# Flow-Induced Stresses and Displacements in Jointed Concrete Pipes Installed by Pipe Jacking Method

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{out}is the soil overburden pressure on the pipe, P is the transient pressure of the fluid, R is the internal radius, and e is the thickness of the pipe.

_{out}(soil pressure), the pipe displacements can be described by Equations (1) and (2), as [5]

_{t}the mass density of the wall material, ${\dot{u}}_{z}$ and ${\dot{u}}_{r}$ the axial and radial pipe velocities, σ

_{r}the axial and radial stresses, and σ

_{φ}the hoop stress. In the present study, the pipes were considered long enough, so that σ

_{z}becomes negligible due to the plane stress principle.

_{φ}and σ

_{r}are presented in Equations (9) and (10), as

#### Literature Review and Motivation

## 2. Materials and Methods

#### 2.1. Model Geometry

#### 2.2. Soil and Material Properties

#### 2.3. Flow Characteristics

#### 2.4. Modeling Procedure

- The surrounding soil is monolith.
- The concrete lining behavior is considered as non-linear.
- A damage plasticity behavior is considered in the concrete lining.
- The CPE8R (eight-node plane strain quadrilateral, biquadratic displacement, reduced integration) elements are used for the simulation of the concrete pipe.
- Based on the Cam-Clay criterion, the soil is considered as a plastic material.
- Dynamic explicit method is applied to solve the finite element equations in the Abaqus FEA.

#### 2.4.1. Acoustic Environment

#### 2.4.2. Interactions between Model Components and Meshing

#### 2.4.3. Transient Flow in the Pipe

_{w}(kg/m

^{3}) is the specific mass of water, k

_{w}(GPa) is the bulk modulus of water, d (m) is the pipe diameter, E (GPa) is the modulus of elasticity of concrete, and e (m) is the thickness of the pipe [27]. The calculated values for a and maximum pressure under the transient flow conditions are presented in Table 2.

## 3. Results

#### 3.1. No-Flow Condition

_{2}) and horizontal (U

_{1}) displacements in the soil environment, respectively, and Figure 10 shows stresses in the pipe wall under no-flow conditions. In Figure 10, as well as in other figures showing stress distribution contours in the following sections, the blue color shows areas in compression, while red shows areas in tension.

#### 3.2. Steady Flow Condition

_{2}) and horizontal (U

_{1}) displacements in the soil environment, respectively, and Figure 13 shows the stresses in the pipe wall under steady flow conditions.

#### 3.3. Transient Flow Condition

_{2}) and horizontal (U

_{1}) displacements in the soil environment, respectively, and Figure 16 shows the stresses in the pipe wall under transient flow conditions.

## 4. Discussion

_{No-flow}, U

_{Steady}, and U

_{Transient}, refer to total displacements under no-flow, steady flow, and transient flow conditions, respectively.

## 5. Conclusions

- Under the no-flow condition, the most significant displacements occurred at the bottom of the section. This can be attributed to the soil inflation phenomenon, as a result of drilling and alteration of stress distribution in the soil environment.
- Under steady flow condition, the soil environment showed small displacements, due to the internal pressure and fluid weight in the pipe.
- By the occurrence of transient pressure due to the event of transient flow in the pipe, the displaced region was enlarged, and the pipe and surrounding soil showed an upward movement.
- Under all scenarios, maximum compressive and tensile stresses were formed at the junction. The maximum value was observed under the transient flow condition, where the tensile stress exceeded the allowable tensile capacity of the concrete. This situation will cause cracks in the pipe wall and consequently lead to water leakage and reduced operational capacity of the pipeline.

## Author Contributions

## Funding

## Conflicts of Interest

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Material | Parameter | Value |
---|---|---|

Soil | Log. of Bulk Modulus | 0.026 |

Poisson’s Ratio | 0.4 | |

Tensile Limit | 0 | |

The Angle of Internal Friction | 23 | |

Log. of Plastic Bulk Modulus | 0.174 | |

Density (Kg/m^{3}) | 1800 | |

Stress Ratio | 0.94 | |

Initial Yield Surface Size (Pa) | 4884 | |

Wet Yield Surface Size | 1 | |

Flow Stress Ratio | 0.778 | |

Concrete | Young’s Modulus (GPa) | 20 |

Compressive Strength (MPa) | 28.3 | |

Tensile Strength (MPa) | 3 | |

Poisson’s Ratio | 0.25 | |

Density (Kg/m^{3}) | 2500 | |

Water | Density (kg/m^{3}) | 1000 |

Bulk Modulus (GPa) | 2.7 |

Parameter | Value |
---|---|

a (m/s) | 854 |

Max. Pressure (MPa) | 2.61 (378.55 psi) |

Scenario | Max. Displacements (mm) | Max. Stresses (MPa) | ||
---|---|---|---|---|

Vertical | Horizontal | Tensile | Compressive | |

No-flow Condition | 5 | 3 | 2.69 (390.15 psi) | 2.14 (310.38 psi) |

Steady Flow | 1 | 1 | 3.86 (559.85 psi) | 6.78 (983.36 psi) |

Transient Flow | 4 | 1 | 8.11 (1174.81 psi) | 1.73 (250.92 psi) |

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**MDPI and ACS Style**

Karakouzian, M.; Karami, M.; Nazari-Sharabian, M.; Ahmad, S.
Flow-Induced Stresses and Displacements in Jointed Concrete Pipes Installed by Pipe Jacking Method. *Fluids* **2019**, *4*, 34.
https://doi.org/10.3390/fluids4010034

**AMA Style**

Karakouzian M, Karami M, Nazari-Sharabian M, Ahmad S.
Flow-Induced Stresses and Displacements in Jointed Concrete Pipes Installed by Pipe Jacking Method. *Fluids*. 2019; 4(1):34.
https://doi.org/10.3390/fluids4010034

**Chicago/Turabian Style**

Karakouzian, Moses, Mehrdad Karami, Mohammad Nazari-Sharabian, and Sajjad Ahmad.
2019. "Flow-Induced Stresses and Displacements in Jointed Concrete Pipes Installed by Pipe Jacking Method" *Fluids* 4, no. 1: 34.
https://doi.org/10.3390/fluids4010034