Meigh and Nixon (1961) showed that, over a number of sites, Cr varied from (430 x N) to (1930 x N)kN/m2.

The relationship most commonly used at the present time is that proposed by Meyerhof (1956): Cr = 400 x N kN/m2

where N = actual number of blows recorded in the standard penetration test.

It goes without saying that, whenever possible, Cr values obtained from actual cone tests should be used in preference to values estimated from N values.

The relationships between N and Cr determined by various workers and the implications involved have been discussed by Meigh (1987).

De Beer and Martens' method

From the results of the in situ tests carried out, a plot of Cr (or N) values against depth is prepared, similar to that shown in Fig. 8.22. With the aid of this plot the profile of the compressible soil beneath the proposed foundation can be divided into a suitable number of layers, preferably of the same thickness, although this is not essential.

In the case of a deep soil deposit the depth of soil considered as affected by the foundation should not be less than 2.OB, ideally 4.OB, where B = foundation width.

The method proposes the use of a constant of compressibility, Cs, where

Cr = static cone resistance (kN/m2) Poi = effective overburden pressure at the point tested:

Total immediate settlement is

Cs Po2 where

Aaz = vertical stress increase at the centre of the consolidating layer of thickness H

p02 = effective overburden pressure at the centre of the layer before any excavation or load application.

Note Meyerhof (1956) suggests that a more realistic value for Cs is Cs = 1.9 —

Such a refinement may be an advantage if the calculations use Cr values which have been determined from Dutch cone penetration tests, but if the Cr values used have been obtained from the relationship Cr = 400 kN/m2, such a refinement seems naive.

Schmertmann's method

Originally proposed by Schmertmann in 1970 and modified by Schmertmann et al. (1978), the method is now generally preferred to De Beer and Martens' approach.

The method is based on two main assumptions:

(i) the greatest vertical strain in the soil beneath the centre of a loaded foundation of width B occurs at depth B/2 below a square foundation and at depth of B below a long foundation;

(ii) significant stresses caused by the foundation loading can be regarded as insignificant at depths greater than z = 2.0B for a square footing and = 4.0B for a strip footing.

The method involves the use of a vertical strain influence factor, Iz, whose value varies with depth. Values of Iz, for a net foundation pressure increase, Ap, equal to the effective overburden pressure at depth B/2, are shown in Fig. 9.4.

The procedure consists of dividing the sand below the footing into n layers, of thicknesses Az,, AZ2, Az,... AZn. If soil conditions permit it is simpler if the layers can be made of equal thickness, Az. The vertical strain of a layer is taken as equal to the increase in vertical stress at the centre of the layer, i.e. Ap multiplied by Iz, which is then divided by the product of Cr and a factor x. Hence:

x =2.5 for a square footing and 3.5 for a long footing Iz = the strain influence factor, valued for each layer at its centre, and obtained from a diagram similar to Fig. 9.4 but redrawn to correspond to the foundation loading Ci = a correction factor for the depth of the foundation

C2 = a correction factor for creep

= 1 + 0.21ogio 10t (t = time in years after the application of foundation loading for which the settlement value is required).

where

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