Settlement Is The Vertical Component Of Soil Deformation Beneath The

Settlement

Settlement is the vertical component of soil deformation beneath the load under consideration. All imposed loads on soils will cause some settlement due to “elastic compression” of the foundation soils. This settlement occurs relatively rapidly and is termed “elastic” or “immediate” settlement.

Components of Total Settlement The total settlement of a foundation comprises three parts as follows

S = Se+Sc+Ss where S = total settlement Se = elastic or immediate settlement Sc = consolidation settlement Ss = secondary settlement

1. Immediate, or those that take place as the load is applied or within a time period of about 7 days. The water in the voids is expelled simultaneously with the application of load and as such the immediate and consolidation settlements in such soils are rolled into one. 2. Consolidation, or those that are time-dependent and take months to years to develop. The Leaning Tower of Pisa in Italy has been undergoing consolidation settlement for over 700 years.

Foundation settlements must be estimated with great care for buildings, bridges, towers, power plants , and similar highcost structures.  The stress change ∆ q from this added load produces a time-dependent accumulation of particle rolling, sliding, crushing, and elastic distortions in a limited influence zone beneath the loaded area.  The statistical accumulation of movements in the direction of interest is the settlement.  In the vertical direction the settlement will be defined as ∆ H. 

Many engineers seemed to have the misconception that any footing designed with an adequate factor of safety against a bearing capacity failure would not settle excessively. Independent settlement analyses also need to be performed  Settlement frequently controls the design of spread footings, especially when B is large, and that the bearing capacity analysis is, in fact, often secondary. 

In saturated silts and clays, particularly those which are normally consolidated, the settlement will be dominated by consolidation, as water slowly drains from these soils to reduce the pore water pressures to the original levels.  Settlement of cohesionless soil primarily occur from the re-arrangement of soil particles due to the immediate compression from the applied load 

To enable settlements to be calculated we have to calculate the change in stresses within a soil mass, due to imposed external loads on the soil.  Elastic stress distributions within the soil are usually based on the theory of Boussinesq and so methods of computing “elastic settlements” usually assume that Boussinesq theory is applicable. 

The principal components of ∆ H are particle rolling and sliding, which produce a change in the void ratio, and grain crushing, which alters the material slightly.  Only a very small fraction of ∆ H is due to elastic deformation of the soil grains.  This would appear reasonable because a stress change causes the settlement, and larger stress changes produce larger settlements. 

Obtaining a reliable stress profile from the applied load. We have the problem of computing both the correct numerical values and the effective depth H of the influence zone.  Theory of Elasticity equations are usually used for the stress computations, with the influence depth H below the loaded area taken from H = 0 to H →∞ (but more correctly from 0 to about 4B or 5B). 



The values from these two problem areas are then used in an equation of the general form H

ΔH = ∫ εdH o

where ε= strain = Δq/Es ; but Δq = f ( H , load ) ,

E s = f ( H , soil variation ) , and H ( as previously noted ) is the estimated depth of stress change caused by the foundation load.

EVALUATION OF MODULUS OF ELASTICITY • The most difficult part of a settlement analysis is the evaluation of the modulus of elasticity Es, that • would conform to the soil condition in the field. There are two methods by which Es can be • evaluated. They are • 1. Laboratory method, • 2. Field method

• For settlement analysis, the values of Es at different depths below the foundation base are required. • One way of determining Es is to conduct triaxial tests on representative undisturbed samples • extracted from the depths required. For cohesive soils, undrained triaxial tests and for cohesionless • soils drained triaxial tests are required.

• Because of the many difficulties faced in selecting a modulus value from the results of • laboratory tests, it has been suggested that a correlation between the modulus of elasticity of soil • and the undrained shear strength may provide a basis for settlement calculation. The modulus E • may be expressed as • Es = Acu

• where the value of A for inorganic stiff clay varies from about 500 to 1500 (Bjerrum, 1972) and cu • is the undrained cohesion. It may generally be assumed that highly plastic clays give lower values • for A, and low plasticity give higher values for A. For organic or soft clays the value of A may vary • from 100 to 500. The undrained cohesion cu can be obtained from any one of the field tests

Field methods • Field methods are increasingly used to determine the soil strength parameters. They have been • found to be more reliable than the ones obtained from laboratory tests. The field tests that are • Normally used for this purpose are1. Plate load tests (PLT)

2. Standard penetration test (SPT) 3. Static cone penetration test (CPT) 4. Pressuremeter test (PMT) 5. Flat dilatometer test (DMPlate load tests, if conducted at levels at which Es is required, give quite reliable values as • compared to laboratory tests. Since these tests are too expensive to carry outT) • • • •

• Many investigators have obtained correlations between Eg and field tests such as SPT, CPT • and PMT. The correlations between ES and SPT or CPT are applicable mostly to cohesionless soils • and in some cases cohesive soils under undrained conditions. PMT can be used for cohesive soils to • determine both the immediate and consolidation settlements together. Some of the correlations of £y with N and qc are given in Table 13.2. These correlations have • been collected from various sources.

METHODS OF COMPUTING SETTLEMENTS • Computation of Elastic Settlements 1. Elastic settlement based on the theory of elasticity 2. Janbu et al., (1956) method of determining settlement under an undrained condition. 3. Schmertmann's method of calculating settlement in granular soils by using CPT values.

Computation of Consolidation Settlement • 1. e-\og p method by making use of oedometer test data. • 2. Skempton-Bjerrum method.

ELASTIC SETTLEMENT BENEATH THE CORNER OF A UNIFORMLY LOADED FLEXIBLE AREA BASED ON THE THEORY OF ELASTICITY • The net elastic settlement equation for a flexible surface footing may be written as, (1 − μ2 ) S e = qn B

Es

If

Where Se = elastic settlement B = width of foundation E s = modulus of elasticity of soil μ = Poissn' s ratio , qn = net foundation pressure, I f = influence factor

• In Eq. (13.20a), for saturated clays, \JL 0.5, and Es is to be obtained under undrained • conditions as discussed earlier. For soils other than clays, the value of ^ has to be chosen suitably • and the corresponding value of Es has to be determined. Table 13.3 gives typical values for /i as • suggested by Bowles (1996).

• 7, is a function of the LIB ratio of the foundation, and the thickness H of the compressible • layer. Terzaghi has a given a method of calculating 7, from curves derived by Steinbrenner (1934), • for Poisson's ratio of 0.5, 7,= F1? • for Poisson's ratio of zero, 7,= F7 + F2. • where F{ and F2 are factors which depend upon the ratios of H/B and LIB. For intermediate values of //, the value of If can be computed by means of interpolation or by • the equation  ( 1 − μ− 2 μ2 ) F2  I f  F1 + 2  1 − μ  

• The values of Fj and F2 are given in Fig. 13.7a. The elastic settlement at any point N qn ( 1 − μ2 ) Se at po13.7b) int N = is given [ I f 1 B1by + I f 2 B2 + I f 3 B3 + I f 4 B4 ] • (Fig. Es

• To obtain the settlement at the center of the loaded area, the principle of superposition is • followed. In such a case N in Fig. 13.7b will be at the center of the area when B{ = B4 = L2 = B3 and • B2 = Lr Then the settlement at the center is equal to four times the settlement at any one corner. The • curves in Fig. 13.7a are based on the assumption that the modulus of deformation is constant with • depth.

• In the case of a rigid foundation, the immediate settlement at the center is approximately 0.8 • times that obtained for a flexible foundation at the center. A correction factor is applied to the • immediate settlement to allow for the depth of foundation by means of the depth factor d~ Fig. 13.8 • gives Fox's (1948) correction curve for depth factor. The final elastic settlement is

Sef = C r d f Se Where Sef = final elastic settlement C r = rigidity factor taken as equal to 0.8 for a highly rigid foudation d f = depth factor from Fig .13.8 Se = settlement for a surface flexible footing

•

KJAERNSLI'S METHOD OF DETERMINING ELASTIC SETTLEMENT UNDER Probably theUNDRAINED most useful chart is that given by Janbu et al., (1956) as modified by Christian and CONDITIONS

• Carrier (1978) for the case of a constant Es with respect to depth.μ0The μ1 qn Bchart (Fig. 13.9) Se = provides Es • estimates of the average immediate settlement of uniformly loaded, flexible strip, rectangular, • square or circular footings on homogeneous isotropic saturated clay. The equation for computing • the settlement may be expressed as

• In Eq. (13.20), Poisson's ratio is assumed equal to 0.5. The factors fiQ and ^ are related to the • DJB and HIB ratios of the foundation as shown in Fig. 13.9. Values of \JL^ are given for various LIB • ratios.

• Rigidity and depth factors are required to be applied to Eq. (13.22) as per Eq. (13.21). In • Fig. 13.9 the thickness of compressible strata is taken as equal to H below the base of the • foundation where a hard stratum The chart given in Fig. 13.9 may be used for the case of ES • increasing with depth by replacing the multilayered system with one hypothetical layer on a rigid is met with.

METHOD OF CALCULATING SETTLEMENT IN GRANULAR SOILS BY USING CRT • The detailed investigations of Schmertmann VALUES (1970), Eggestad, (1963) and others, • indicate that the greatest strain would occur at a depth equal to half the width for a square or circular • footing. The strain is assumed to increase from a minimum at the base to a maximum at B/2, then • decrease and reaches zero at a depth equal to 2B.

• For strip footings of L/B > 10, the maximum strain • is found to occur at a depth equal to the width and reaches zero at a depth equal to 4B. The modified • triangular vertical strain influence factor distribution diagram as proposed by Schmertmann (1978) • is shown in Fig. 13.10. The area of this diagram is related to the settlement. The equation (for • square as well as circular footings) is

2B

S = C 1C 2 qn ∫ 0

Iz Δz Es

Where, S = total settlement , qn = net settlement , q = total foundation pressure , qo′ = effective overburden pressure at foundation level , Δz = thickness of elemental layer , I z = vertical strain inf luence factor , C1 = depth correction factor , C 2 = creep factor . The equations for C1 and C 2 are q′ C 1 = 1 − 0. 5 0 qn t 0.1 t is time in years for which period settlement is required .

C 2 = 1 + 0.2 log10