# Multi-Failure Mode Assessment of Buried Concrete Pipes Subjected to Time-Dependent Deterioration, Using System Reliability Analysis

## Abstract

This article presents a reliability-based methodology for assessment of corrosion-affected, reinforced concrete sewers, considering serviceability and ultimate strength as limit state functions for multi-failure mode assessment. A stochastic model for system failure analysis is developed, which relates to key factors that affect concrete corrosion in a concrete sewer system in Harrogate in the United Kingdom. A time-dependent Monte Carlo simulation method is employed to quantify the probability of failure of concrete sewers with 70-cm diameter due to two categories of failure modes (serviceability and ultimate strength). Factors that affect the failure due to concrete corrosion are also studied by way of parametric sensitivity analysis.

## Keywords

System reliability analysis Multi-failure mode assessment Time-dependent deterioration Concrete sewers Monte Carlo simulation Concrete durability## List of Symbols

*a*Depth of the equivalent rectangular stress block (mm)

*A*Acid-consuming capability of the wall material

- \( A_{\text{s}} \)
Area of tension reinforcement in length

*b*(mm^{2}/m)*b*Unit length of pipe (1000 mm)

- \( B_{1} \)
Crack control coefficient for effect of spacing and number of layers of reinforcement

*c*Average rate of corrosion (mm/year)

- \( C_{1} \)
Crack control coefficient for type of reinforcement

- \( d \)
Distance from compression face to centroid of tension reinforcement (mm)

- \( d_{\text{b}} \)
Diameter of rebar in inner cage (mm)

- [DS]
Dissolved sulfide concentration (mg/l)

- \( f^{\prime}_{\text{c}} \)
Design compressive strength of concrete (MPa)

- \( f_{\text{y}} \)
Design yield strength of reinforcement (MPa)

*F*Crack width control factor

- \( F_{\text{c}} \)
Factor for effect of curvature on diagonal tension (shear) strength in curved components

- \( F_{\text{d}} \)
Factor for crack depth effect resulting in increase in diagonal tension (shear) strength with decreasing \( d \)

- \( F_{\text{N}} \)
Coefficient for effect of thrust on shear strength

- \( h \)
Overall thickness of member (wall thickness) (mm)

- \( i \)
Coefficient for effect of axial force at service load stress

*k*Acid reaction factor

*J*pH-dependent factor for proportion of H

_{2}S*w*Width of the stream surface

*P*′Perimeter of the exposed wall

- \( M_{\text{s}} \)
Service load bending moment acting on length

*b*(N mm/m)- \( M_{u} \)
Factored moment acting on length

*b*(N mm/m)- \( N_{\text{s}} \)
Axial thrust acting on length

*b*, service load condition (+ when compressive, − when tensile) (N/m)- \( N_{u} \)
Factored axial thrust acting on length

*b*(+ when compressive, − when tensile) (N/m)*S*Slope of the pipeline

*t*Elapsed time

*u*Velocity of the stream (m/s)

- \( V_{\text{b}} \)
Basic shear strength of length

*b*at critical section- \( {{\Upphi}} \)
Average flux of H

_{2}S to the wall- \( \phi_{\text{f}} \)
Strength reduction factor for flexure

- \( \phi_{\text{v}} \)
Strength reduction factor for shear

- \( \Updelta \)
Reduction in wall thickness due to corrosion (mm)

- \( \Updelta_{\hbox{max} } \)
Maximum permissible reduction in wall thickness (structural resistance or limit) (mm)

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