Abbs (1983) proposed a p-y curve model for weak carbonate rock for offshore platforms in the middle east based on a large number of unconfined compressive tests where weak carbonate rock encountered brittle failure at less than 1 per cent strain.
For low strain condition, the behavior of weak carbonate rock is controlled by the inter-particle cementation and by the deformability of the rock mass. At larger strain, the inter-particle bonding breaks down and it is expected that the stress-strain behaviour will principally be controlled by the frictional properties of the material.
Therefore, the proposed p-y curve model is based on a hybrid approach to capture the brittle nature of weak carbonate rocks, assuming that the pre-peak response could be simulated using a stiff clay model and the ultimate (residual) lateral resistance approaches that of a loose sand. Note that this p-y curve model generally applies to the unconfined compressive strength in the range from 0.5 to 5 MPa.
The p-y curve model for weak carbonate rock implemented in the PileLAT program consists of the the following parts:
An initial intact rock resistance curve represented by static stiff clay with water model (static case) proposed by Reese et al. (1975). and
Residual rock frictional resistance curve calculated with using the procedure for sand (cyclic case) proposed by Reese et al. (1974). A residual friction angle is used to define the strength. The transition between the two curves occurs sharply, with an additional displacement of 10% from the end of the intact rock response to the start of the residual friction response.
The following figure shows the typical p-y curve for the weak carbonate rock based on the recommendation by Abbs (1983).
The initial intact rock resistance curve is drawn in green and the residual rock resistance curve is in purple. The transition curve from the initial intact rock resistance curve to residual rock resistance curve is highlighted in orange color. Note that the fall from the peak to the residual curve at an additional displacement of 10% from the end of the initial intact rock resistance curve is arbitrary. The proposed slope is convenient from a computational point of view and represents the most dramatic fall that is anticipated from the more brittle materials encountered in the field.
Pc is the ultimate soil resistance per unit length of pile and is determined using the equations as below:
where D is the pile diameter, Ca is the average undrained shear strength over the depth X, Cu is the undrained shear strength at depth X. Eps50 is the strain factor which is the strain at one-half of the maximum stress for an undrained tri-axial compression test and is based on the table below which is extracted from Reese and Van Impe (2010).
As is the empirical factor and is determined based on the ratio of the calculation depth (z as per the figure below) to the pile diameter (b as per the figure below). The figure blow is extracted from Reese and Van Impe (2010) and is used in the PileLAT program to calculate the value of As.
Ks is the modulus coefficient and is the initial slope of the p-y curve. The following table can be adopted to select the preliminary value of the subgrade modulus based on the undrained shear strength when no testing results are available. This is the default option adopted in the PileLAT program but can be modified by the users if required. Note that the undrained shear strength is half of unconfined compressive strength.
For the residual rock frictional resistance curve (in purple), the friction angle shall be residual values based on previous experience and test results. Note that carbonate materials always exhibit high peak friction angles near or above 40 degree but after very few cycles of shear the values frequently reduce to a residual value of between 24 and 33 degrees. This reduction in friction angle is largely due to particle crushing which is dependent upon normal stress level nd occurs much in carbonate rocks than in siliceous materials.
The inputs required for weak carbonate rock in the PileLAT program are shown in the figure below. The parameters are (1) total unit weight, (2) unconfined compressive strength, UCS, (3) rate of change of UCS with the depth, (4) residual friction angle, (5) strain factor and (6) modulus coefficient.
Our PileLAT program provides a very useful function named "PYAnyTool" for the users to view the p-y curve at any depth within the foundation. One typical example is showed in the figure below where the p-y curve for weak carbonate rock model is displayed for the node point of 8 m below the pile head. Note that the users can add or delete more p-y curves at different depths if required.
Clicking the "Results" button will display the calculation summary dialog for the p-y curve at the selected depth. The detailed p-y data are show in the table on the left side of the dialog. The calculation details including calculation depth, effective vertical stress, UCS value, peak ultimate soil resistance and residual ultimate soil resistance are displayed in the right side of the dialog.
In our PileLAT program, multiple p-y curve plots at various nodes selected by the users can be displayed from the p-y curve output window as shown in the figure below.
References:
Abbs, A. F. (1983). Lateral pile analysis in weak carbonate rocks. Geotechnical Practice in Offshore Engineering, Proc. Offshore technology conference, Austin, Texas, Paper OTC 4852, 546-556.
Reese, L.C., Cox, W. R., and Koop, F.F. (1975). Field testing and analysis of laterally loaded piles in stiff clay, Offshore Technology Conference, Houston, Texas, OTC-2312-MS.
Reese, L.C., Cox, W. R., and Koop, F.F. (1974). Analysis of laterally loaded piles in sand, Offshore Technology Conference, Houston, Texas, OTC-2080-MS.
Reese, L.C., and Van Impe, W.F. (2001). Single piles and pile groups under lateral loading. A.A.Balkema, Rotterdam, Netherlands
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