XII Congreso Nacional de Ingeniería Sísmica
Structural Reliability in Deep Foundations
Reliability assessment of an optimized property-line pile–cap system (cap 0.60 × 1.20 × 1.50 m, pile D = 1.0 m and L = 7.0 m) under a 1500 kN axial load, combining a nonlinear OpenSeesPy model with 10,000 Monte Carlo realizations and a strut-and-tie design of the cap.
Video · 53 s
The paper in one minute
The property-line pile and cap modelled in OpenSeesPy, ten thousand Monte Carlo runs on soil stiffness and drilling eccentricity, the reliability index next to the failure probability counted in the simulation, and the strut-and-tie design of the cap that follows from that demand.
Research Overview
Deterministic design of deep foundations leaves the variability of soil–structure interaction out of the calculation and tends to produce oversized geometries, with greater impact when the foundation must remain inside the property line. The paper, presented at the XII Congreso Nacional de Ingeniería Sísmica hosted by the Escuela Colombiana de Ingeniería Julio Garavito, evaluates a property-line pile–cap system designed for performance, without a global factor of safety.
The column load of 1500 kN sits 0.30 m off the pile axis and a 100 kN lateral load acts at the column head, 3.0 m above the cap, so the cap carries an overturning moment from both and from P–Δ effects. The study first checks the kinematic serviceability limit of 75 mm (ASCE 41-17 and FHWA) in probabilistic terms, and then follows that demand through the cap, treated as a D-region with a strut-and-tie model.
Results
- Mean lateral displacement of 45.28 mm at the column head (13.8 mm at the pile head), about 40% below the 75 mm limit of ASCE 41-17 and FHWA
- Reliability index β = (75 − 45.28) / 6.70 = 4.44 by second moment, which under a normal response means Pf ≈ 4.5 × 10⁻⁶
- Counting the simulation directly, 17 of the 10,000 runs exceed 75 mm: Pf ≈ 1.7 × 10⁻³ (β ≈ 2.9, estimator COV 24%). The lognormal soil stiffness skews the response and the tail is heavier than the normal fit; β ≈ 2.9 remains above the β = 1.5 target of EN 1990 for irreversible serviceability states over 50 years
- Design moment of 817.92 kN·m: 450 kN·m from the nominal eccentricity, 67.92 kN·m from P–Δ and 300 kN·m from the lateral load, with a tie force Tu = 817.92 / 1.25 = 654.34 kN
- The CCT node shows that No. 10 column bars need mechanical anchorage in a 0.60 m wide cap, with transverse reinforcement ρ⊥ ≥ 0.003 (No. 5 @ 200 mm) against bursting and splitting
Methodology
Two-dimensional OpenSeesPy model of a 7.0 m pile with D = 1.0 m, discretized every 0.50 m, with cracked stiffness 0.35 Ig (ACI 318-19), elastic–perfectly plastic soil springs (pu = 9 cu D) and a P–Δ geometric transformation. The cap is a rigid link that carries the column, 0.40 × 0.80 m and 3.0 m high, onto the pile head. With pu = 9 cu D none of the springs yields in the 10,000 runs, so the soil response stays linear and P–Δ is the nonlinear term.
Two random variables drive the 10,000 Monte Carlo realizations: the subgrade modulus ks, lognormal with a mean of 15,000 kN/m³ and COV = 30% (Phoon and Kulhawy), and the accidental drilling eccentricity δe, normal with zero mean and σ = 0.05 m.
The scope covers axial load, eccentricity moments and a 100 kN lateral load at the column head. The element is not part of the seismic-force-resisting system, so seismic or wind demands on the structure were not evaluated.
Project Details
- Type
- Conference Paper
- Event
- 12CNIS
- Presented
- June 2026
- Proceedings
- pp. 252–260
- Focus Area
- Performance-based foundation design
- Methods
- OpenSeesPy · Monte Carlo · STM
- Host Institution
- Escuela Colombiana de Ingeniería Julio Garavito
- Event Link
- View Event Page