Introduction

For lateral loads on a pile, p-y curves are widely used based on the American Petroleum Institute (API) recommended practices (API 2000) even for large diameter piles with short embedment (monopiles). However, the p-y curves in API 2000 were developed based on slender piles and this may not be appropriate for large-diameter monopiles. Recently, the PISA (Pile Soil Analysis) research project was carried out to study the behavior of monopiles and overcome the limitations of previous methods. In this article, the pile resistance of monopiles using both methods is analyzed and compared. 

API method

The p-y model in API was developed based on field tests of small diameter flexible piles. The pile is modelled as an Euler-Bernoulli (slender) beam element. The reaction of a pile under a lateral load is modelled by p-y curves where p and y are the reaction and displacement of the pile at a certain depth (Fig. 1), respectively. The API includes p-y curves for soft clay, stiff clay, and sand.

Additional details about API method and these p-y curves can be found in literature.

Fig. 1. p-y model in the API method.

PISA method

A large diameter, short monopile subjected to a lateral load can be represented in one dimension (1D) in the PISA method (Burd et al. 2020a). In addition to a distributed lateral load, which is modelled by p-y curves, three other components of soil reaction are assumed to act on the monopile, i.e., distributed moment, lateral force and moment at the base (Fig. 2).

The soil reaction curves can be derived from 3D models and this is called the numerical-based design approach. The soil reaction curves can also be based on pre-defined functions and this is called the rule-based design approach. The monopile is represented by Timoshenko beam theory. This allows the shear strains in the pile to be incorporated in the analysis in an approximate way.

Fig. 2. PISA design model: (a) idealization of the soil reaction components acting on the pile; (b) 1D finite-element implementation of the model showing the soil reactions acting on the pile (Burd et al. 2020b)

Comparison of monopile relation using the API and the PISA method

Numerical models

Monopiles analyzed using the PISA method - implemented in the PLAXIS Monopile Designer program - are performed based on the numerical-based design for this comparison. This analysis involves a 3D Finite Element (FE) model to get the most accurate result. The 3D model-based reaction components using the PISA method are then used for 1D model calculation. For the 1D model using the API method, the reaction curves are built up based on the API guidance and imported into the PLAXIS Monopile Designer, which is based on the rule-based design approach.

Medium-scale field pile tests in the PISA project are selected to analyze and compare the results from the API and PISA methods for monopiles. The sites of the project were the Cowden over consolidated low-plasticity glacial clay till and the Dunkirk normally consolidated dense sand (Zdravkovic et al. 2020). So, the monopiles to be analyzed are in clay and sand.

To simulate the clay and sand at Cowden and Dunkirk, the NGI-ADP and Hardening Soil with small strain-stiffness (HSsmall) constitutive models were used. All soil parameters are mainly based on the previous studies from (Minga and Burd 2019a; b).

The monopiles with the diameter (D) of 0.762 m, embedment (L) of 3.98 and 4.0 m were used for this comparison study. The ratio of embedment to diameter is relatively small, i.e., L/D ~ 5.2, and the load applied at the pile head is about 10 m above the ground surface for both piles. The pile geometries at the Cowden site (clay) and Dunkirk site (sand) are shown in Table 1 below.

Pile	D (m)	L (m)	t (m)	h (m)	L/D	Remarks
CM9	0.762	3.98	0.011	9.98	5.50	Cowden site (clay)
DM4	0.762	4.00	0.014	10.00	5.25	Dunkirk site (sand)

Note: D: pile diameter; L: pile embedded length; h: load eccentricity/ stickup height; t: pile wall thickness.

Fig. 3. Load-displacement curves: (a) CM9: L/D = 5.2; (b) DM4: L/D = 5.25

Calculation results

The 3D model was analyzed with PLAXIS 3D, and the 1D models using PISA (1D-PISA) and API (1D-API) methods in PLAXIS Monopile Designer. The load-displacement curves at the ground surface are shown in Fig. 3.

For the pile in clay (Fig. 3a), it is seen that the results from the 3D model and 1D-PISA are very close to the measurement while the result from 1D-API is far from the measurement.
For the pile in dense sand (Fig. 3b), the load-settlement curves from all three approaches are quite close to the measured data but the curve of 1D-API deviates after the pile displacement at the ground surface reaches around 0.06 m.

At 0.1D of pile displacement at the ground surface, which is assumed to consider the pile’s bearing capacity, the pile resistance of 1D-PISA and 3D model results are in a very good match and well agrees with the measured data for the pile in both clay and sand. However, the resistance of the pile modelled using the 1D-API method is around 50% and 12% smaller than that from 1D-PISA result in clay and sand, respectively.

Conclusions

The 3D model in PLAXIS 3D, 1D-PISA, and 1D-API models in PLAXIS Monopile Designer were performed for monopiles (L/D ~ 5.2) in clay and sand.
The results show that the load-displacement curves of the monopiles of the 3D model and 1D-PISA are very close to each other and close to the measured data. The pile resistance at 0.1D pile displacement at the ground surface from 1D-API results show underestimated values compared to the 1D-PISA method, especially for monopiles in clay. This proves that the influence of the distributed moment, base shear and base moment is significant in the monopile analysis.

The PLAXIS Monopile Designer that uses the PISA method and can utilize the results of a PLAXIS 3D model would give reliable results of monopile analysis.