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T-Z and Q-Z Curves for Axially Loaded Piles

Settlement prediction of single piles under axial loading is as important as the estimation of ultimate axial capacity which is the sum of ultimate total shaft resistance and end bearing resistance. Settlement control usually receives the most intention from geotechnical designers who usually have difficulties in complying with the settlement requirements as specified in many design specifications or standards if there is no thorough understanding of the mechanism involved in the settlement analysis of single piles under axial loading.

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Numerical simulation of the load transfer curves such as T-Z curves for shaft resistance and Q-Z curves for end bearing resistance is a practical approach for the conditions where layered soil profiles and/or many potential load cases and trial designs need to be undertaken.

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For the load transfer method, the pile settlement at the top under the axial load will be estimated with using T-Z curves to model the shaft displacement with the mobilization of the skin friction and Q-Z curves to model the response of the pile toe displacement to the mobilized end bearing resistance force.

 

T-Z Curve Models in PileAXL Program

 

T-Z Curves  

 

There are nine different T-Z curves available for modeling the mobilization of shaft resistance with settlement:

 

  1. T-Z curve – API Clay. It is based on the recommendation from API 2A-WSD (2000). Note that T-Z curve for clay is the same as the one from API RP2GEO (2011).

  2. T-Z curve – API Sand. It is based on the recommendation from API 2A-WSD (2000).

  3. T-Z curve – API RP2GEO Sand. It is based on the recommendation from API RP2GEO (2011).

  4. T-Z curve – Coyle and Reese Clay (1966). It is based on the recommendation from Coyle and Reese (1966).

  5. T-Z curve – Mosher Sand (1984). It is based on the recommendation from Mosher Sand (1984). Note that the initial modulus of side resistance is required for this T-Z curve model.

  6. T-Z curve – Reese and O’Neill Clay (1989). It is based on the recommendation from Reese and O’Neill (1989).

  7. T-Z curve – Reese and O’Neill Sand (1989). It is based on the recommendation from Reese and O’Neill (1989).

  8. T-Z curve – O’Neill and Hassan Rock (1994). It is based on the recommendation from O’Neill and Hassan (1994). Note that the elastic modulus  is required for this T-Z curve model.

  9. T-Z curve – user-defined. User-defined T-Z curve can be input by the users in the PileAXL program. Currently, a maximum number of 10 points are allowed in the program. The required input parameters for user-defined data are (1) z/D: the ratio of the input settlement (z) to the pile diameter and (2) t/tmax: the ratio of the input mobilised shaft resistance (t) to the ultimate shaft resistance (tmax).

 

Q-Z Curve Models in PileAXL Program

 

Q-Z Curves  

 

There are eight different Q-Z curves available for modeling the mobilization of end bearing resistance with settlement:

 

  1. Q-Z curve – API Clay. It is based on the recommendation from API 2A-WSD (2000). Note that Q-Z curve for clay/sand is the same as the one from API RP2GEO (2011).

  2. Q-Z curve – API Sand. It is based on the recommendation from API 2A-WSD (2000). Note that Q-Z curve for clay/sand is the same as the one from API RP2GEO (2011).

  3. Q-Z curve – Skempton (1951). It is based on the concept of Skempton (1951) which predicts the load in end bearing of a pile in clay as a function of the pile tip movement.

  4. Q-Z curve – Vijayvergiva (1977). It is based on the concept of Vijayvergiva(1977) which predicts the load in end bearing of a pile in sand as a function of the pile tip movement.

  5. Q-Z curve – Reese and O’Neill Clay (1989). It is based on the recommendation from Reese and O’Neill (1989).

  6. Q-Z curve – Reese and O’Neill Sand (1989). It is based on the recommendation from Reese and O’Neill (1989).

  7. Q-Z curve – Elastic-Plastic Model. Note that Young’s modulus  and Poisson’s ratio  are required for this Q-Z curve model.

  8. Q-Z curve – user-defined. User-defined Q-Z curve can be input by the users in the PileAXL program. Currently, a maximum number of 10 points are allowed in the program. The required input parameters for user-defined data are (1) z/D: the ratio of the input settlement (z) to the pile diameter and (2) Q/Qp: the ratio of the input mobilised end bearing resistance (Q) to the ultimate end bearing resistance (Qp).

 

PileAXL TZ Curve Information.PNG
Single Piles and Pile Groups under General Loading
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