PDR Method – Combined Piled-Raft Foundation Calculator

PDR Method – CPRF Calculator

This calculator implements the simplified Poulos–Davis–Randolph load-sharing/stiffness approach. It is intended for preliminary engineering calculations and checking. It is not a substitute for a project-specific geotechnical investigation, detailed soil–structure interaction analysis, structural design, or the governing Indian Standard/project specifications.

1. Basic Foundation Data

Total service load Q (kN)

Number of piles n

Pile diameter D (m)

Pile length L (m)

Raft length Bx (m)

Raft width By (m)

2. Foundation Stiffness

Enter stiffness values obtained from your selected raft/pile analysis method. Units: kN/m.

Raft stiffness Kr (kN/m)

Pile-group stiffness Kpg (kN/m)

Interaction factor αrp 0 to <1. Use the calculated value below only when the adopted Randolph formulation is appropriate.

3. Optional Randolph Interaction-Factor Calculation

This section calculates αrp from an adopted simplified Randolph-type formulation. Review the formulation and soil parameters for the actual project before using the value.

Average soil shear modulus Gavg (kPa)

G at pile shaft/near pile Gl (kPa)

G at pile base Gb (kPa)

Poisson's ratio ν

Use calculated αrp? No – use entered αrpYes – use calculated αrp

4. PDR Calculation

5. Results

Raft load Qr

–

kN

Pile-group load Qp

–

kN

Raft share

–

%

Pile-group share

–

%

Combined stiffness Kpr

–

kN/m

Average settlement s

–

mm

Load per pile (average)

–

kN/pile

Used αrp

–

–

Calculation Details

Parameter	Value	Unit

6. Equations Used

Raft load fraction:

X = [(1 − αrp) Kr] / [Kpg + (1 − 2αrp) Kr]

Raft load:

Qr = X × Q

Pile-group load:

Qp = (1 − X) × Q

Combined stiffness:

Kpr = [Kpg + (1 − 2αrp)Kr] / [1 − αrp²(Kr/Kpg)]

Average settlement:

s = Q / Kpr

Equivalent radius per pile:

rc = √[Ar / (nπ)]

Adopted simplified Randolph-type influence radius:

rm = [0.25 + ξ{2.5ρ(1−ν) − 0.25}]L

ρ = Gavg / Gl     ξ = Gl / Gb

Interaction factor:

αrp = 1 − ln(rc/rp) / ln(rm/rp)

The interaction-factor formulation is sensitive to the adopted soil stiffness model and definitions. Verify the exact formulation required by the governing reference before using it for a final design.

7. Engineering Checks

Run the calculation to display checks.

Important Limitations

• This tool calculates global load sharing and average settlement only.
• It does not determine individual pile loads for corner, edge and interior piles.
• It does not calculate pile structural capacity, geotechnical ultimate capacity, raft bending, punching shear, one-way shear, contact-pressure distribution, lateral loads or seismic effects.
• The quality of Kr, Kpg and αrp controls the result. They should come from appropriate soil parameters, pile/raft geometry, load-transfer analysis, field testing and/or a validated numerical model.
• For important projects, compare the simplified result with an appropriate 3D soil–structure interaction model and field-test data.

PDR Method – CPRF Solved Numerical Example

This document presents a step-by-step manual calculation of a Combined Piled Raft Foundation (CPRF) using the simplified Poulos–Davis–Randolph (PDR) stiffness approach, matching the logic embedded in the interactive calculator script.

1. Input Parameters

The following baseline parameters are considered for this standard calculation example:

Category	Parameter	Symbol	Value	Unit
Basic Foundation Data	Total Service Load	\( Q \)	20,000	kN
	Number of Piles	\( n \)	16	nos
	Pile Diameter	\( D \)	0.60	m
	Pile Length	\( L \)	20.0	m
	Raft Length	\( B_x \)	10.0	m
	Raft Width	\( B_y \)	10.0	m
Foundation Stiffness	Unpiled Raft Stiffness	\( K_r \)	100,000	kN/m
	Pile Group Stiffness	\( K_{pg} \)	400,000	kN/m
Soil Parameters (Optional)	Average Soil Shear Modulus	\( G_{avg} \)	25,000	kPa
	Shear Modulus at Shaft	\( G_l \)	25,000	kPa
	Shear Modulus at Base	\( G_b \)	25,000	kPa
	Poisson's Ratio	\( \nu \)	0.30	-

2. Step-by-Step Calculation Manual

Step 1: Calculate Geometric and Interaction Properties

First, evaluate the raft area \( A_r \) and pile radius \( r_p \):

• \( A_r = B_x \times B_y = 10.0 \times 10.0 = \mathbf{100.0\text{ m}^2} \)
• \( r_p = D / 2 = 0.60 / 2 = \mathbf{0.30\text{ m}} \)

Next, determine the equivalent raft area radius per pile (\( r_c \)):

r_c = √[ A_r / (n × π) ]

$$ r_c = \sqrt{\frac{100}{16 \times \pi}} = \sqrt{\frac{100}{50.2655}} = \sqrt{1.9894} = \mathbf{1.4105\text{ m}} $$

Now evaluate the simplified Randolph influence factors (\( \rho \), \( \xi \), and \( r_m \)):

• \( \rho = G_{avg} / G_l = 25000 / 25000 = \mathbf{1.00} \)
• \( \xi = G_l / G_b = 25000 / 25000 = \mathbf{1.00} \)

r_m = [0.25 + ξ {2.5 ρ (1 − ν) − 0.25}] × L

$$ r_m = [0.25 + 1.00 \times \{2.5 \times 1.00 \times (1 - 0.30) - 0.25\}] \times 20 $$

$$ r_m = [0.25 + \{1.75 - 0.25\}] \times 20 = [0.25 + 1.50] \times 20 = 1.75 \times 20 = \mathbf{35.00\text{ m}} $$

Calculate the Raft-Pile Interaction Factor (\( \alpha_{rp} \)):

α_rp = 1 − [ ln(r_c / r_p) / ln(r_m / r_p) ]

$$ \ln(r_c / r_p) = \ln(1.4105 / 0.30) = \ln(4.7017) = 1.5479 $$

$$ \ln(r_m / r_p) = \ln(35.00 / 0.30) = \ln(116.667) = 4.7593 $$

$$ \alpha_{rp} = 1 - \left( \frac{1.5479}{4.7593} \right) = 1 - 0.3252 = \mathbf{0.6748} $$

Note: If manual/fixed interaction factor is adopted (e.g. \( \alpha_{rp} = 0.50 \)), substitute that value in subsequent equations. Below, we continue using the calculated value \( \mathbf{\alpha_{rp} = 0.6748} \).

Step 2: Calculate Load Sharing Proportion (Raft Fraction X)

The load fraction taken by the raft (\( X \)) is given by:

X = [ (1 − α_rp) × K_r ] / [ K_pg + (1 − 2 α_rp) × K_r ]

Calculate numerator and denominator separately:

• Numerator: \( (1 - 0.6748) \times 100,000 = 0.3252 \times 100,000 = \mathbf{32,520} \)
• Denominator: \( 400,000 + (1 - 2 \times 0.6748) \times 100,000 = 400,000 + (-0.3496) \times 100,000 = 400,000 - 34,960 = \mathbf{365,040} \)

$$ X = \frac{32,520}{365,040} = \mathbf{0.089086} \quad (\text{or } \approx 8.91\%) $$

Step 3: Calculate Load Distribution (Q_r and Q_p)

Using the total load \( Q = 20,000\text{ kN} \):

Q_r = X × Q

$$ Q_r = 0.089086 \times 20,000 = \mathbf{1,781.72\text{ kN}} $$

Q_p = (1 − X) × Q

$$ Q_p = (1 - 0.089086) \times 20,000 = 0.910914 \times 20,000 = \mathbf{18,218.28\text{ kN}} $$

Average Load per Pile:

$$ Q_{pile} = \frac{Q_p}{n} = \frac{18,218.28}{16} = \mathbf{1,138.64\text{ kN/pile}} $$

Step 4: Calculate Combined CPRF Stiffness and Settlement

The combined stiffness of the piled raft system (\( K_{pr} \)) is calculated as:

K_pr = [ K_pg + (1 − 2 α_rp) K_r ] / [ 1 − α_rp² (K_r / K_pg) ]

• Numerator: \( 365,040 \) (calculated in Step 2)
• Denominator term: \( 1 - (0.6748)^2 \times \left( \frac{100,000}{400,000} \right) = 1 - 0.455355 \times 0.25 = 1 - 0.113839 = \mathbf{0.886161} \)

$$ K_{pr} = \frac{365,040}{0.886161} = \mathbf{411,934.17\text{ kN/m}} $$

Finally, calculate average total settlement (\( s \)):

s = Q / K_pr

$$ s = \frac{20,000}{411,934.17} = 0.04855\text{ m} = \mathbf{48.55\text{ mm}} $$

3. Summary of Output Results

Raft Load (\( Q_r \))

1,781.72 kN

Share: 8.91%

Pile Group Load (\( Q_p \))

18,218.28 kN

Share: 91.09%

Combined Stiffness (\( K_{pr} \))

4,11,934 kN/m

CPRF System

Average Settlement (\( s \))

48.55 mm

Global Average

Final Result Verification Table

Output Parameter	Calculated Value	Unit	Engineering Verification
Used Interaction Factor (\( \alpha_{rp} \))	0.6748	-	Valid range \( [0 \le \alpha_{rp} < 1] \)
Raft Share (\( Q_r / Q \))	8.91	%	Raft carries minor portion due to higher pile stiffness
Pile Group Share (\( Q_p / Q \))	91.09	%	Piles carry majority of structural load
Average Load per Pile	1,138.64	kN/pile	Equally distributed across 16 piles
Equilibrium Check (\( Q_r + Q_p \))	20,000.00	kN	Matches Applied Load (100% Balanced)