- Develop a Soil Model based on the available geotechnical data.
- Divide the Soil Model into the Upper Zone (UZ), the depth influenced by the Geopier® reinforcement, and the Lower Zone (LZ) below the depth of Geopier reinforcement.
- Estimate footing settlement by calculating the deformation within the UZ and the LZ, independently, and adding the two. Deformation within the UZ will occur essentially as loads are applied. Deformation within the LZ will occur at a rate dependent on the soil type.
Upper Zone settlement analysis:
Detailed upper zone calculations are described by Lawton and Fox (1994) and Lawton et al. (1994), and are summarized below.- Assuming the footing is rigid relative to the foundation materials, stresses applied to the composite foundation materials depend on their relative stiffness (Rs) and area coverage. For static equilibrium, the total downward force (Q) on the footing equals the resistance provided by the Geopier (Qg) and matrix soil (Qs):
Q = q A = Qg + Qs = qg Ag + qs As (1)
Where:
q = footing design bearing pressure
A = footing plan area
qg = stress applied at top of Geopier element
qs = stress applied to soil between the piers at bottom of footing
Ag = total crossectional area of all Geopier elements in the pattern
As = total crossectional area of soil between Geopier elements beneath footin
- Because the settlement of the footing portion bearing on the pier will equal the settlement of the footing portion bearing on the matrix soil, the foundation settlement (s) can be estimated by applied stresses (qg and qs) and stiffness modulus (kg and ks) of Geopier and matrix soil:
s = qg / kg = qs / ks (2)
- Rewrite equation 2 to express the matrix soil stress in terms of the Geopier stress and the ratio of the pier and matrix soil modulus values (Rs):
qs = qg (ks / kg) = qg / (kg / ks) = qg / Rs (3)
- Combine Equations 1 and 3 and define area ratio (Ra) as the ratio of Ag to A:
q = {qg [Ra Rs + 1 - Ra] / Rs } (4)
- Rewrite qg in terms of q:
qg = {q Rs / [Ra Rs + 1 - Ra] } (5)
- Upper-zone settlements are then computed using Equations 2 and 5. Calculations are applied either to the entire Upper-zone as one layer, or the Upper-zone can be divided into sub-layers with a qg value assigned to each layer based on the vertical stress distribution within the Upper-zone as established by field research and finite element analysis.
Lower Zone settlement analysis alternative approaches:
- Analyze using conventional elastic modulus theories, selecting appropriate modulus values based on sampler driving resistance and/or Cone Penetrometer Test (CPT) data. Divide the LZ into three or four layers depending on soil stratigraphy.
- Analyze using Schmertmann’s strain influence diagram, dividing the LZ into 4 layers and selecting appropriate Soil Type Factors (STF) and Standard Penetration Test (SPT) values from the geotechnical information.
- Analyze using conventional consolidation theory (Terzaghi and Peck), dividing the LZ into layers and applying appropriate compression index values, consolidation ratios, and/or effective stress relief from overburden removal (if any). The Westergaard stress distribution is typically applied beginning at the bottom of the footing, which is believed to yield greater settlement estimates for the LZ than actually occur [because the presence of the piers results in a more efficient stress transfer and stress dissipation with depth below the footing bottom than that which occurs for conventional spread footings (Lawton, 1999)].
- Assuming the footing is rigid relative to the foundation materials, stresses applied to the composite foundation materials depend on their relative stiffness (Rs) and area coverage. For static equilibrium, the total downward force (Q) on the footing equals the resistance provided by the Geopier (Qg) and matrix soil (Qs):
- Combine UZ and LZ settlement estimates. Apply engineering judgement, considering the relative validity of each LZ analysis approach for the soil types and conditions modeled.
