Abstract
In this paper, a simple but feasible approach is proposed to predict the timedependent load carrying behaviours of jacked piles from CPTu measurements. The corrected cone resistance, which considers the unequal area of the cone rod and the cone, is used to determine the soil parameters used in the proposed approach. The pile installation effects on the changes in the stress state of the surrounding soil are assessed by an analytical solution to undrained expansion of a cylindrical cavity in K_{0}consolidated anisotropic clayey soil. Considering the similarity and scale effects between the piezocone and the pile, the CPTu measurements are properly incorporated in the shaft and end resistance factors as well as in the loadtransfer curves to predict the timedependent load carrying behaviours of the pile. Centrifuge model tests are conducted and the measured load carrying behaviours of the model piles are compared with the predictions to validate the proposed approach. The proposed approach not only greatly saves the time of conducting timeconsuming pile load tests, but also effectively avoids solving the complex partial differential equations involved in the consolidation analysis, and hence is feasible enough to determine the timedependent load carrying behaviours of jacked piles in clay.
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Abbreviations
 \( A,B \) :

Parameters for simplifying expression
 \( A_{1} , A_{2} \) :

Crosssectional areas of the cone rod and cone shaft
 \( A_{\text{p}} \) :

Crosssectional area of pile
 \( A_{{{\text{s}},i}} \) :

Area of pile shaft in soil layer \( i \)
 \( a \) :

Net area ratio
 \( a_{\text{b}} \left( t \right),a_{{{\text{s}},{\text{z}}}} \left( t \right) \) :

Timedependent model parameters of the loadtransfer curve for pile toe and shaft, respectively
 \( b_{\text{b}} \left( t \right),b_{{{\text{s}},{\text{z}}}} \left( t \right) \) :

Timedependent model parameters of the loadtransfer curve for pile toe and shaft, respectively
 \( C_{\text{q}} \left( t \right) \) :

Timedependent pile toe resistance factor
 \( c_{\text{h}} \) :

Horizontal consolidation coefficient
 \( D_{\text{pile}} ,D_{\text{CPTu}} \) :

Diameters of pile and piezocone
 \( e \) :

Void ratio
 \( F_{\text{su}} \left( t \right), F_{\text{qu}} \left( t \right) \) :

Timedependent pile shaft bearing capacity and pile toe capacity
 \( f_{\text{s}} \) :

Sleeve friction
 \( f_{\text{su}} \) :

Ultimate shaft resistance
 \( f_{{{\text{su}},i}} \left( t \right) \) :

Timedependent ultimate shaft resistance in layer \( i \)
 \( f_{{{\text{su}},{\text{z}}}} \left( t \right) \) :

Timedependent ultimate shaft resistance at depth z
 \( G \) :

Shear modulus
 \( G_{0} \) :

In situ shear modulus
 \( K_{0} \) :

Coefficient of earth pressure at rest
 \( K_{{0,{\text{b}}}} \left( t \right) \) :

Timedependent initial stiffness of pile toe
 \( K_{{0,{\text{z}}}} \left( t \right) \) :

Timedependent initial stiffness of the soil column with unit length at the pile–soil interface
 \( k_{\text{h}} \) :

Horizontal coefficient of permeability
 \( L \) :

Length of pile
 \( M \) :

Slope of critical state line
 \( N_{\text{c}} \) :

Pile toe resistance factor
 \( N_{\text{ke}} \) :

Cone resistance factor
 \( {\text{OCR}} \) :

Overconsolidation ratio
 \( p_{0}^{{\prime }} \) :

Farfield geostatic mean effective stress
 \( p^{{\prime }} \left( t \right) \) :

Mean effective stress of the soil adjacent to the pile shaft during consolidation
 \( p_{\text{f}}^{{\prime }} \) :

Mean effective stress of soil in the vicinity of the pile immediately after pile installation
 \( Q_{\text{u}} \left( t \right) \) :

Timedependent total load carrying capacity
 \( q_{\text{b}} \left( t \right) \) :

Mobilized resistance at pile toe
 \( q_{\text{bu}} \) :

Ultimate pile toe resistance
 \( q_{\text{bu}} \left( t \right) \) :

Pile toe resistance at any time after pile installation
 \( q_{\text{c}} \) :

Cone tip resistance
 \( q_{\text{e}} \) :

Effective cone tip resistance
 \( \bar{q}_{\text{e}} \) :

Average effective cone resistance in pile toe influence zone
 \( q_{\text{t}} \) :

Corrected cone tip resistance
 \( R_{\text{f}} \) :

Failure ratio
 \( r \) :

Radial distance from pile axis
 \( r_{\text{m}} \) :

Limiting radius beyond which shear stress induced by pile loading is negligible
 \( r_{\text{p}} \) :

Pile radius
 \( \gamma_{\text{w}} \) :

Unit weight of water
 \( r_{\text{y}} \) :

Radius of plastic zone developed around pile
 \( s_{{{\text{u}},{\text{tc}}}} , s_{{{\text{u}},{\text{ps}}}} \) :

Undrained shear strengths of soil under triaxial compression condition and plane strain condition, respectively
 \( T \) :

Nondimensional time
 \( T_{\text{pile}} ,T_{\text{CPTu}} \) :

Nondimensional time for dissipation of normalized excess pore pressure around the pile and piezocone, respectively
 \( t_{\text{pile}} ,t_{\text{CPTu}} \) :

Real consolidation time of the soil around the pile and piezocone
 \( U_{\text{pile}} \left( t \right),U_{\text{pile}} \left( t \right) \) :

Degrees of consolidation of the soil around the pile and piezocone
 \( u \) :

Pore water pressure
 \( u_{1} ,u_{2} ,u_{3} \) :

Measured pore water pressures at cone tip, shoulder and shaft
 \( v^{{\prime }} \) :

Effective Poisson’s ratio
 \( W_{\text{b}} \) :

Displacement at pile toe
 \( W_{{{\text{s}},z}} \) :

Pile–soil relative displacement at depth \( z \)
 \( \alpha \) :

Shaft resistance factor of total stress method
 \( \alpha_{\text{c}} \left( t \right) \) :

Timedependent shaft resistance factor
 \( \beta \) :

Shaft resistance factor of effective stress method
 \( \Delta u \) :

Excess pore water pressure
 \( \Delta u_{\text{pile}} ,\Delta u_{\text{CPTu}} \) :

Excess pore water pressure around the pile and the piezocone
 \( \Delta u_{\text{t}} \) :

Limit excess pore water pressure developed at the wall of an expanding spherical cavity
 \( \eta_{0} \) :

Initial stress ratio of soil
 \( \eta_{\text{y}}^{*} \) :

Relative stress ratio at the elastic–plastic boundary
 \( \kappa \) :

Slope of swelling line in \( e \)ln \( p^{{\prime }} \) plane
 \( \Uplambda \) :

Plastic volumetric strain ratio
 \( \lambda \) :

Slope of compression line in \( e \)ln \( p^{{\prime }} \) plane
 \( \upsilon \) :

Specific volume
 \( \xi \) :

Parameter for simplifying expression
 \( \rho_{\text{s}} \) :

Ratio of undrained shear strength at any given time after installation to in situ undrained shear strength
 \( \rho_{\text{G}} \) :

Ratio of shear modulus at any given time after installation to in situ shear modulus
 \( \sigma_{\text{r}}^{{\prime }} ,\sigma_{\text{z}}^{{\prime }} \) :

Radial and vertical effective stresses
 \( \sigma_{\text{u}} \) :

Limit expansion pressure
 \( \sigma_{{{\text{v}}0}}^{{\prime }} \) :

Effective vertical stress
 \( \sigma_{\text{rf}}^{\prime} ,\sigma_{\text{zf}}^{\prime} \) :

Radial and vertical effective stresses at failure
 \( \tau_{\text{rzf}} \) :

Shear stress at failure
 \( \tau_{{{\text{s}},{\text{z}}}} \left( t \right) \) :

Mobilized shaft shear resistance
 \( \varphi^{{\prime }} \) :

Internal effective friction angle of soil
 \( \chi \) :

Ratio of soil shear modulus at middle depth to that of the pile toe
 \( \psi_{\text{f}} \) :

Stresstransformed parameter under plane strain condition
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Acknowledgements
The authors are grateful for the financial support provided by the National Natural Science Foundation of China (Grant No. 41772290) for this research work.
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Li, L., Li, J., Sun, D. et al. A feasible approach to predicting timedependent bearing performance of jacked piles from CPTu measurements. Acta Geotech. 15, 1935–1952 (2020). https://doi.org/10.1007/s1144001900875x
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Keywords
 Centrifuge model test
 Corrected cone resistance
 CPTu measurements
 Load carrying behaviours
 Timedependent