Schmertmann’s method

Schmertmann’s method

The Schmertmann’s method (1970) calculates settlement from layer stiffness data or cone tip bearing resistance, qc, obtained from a Cone Penetration Test (CPT). The method assumes a simplified triangular strain distribution and calculates the settlement accordingly. A time factor can also be included to account for time dependent (creep) effects.

The equation for settlement is: 

       (26)

Where

C1 = the correction to account for strain relief from excavated soil, 

= effective overburden pressure at bottom of the footing

= the net applied footing pressure =

C2 = correction for time-dependent creep, 

  t = time (years)

C3 = correction for shape of footing 

Esi = equivalent modulus of elasticity of soil layer i

= thickness of soil layer 

(Iz)i = the influence factor at the center of soil layer i as described below.

1.1 Influence factors

The influence factor, Iz is based on an approximation of strain distributions below the footing and was originally formulated in 1970 and then improved in 1978.

1978 formulation

This is described in Schmertmann et al. (1978). With this method, the peak value for Iz is calculated by

           (27)

Where is the effective overburden pressure at the depth of Izp.

The depth of Izp depends on the shape of the load. For an axisymmetric load (a circle or a square), Izp occurs at a depth of B/2. For the plane strain case (length of the load is > 10x the width), the Izp occurs at a depth of B. The values for Iz (shown in the figure below) are calculated as follows:

Axisymmetric: Iz varies linearly from 0.1 at the bottom of the footing to Izp at a depth of B/2. The strain influence factor then decreases to zero at a depth of 2B.

Plane strain: Iz varies linearly from 0.2 at the bottom of the footing to Izp at a depth of B. The strain influence factor then decreases to zero at a depth of 4B.

In the Schmertmann calculator, Iz is calculated using the axisymmetric equations for circle and square loads. For rectangular loads in which the length is greater than ten times the width, the plane strain approach is used. For rectangular loads in which the length is less than ten times the width, a linear interpolation between the axisymmetric and plane strain case is performed, dependent on the length to width ratio.

Figure 7. Strain influence factors from Schmertmann et al. (1978)

1.2 Equivalent Modulus of Elasticity, Es 

Es from Cone Penetration Test (CPT) results

*Adapted from Coduto, Donald P., (2001)

Es from Standard Penetration Test (SPT) results

       (28)

Where:

Es = equivalent modulus of elasticity

β0, β1 = correction factors from following table

OCR = overconsolidation ratio

N60 = SPT N-value corrected for field procedures

*Adapted from Coduto, Donald P., (2001)