Schmertmann Method (CPT)
Settlement of spread footing using CPT tests according to Schmertmann theory is based on the formula:
Where: | s | - | settlement of spread footing |
C1 | - | correction factor for footing depth | |
C2 | - | correction factor for creep settlement | |
σol | - | stress in the footing bottom | |
Izi | - | strain influence factor at the center of the ith sublayer | |
hi | - | thickness of the ith sublayer | |
χ | - | modulus factor | |
qci | - | average value of cone penetration resistance in the ith sublayer |
The formula is derived for imperial units [tsf, ft] - the program calculates automatically in the units used in the program.
Correction factor for footing depth C1 is determined as follows:
Where: | σor | - | geostatic stress in the footing bottom |
Correction factor for creep settlement C2 is determined as follows:
Where: | tyr | - | time in years after the application of load |
Modulus factor χ depends on the ratio of footing length l and footing width b:
l/b = 1 -> χ = 2,5
l/b = 10 -> χ = 3,5
Intermediate values χ are interpolated.
Strain influence factor Iz is located on the horizontal axis of the following chart. The depth below the footing base is located on the vertical axis.
Determination of Iz factor (Schmertmann, 1978)
Diagram of the factor Iz also depends on the ratio of footing length l and footing width b.
For the ratio l/b = 1 maximum value of strain influence factor Izp is in the depth b/2 below the footing bottom and overall settlement is calculated to the depth 2b below the footing bottom.
For the ratio l/b = 10 maximum value of strain influence factor Izp is in the depth b below the footing bottom and overall settlement is calculated to the depth 4b below the footing bottom.
The ,aximum value of strain influence factor Izp is determined as follows:
Where: | σzp | - | geostatic stress in the depth of b/2 (for ratio l/b = 1) or b (l/b = 10) below the footing bottom |
Strain influence factor Iz is interpolated for intermediate values of ratio l/b (1 < l/b < 10).
Literature:
Schmertmann, J.H. (1970). Static cone to compute static settlement over sand. ASCE Journal of SoilMechanics & Foundations Division, 96 (3), 1011-1043.
Schmertmann, J.H., Hartmann, J.P. and Brown, P.R. (1978). Improved strain influence factor diagrams,ASCE Journal of the Geotechnical Engineering Division, 104 (GT8), 113