P-Y Curve Generator

Intro

This plug-in generates lateral soil resistance (P–Y) curves for pile foundations based on internationally recognized formulations such as API RP2A, Matlock (1970), Reese et al. (1974/1975), and various rock models. It integrates seamlessly with MIDAS Civil NX/Gen and supports detailed soil–structure interaction modeling by producing depth-dependent nonlinear springs for lateral analysis.

The tool evaluates multilayered soil profiles, automatically detects layer transitions, and computes P–Y curves at each pile node using rigorous geotechnical formulations, equivalent depth adjustments, and soil-specific resistance models. It enables fast generation, visualization, and export of spring data for structural analysis workflows.

Developed with

• • MIDAS CIVIL NX 2025(v2.x)

Supported P–Y Models

Clay Models

• Soft Clay – API RP2A (Matlock 1970)

• Stiff Clay – Reese et al. (1975), without Free Water

(Reese et al. (1975), with Free Water has not been implemented yet. Only the unit weight is automatically considered.)

Sand Models

• API Sand

• Reese et al. (1974) Sand

Rock Models

• Weak Rock – Reese (1997)

• Strong Rock – Tunner (2006), Vuggy Limestone

Supported Pile Types

• Pipe

• Solid Round

• H-Section

• Box

• Solid Rectangle

Verification

This chapter presents the verification of the P–Y curve generation module implemented in the plugin. The document includes quantitative comparisons between the lateral soil resistance curves produced by the module and the corresponding results obtained from external reference programs. Independent hand calculations were also performed to validate the theoretical implementation, layer transitions, and equivalent-depth procedures. These checks confirm that the governing P–Y formulations, depth-dependent soil properties, and integration logic are implemented accurately and consistently within the plugin.

Soil Layer Properties Table

1 – Soft Clay (API RP2A, Matlock 1970), 0.0–2.0 m, γ=18.0, c=50, strain50=0.01

2 – Sand (API RP2A), 2.0–4.0 m, γ=18.0, φ=30°, kpy=default

3 – Sand (Reese et al., 1974), 4.0–6.0 m, γ=18.85, φ=36.9°, kpy=5000

4 – Stiff Clay (Reese et al., 1975), 6.0–8.0 m, γ=19.0, c=100, strain50=0.005

5 – Weak Rock (Reese 1997), 8.0–10.0 m, γ=22.0, qu=5000, RQD=50%, krm=0.005, E=5000

6 – Strong Rock (Tunner 2006), 10.0–50.0 m, γ=24.0, qu=20000

Pile Geometry Summary

• Total Length: 15.0 m

• Section Type: Circular

• Diameter: 1.20 m

• p-multiplier: 1.0

• Shift: 0 m

Compare Sheet

• Depth 0.0 m : Soft Clay (API RP2A, Matlock 1970)

• Depth 2.50 m : Sand (API RP2A)

• Depth 4.50 m : Sand (Reese et al., 1974)

• Depth 6.50 m : Stiff Clay (Reese et al., 1975)

• Depth 8.50 m : Weak Rock (Reese 1997)

• Depth 10.50 m : Strong Rock (Tunner 2006, Vuggy Limestone)

Plugin-Implemented Theoretical Features

Layered Soil and Equivalent Depth (Georgiadis Method)

When differing soil layers exist along the pile length, lateral resistance must be evaluated by equivalent depth transformation. The accumulated resistance of upper layers is converted into an equivalent starting depth for the next layer:

\(\int_0^{h_{eq,i}} p_i(z)\, dz = f0_i\)

This ensures each layer’s P–Y behavior begins from the correct resistance state.

Node Influence Zone and Spring Assembly

Each pile node receives an influence zone:

Lateral reaction:

\(P(y)=\int_{z_1}^{z_2} p(y,z)\,dz\)

This captures layer changes, diameter changes, and nonlinear stiffness variation with depth.

Effective Diameter for Non-Circular Sections

Most classical P–Y formulations—including Reese et al. (1974), Reese et al. (1975), Matlock (1970), and API RP2A—are derived from tests performed on circular piles. Therefore, the lateral resistance equations are normalized with respect to the pile diameter D.

For non-circular sections (H-piles, box sections, rectangular piles), the soil–structure interaction does not directly match the assumptions used in these formulations. To apply these models consistently, the section must be converted into an equivalent circular pile that has the same soil–contact perimeter.

If a circular pile of diameter \( D_{\text{eff}} \) has the same perimeter:

\[ \boxed{ D_{\text{eff}} = \frac{P_{\text{shape}}}{\pi} } \]

where \(P_{\text{shape}}\) is the perimeter of the actual pile cross-section.

Classical P–Y formulas use circular piles. Non-circular sections are converted to an equivalent circular diameter via:

Group Pile and Battered Pile

Group Effect:

When piles are installed in a group with close spacing, the group carries less load than a single pile subjected to the same lateral displacement. This reduction is known as the group effect, which occurs because the resistance zones around individual piles overlap, resulting in a decrease in lateral soil resistance.

The p-multiplier value is influenced by:

• pile spacing, and

• the location of the pile within the group.

Piles in the leading row generally have higher p-multipliers than those in the trailing rows, because the trailing piles experience greater overlap of their soil-resistance zones. In design practice, the average p-multiplier of all piles in the group is often used to represent the overall group efficiency.

Mokwa and Duncan (2001) proposed a design chart to estimate p-multipliers based on pile spacing and pile-group configuration. Figure 3 summarizes previous experimental data, including full-scale lateral load tests and centrifuge tests, while Table 1 presents the numerical values derived from this design chart.

Battered Piles:

Kubo (1965) and Awoshika & Reese (1971) investigated the influence of batter angle on the behavior of laterally loaded battered piles. Kubo conducted both model tests and full-scale field experiments, while Awoshika and Reese performed tests on 2-inch diameter piles in sand.

Their studies showed that introducing a batter—either positive or negative—causes the mobilized soil resistance to increase or decrease compared to a vertical pile. The magnitude of this change can be obtained from the corresponding curve, which provides a ratio of soil resistance derived by comparing the groundline deflection of a battered pile with that of a vertical pile. This ratio is entirely based on experimental observations.

Spring Assembly (Force–Deformation Function)

Each pile node is assigned an influence zone:

• First node: from ground surface to mid-depth

• Intermediate nodes: mid-depth between adjacent nodes

• Last node: from previous mid-depth to tip

Lateral resistance for each displacement y is computed as:

\[ P(y) = \int_{z_1}^{z_2} p(y, z)\, dz \]

This process captures:

• Layer changes inside an element

• Diameter or sectional property changes

• Nonlinear stiffness variation with depth

Result: physically accurate nonlinear springs for lateral pile–soil interaction.

Example

During the P–Y force integration for Node 8130, the algorithm evaluates the soil reaction along the node’s influence zone, which spans from pile depth 9.0 m to 10.0 m. This corresponds to soil depths from 5.20 m to 6.20 m.

The influence zone crosses two different soil layers:

• Layer 3: Reese Sand (soil depth ≈ 5.20 m to 5.98 m)

• Layer 4: Stiff Clay (soil depth ≈ 6.09 m to 6.20 m)

For the displacement value –1.255879 m, the module evaluates the lateral soil resistance \( p(y,z) \) at 10 subdivision points. Each point uses the correct soil model depending on its layer:

• Reese Sand → higher stiffness, p ≈ –1500 to –1950 kN/m

• Stiff Clay → lower resistance, p ≈ –920 kN/m

After evaluating all 10 points, the values are numerically integrated using the trapezoidal method to obtain:

\[ P = -1607.42\ \text{kN} \]

This represents the total P–Y spring force contribution for the given displacement at Node 8130, correctly capturing the transition between Reese Sand and Stiff Clay in the influence zone.

=== P-Y Integration : Node 8130, Pile Depth 9.50 m (Soil Depth 5.70 m) === Influence Zone (pile): 9.00 m ~ 10.00 m (length: 1.00 m) Influence Zone (soil): 5.20 m ~ 6.20 m Integration points: 10 Number of Calculate Point: 5 First displacement: -1.255879 m Starting integration for displacement -1.255879 m...  [0] Pile 9.00 m / Soil 5.20 m (elev. -5.20 m): Layer 3 (Reese Sand), p = -1520.44 kN/m  [1] Pile 9.11 m / Soil 5.31 m (elev. -5.31 m): Layer 3 (Reese Sand), p = -1570.40 kN/m  [2] Pile 9.22 m / Soil 5.42 m (elev. -5.42 m): Layer 3 (Reese Sand), p = -1631.28 kN/m  [3] Pile 9.33 m / Soil 5.53 m (elev. -5.53 m): Layer 3 (Reese Sand), p = -1694.03 kN/m  [4] Pile 9.44 m / Soil 5.64 m (elev. -5.64 m): Layer 3 (Reese Sand), p = -1757.57 kN/m  [5] Pile 9.56 m / Soil 5.76 m (elev. -5.76 m): Layer 3 (Reese Sand), p = -1821.88 kN/m  [6] Pile 9.67 m / Soil 5.87 m (elev. -5.87 m): Layer 3 (Reese Sand), p = -1888.51 kN/m  [7] Pile 9.78 m / Soil 5.98 m (elev. -5.98 m): Layer 3 (Reese Sand), p = -1959.98 kN/m  [8] Pile 9.89 m / Soil 6.09 m (elev. -6.09 m): Layer 4 (Stiff Clay), p = -919.23 kN/m  [9] Pile 10.00 m / Soil 6.20 m (elev. -6.20 m): Layer 4 (Stiff Clay), p = -927.35 kN/m  → Integration Result: P = -1607.42 kN (disp = -1.255879 m)

Benefits of this plugin

• Generates depth-dependent P–Y springs for multilayer soil systems

• Accurately reflects layer transitions using equivalent-depth integration

• Supports all major soil resistance models used in modern pile design

• Provides P–Y curves, soil profile charts, and layer summaries

• Fully compatible with MIDAS Civil/GEN NX nonlinear boundaries

• Allows exporting spring force–displacement tables

How to use this plugin?

1) Input soil layers

The plugin uses Ground Level as the vertical reference. Depths below ground level are entered as positive values, and elevations above ground level are entered as negative values.
This convention is based on borehole data.
Accordingly, if the groundwater level is above the ground surface, it should be entered as a negative value.

2) Input pile geometry 

File input can be imported directly by selecting elements in a MIDAS product and
clicking the “Import from MIDAS Product”

If the pile group layout in the model is rotated relative to the global coordinate system, a rotation angle can be specified to correctly define the direction of soil behavior.

the “Group Effect Calculator” on the right-side panel allows users to compute the p-multiplier automatically or enter a custom p-multiplier value manually, enabling convenient consideration of group piles and battered piles.

The p-multiplier can be specified independently for the X and Y directions, and multiple values can be entered simultaneously by dragging across a range of cells, similar to Excel.

3) Pile-Soil Assignment

Pile–Soil Assignment When creating a p–y curve case, users can specify the previously defined pile
information, soil profile, and pile shift values. This allows the creation of detailed and customizable analysis cases tailored to various pile–soil conditions.

The p–y curve is generated only after clicking the “Save and Generate Non-Linear Spring” button.

4) Review charts and Generate Modelling

Users can review the generated boundary condition calculations, and by clicking “Generate Boundary Condition Modelling”, the corresponding boundary conditions can be created directly in the MIDAS product.