Chapter four Settlement of shallow foundations 4.1 Introduction: Foundation settlements must be estimated with great care for buildings, bridges, towers, power plants, and similar high-cost structures. For structures such as fills, earth dams, and retaining walls a greater margin of error in the settlements can usually be tolerated. Settlements are usually classified as follows: 1. Immediate settlement Si: or elastic, it takes place as the load is applied or within a time period of about 7 days. 2. Consolidation settlement Sc: is time-dependent and take months to years to develop. 3. Secondary settlement Ss: occurs at the end of primary consolidation.

St = Si + Sc + Ss Where St is the total settlement

. Immediate settlement analyses are used for all fine-grained soils including silts and clays with a degree of saturation S ≤ 90 % and for all coarse-grained soils with a large coefficient of permeability [say, above 10-3 m/s]. Consolidation settlement analyses are used for all saturated fine grained 4.2 Immediate settlement: It is important to point out that, a foundation could be considered flexible or rigid (according to its relative stiffness Kr).

When a flexible foundation on an elastic medium is subjected to a uniformly distributed load, the contact pressure will be uniform, as shown in Figure 4.1a and the settlement profile of the foundation is sagging. If a similar foundation is placed on granular soil it will undergo larger elastic settlement at the edges rather than at the center (Figure 4.1b); however, the contact pressure will be uniform. The larger settlement at the edges is due to the lack of confinement in the soil.

If a fully rigid foundation is placed on the surface of elastic medium, the settlement will remain the same at all points; however, the contact distribution will be as shown in Figure 4.2.a. If this rigid foundation is placed on granular soil, the contact pressure distribution will be as shown in Figure 4.2.b, although the settlement at all points below the foundation will be the same For a shallow foundation subjected to a net force per unit area qo,

the Poisson’s ratio and the modulus of elasticity of the soil supporting are μs and Es, respectively , (as in the following figure)

B: width of footing ; L: length of footing The values of α for various length to width ratios (L/B) are shown in figure (4.3) The average immediate settlement for a flexible foundation can be expressed as :

• If the foundation is Rigid, the immediate settlement will be:

• If the foundation is flexible, the immediate settlement is :

Fig.4.3

Remark: if an incompressible layer of rock is located at a limited depth, the actual settlement may be less than that calculated by the previous equations. However if the depth H is greater than 2B to 3B, the actual settlement would not change considerably

Fig.4.4

Fig.4.5

4.3 Immediate Settlement of Foundation on Saturated Clay The average immediate settlement of flexible foundations on saturated clay soils (Poisson's ratio μs = 0.5) may be computed as :

Where: A1 : is function of H/B and L/B , (fig. 4.4) A2 : is function of DF/B, (fig.4.5)

4.4 Immediate Settlement of foundation on Sandy Soil

[Schmertmann Method] Immediate settlement of granular soils can also be evaluated by use of a semi-empirical strain influence factor:

Iz = strain influence factor. C1 = a correction factor for the embedment depth. C2 = a correction factor to account for creep in soil. = 1 + 0.2 log (time in years / 0.1) = stress at the foundation level (gross pressure) q = γ.DF

The variation of (Iz) with depth below the foundation ( Fig.4.6 )

* For square or circular footings: (L/B = 1) Iz = 0.1 at z = 0 Iz = 0.5 at z = z1 = 0.5B Iz = 0 at z = z2 = 2B * For foundations L/B 10: Iz = 0.2 at z = 0 Iz = 0.5 at z = z1 = B Iz = 0 at z = z2 = 4B where (B x L) are the foundation dimensions. For L/B between 1 and 10, necessary interpolations can be made.

The procedure to calculate elastic settlement is given as (fig.4.6):

Step 1. Plot the foundation and the variation of Iz with depth to scale Step 2. Using the correlation from standard penetration resistance (N) or cone penetration resistance (qc), plot the actual variation of Es with depth Step 3. Approximate the actual variation of Es into a number of layers of soil having a constant Es, such as Es(1), Es(2), . . . , Es(i), . . . Es(n) Step 4. Divide the soil layer from Z = 0 to Z = Z2 into a number of layers by drawing horizontal lines. The number of layers will depend on the break in continuity in the Iz and Es diagrams. Step 5. Prepare a table to obtain Step 6. Calculate C1 and C2. Step 7. Calculate Si

4.5 Range of Soil Parameters for Computing (Si): The equation for calculating the immediate settlement (Si) contain the elastic parameters Es and μs. In the absence of representative values obtained from laboratory tests, one may use the approximate range of values shown in Table 4.1:

Other practical correlations are given as follows: 1- From SPT:

Es (KN/m²) = 766 N

Es (U.S. tons/ft²) = 8 N

Table 4.1

2- From CPT: Es = 3.5 qc 3- Knowing Cu (undrained cohesion of clayey soil):

* NC clays Es = (250 to 500) Cu

* OC clays Es = (750 to 1000) Cu

Example Estimate the settlement of a square footing 7’x7’ placed on a fine medium dense sand ,embedded 4 ft below the ground surface, and subjected to 200Kips; use Schmertmann method, assuming that Es/N = 14 where Es is in Ksf

4.6 Immediate Settlement of Eccentrically Loaded Foundations: An eccentrically loaded foundation will undergo vertical settlement and rotation, as shown in Fig. (3.27). The procedure for determining these quantities is as follows: 1.) Qult (ecc.) = q'u x A'

= q'u x B' x L'; (A' = effective area) 2.) FS = Qult (ecc) / Q ; (Q = applied load on footing) 3.) Determine Qult (e = 0) assuming no eccentricity (e = 0).

Fig.3.27

4.) Determine Qult (e = 0) / Q(e = 0). 5.) For the load Q(e = 0), estimate the settlement of the foundation

Si(e = 0).

6.) The settlement (Si) and the rotation (t) are then:

β1& β2= Factors dependent on L/B ratio (Fig. 4.7). Note that β1 is related to vertical displacement and the factor β2 is related to the rotation of the foundation.

Fig.4.7

4.7 Consolidation Settlement: The settlements of fine-grained, saturated cohesive soils will be time-dependent • Preconsolidation pressure Pc : Soil has a memory of the stress and other changes that have occurred during their history. These changes are preserved in the soil structure. When the soil is loaded to a stress level greater than it ever experienced in the past, the soil structure is no longer able to sustain the increased load and the structure starts to break down.

To obtain the preconsolidation pressure

OCR = Po/Pc If OCR=1 -> Normally consolidated Clays NC If OCR>1 -> Overconsolidated Clays OC If OCR<1 -> Underconsolidated Clays UC consolidation theory, is usually used through the following equations: 1- Normally Consolidated Clay:

2- Overconsolidated Clay: i-) For Po + ∆p Pc ii-) For Po + ∆p >> Pc

Cc: compression index Cs:(or Cr) swelling or recompression index Po: (or σ’v)effective overburden stress Pc: preconsolidation pressure H: thickness of soil layer eo: initial void ratio ∆p: increase in Po from a depth z

4.8Allowable Settlement: All structures can tolerate some differential and total settlement without affecting their structural integrity or creating an aesthetic problem. Allowable displacement criteria in common use are given inTable4.2. The magnitude of the allowable differential settlement depends on the characteristics of the structure. Differential Settlement: Differential settlement is the difference in the settlement of two adjacent footings (or piles) that are tied together with a structure. meaning that one footing has settled much more than the other. Design limits on differential settlement are frequently set in totally unrealistic terms. In fact each structure should be considered individually, and the values given in Tables 3 and 4 should be used only as a guide. An estimate of the allowable differential settlement can be found from: ∆(∆)H =θall . S where θall is the allowable rotation of the foundation between two columns spaced a distance S

Example. Estimate an allowable differential settlement for a reinforced concrete frame building 20 stories high, if the column spacing is 30 feet and they are supported on spread footings? ∆(∆)H =θall . S = (1/500)(30)(12)= 0.72 inches