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🚧 Automated Anchored Sheet Pile Wall Design with Optimization

Adisorn O. | ALPS Consultants



📌 The Problem with Traditional Methods



Anchored sheet pile (SP) walls are typically designed using fixed-end or free-end methods* based on assumed earth pressures and trial embedment. These methods:


  • Treat anchor force T and passive resistance F_p as known outcomes

  • Don’t explicitly address how T is mobilized in the field

  • Lack optimization — leading to overdesign or unsafe assumptions

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Fig. Anchored sheet pile wall (problem statement)

Note:

*In Free-end (free-earth) method the Fp = 0 and hence x4 = 0. The equilibrium is then achieved by Fa1, Fp2, and T only. The moment equilibrium about the anchor point is used to solve for x1, and the force equilibrium is used to solve for T.


For Fixed-end (fixed-earth) method, Fp > 0 and hence x4 > 0. Either embedment depth x1 or pretention force T is solved iteratively, i.e. bisection method or secant method, to get the value of T and Fp that are in equilibrium, i.e. (FS = 1.0). Once Fp is known, x4 can be computed.


🚀 Our Solution: AI-Powered Optimization



We developed a metaheuristic optimizer that minimizes wall embedment while satisfying the constraints:


  • Force equilibrium

  • Factor of Safety (FS) > 2.0 (moment about toe)

  • Geotechnical reality: Fa1, Fa2, Fp are computed from φ, γ, H



Objective:

min(x_1 + x_4) -- embedment depth

Where:


  • x_1 = depth to toe

  • x_4 = passive wedge depth

  • x_3 = anchor depth

  • T = anchor tension





🔍 What Makes This Tool Unique?


Feature

Traditional

Our Optimizer

Optimization

❌ No

✅ Yes

Passive wedge as variable

❌ Ignored

✅ Designed

Mobilization of T

❌ Assumed

✅ Considered

Soil parameters (φ)

✅ Manual

✅ Auto Ka/Kp

Output

Embedment

Embedment + FS + T + Visualization



🧠 Key Insight: Anchor Tension ≠ Reality



In passive systems (no pretension), tension T only develops if the wall moves enough.


Traditional methods:


  • Compute T as equilibrium outcome

  • Ignore whether that force is actually mobilized



Our tool exposes this gap, allowing engineers to:


  • Suggest the pretension force applied to the anchor

  • Suggest the extended depth to develop passive wedge beneath the toe



🧪 Sample Output


✅ Auto-generated wall + forces plot

✅ Convergence plot of optimization

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--- OPTIMIZED DESIGN REPORT (v4) ---

Backfill height H = 3.00 m

phi_backfill = 30.0 deg -> Ka_back = 0.333

phi_soil_below_drag = 32.0 deg -> Kp_below = 3.255

x1 (toe depth) = 2.000 m

x4 (passive wedge) = 1.955 m

x1+x4 (embedment) = 3.955 m

T (anchor tension) = 149.33 kN/m

x3 (anchor depth) = 0.50 m

Fa1 (active R) = 75.00 kN/m

Fp2 (passive L) = 39.06 kN/m

Fp (passive) = 111.95 kN/m

FS (toe rotation) = 2.000

Equilibrium Fx = -1.433 kN/m

✓ SAFE and STABLE design.



📈 Applications



  • Deep excavations and ports

  • Basement retaining walls

  • Anchor behavior simulation

  • Teaching geotechnical interaction



🎯 Why It Matters


This tool brings anchored wall design into the age of AI-assisted engineering — moving beyond charts and assumptions, into intelligent, adaptive, and transparent design.

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