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Some notes on Rowe and Armitage method for rock socket design

Rowe and Armitage method is one of the main methods for the design of rock socketed piles. This method uses a series of numerical solutions to account for nonslip and slip between the pile shaft and the surrounding rock. The numerical derived charts shown in the figure below are used to determine the required socket length based on the applied load and the design settlement.

Although this method is commonly used for the rock socket design, it is worth mentioning there are some limitations as below:

  1. This method cannot be used when certain combinations of input parameters (Pile diameter D, Pile Modulus Ec, Rock Modulus Em, Pile Length L, etc..) are outside of the range of the design charts.

  2. Although intended to calculate the required socket length based on the input parameters, this method can be repeated with a series of input settlements to give a complete relationship between load and settlement. However, this process involves a tedious manual process to locate the design parameters from various charts. Interpolation or extrapolation could be required under some circumstances.

  3. This method is not compatible with the limit state design requirements where the designers are required to demonstrate that the strength limit state and serviceability limit state are satisfied. It is also difficult to incorporate the geotechnical strength reduction factors as per AS 2159.

  4. This method tends to overpredict the load capacity of the rock socket as reported in the paper of "Revisiting method for the design of rock socketed piles" by Johnston (2020) in ASCE.

  5. This method is not suitable for designing the rock socket with considering side resistance only.

The PileAXL program does not include the chart-based design procedure of the Rowe and Armitage method for rock socket design, but it does incorporate the recommended relationships of ultimate shaft resistance fs, ultimate end bearing resistance fb and rock modulus Em from the Rowe and Armitage method. Load settlement curves are calculated using load transfer method based on T-Z and Q-Z curves.


The following relationship for ultimate shaft resistance fs is adopted in the PileAXL program for bored piles or drilled shafts into weathered rock based on Rowe and Armitage (1987) .

where UCS is the unconfined compressive strength (UCS) in MPa, and alpha and beta are the factors for shaft resistance.

For regular clean sockets (roughness R1, R2 and R3 as defined in the table above, the shaft resistance factors are adopted as below based on Rowe and Armitage (1987):

For clean, rough (R4) sockets, the shaft resistance factors are adopted as below based on Rowe and Armitage (1987):

The ultimate end bearing resistance fb based on Rowe and Armitage (1987) is calculated using the relationship below:

where UCS is the unconfined compressive strength (UCS) in MPa and Ncr is the bearing capacity factor which is adopted as 2.5 based on Rowe and Armitage (1987).


The following dialog shows the parameter input dialog of weathered rock – Rowe and Armitage for bored piles or drilled shafts in the PileAXL program. The required input parameters for this method are summarized as below:

  1. Total unit weight.

  2. Unconfined compressive strength, UCS.

  3. Rate of change for UCS along the depth below the layer top.

  4. Factor for shaft resistance, Alpha

  5. Factor for shaft resistance, Beta

  6. Bearing capacity factor, Ncr

One example is used to shown the application of Rowe and Armitage method included in the PileAXL program. This example involves a 750 mm diameter rock socket in weak rock to carry a working load of 4 MN. The details for this example are provided in Appendix A3 from CIRIA Report 181 (Gannon et al., 1999). This example has been used to demonstrate the rock socket design approach in CIRIA Report 181 with four different methods of estimation of load-carrying capacity and settlement of piles socketed into weak rock. Those four methods include: (1) Williams, Johnston and Donald (1980), (2) Rowe and Armitage (1987a,b), (3) Kulhawy and Carter (1992) and (4) Fleming (1992).

The figure above shows the ground profile with the pile length and loading conditions for this example. Axial force applied at the pile head is 4000 kN. Weak rock in this example has an unconfined compressive strength of 4 MPa. The rock mass modulus is adopted to be 300 MPa and the Poisson’s ratio is 0.2. The unit weight for this weak rock is adopted to be 24 kN/m3. The pile diameter is 750 mm and the design settlement is set as 10 mm.


The figure below shows the pile settlement curves of the pile lengths varying between 1 and 4 m. The pile length of 1.6 m results in a settlement value of about 10 mm under the applied load of 4 MN.

The figure below is extracted from CIRIA Report 181 (Gannon et al., 1999) and shows the analysis results for rock socket based on four different analysis methods. It can be seen that different analysis approaches result in different estimation of the socket length.

While the analysis using the PileAXL program appears to give the rock socket length similar to that from the method of Rowe and Armitage (1987a,b), the settlement estimated by the PileAXL program is 10 mm which is higher than that (7.44) from the method of Rowe and Armitage (1987a,b) for the same axial load of 4 MN.

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