Description
ABSTRACT
The performance of buried pipelines in areas subjected to permanent ground displacements is an important engineering consideration in the gas distribution industry, since the failure of such systems poses a risk to public and property safety. Although, the ground movements and its variations over time can be detected and mapped with reasonable confidence, these data are of little use due to a lack of reliable models to correlate such displacements to the condition of the buried pipe. The objective of this thesis is to develop methods to estimate the pipe performance based on the measured ground displacement.
An analytical method was developed to estimate the pipe performance when the pipe is subjected to tensile loading caused by the relative ground movements occurring along the pipe axis. As a part of the derivation, a modified interface friction model was developed considering the increase in friction due to constrained dilation of the soil, and the impact of mean effective stress on soil dilation. This interface friction model was combined with a nonlinear pipe stress–strain model to derive an analytical solution to represent the performance of the pipe. Using the proposed model, axial force, strain, and mobilized frictional length along the pipe can be obtained for a measured ground displacement can be obtained. Large-scale field pipe pullout tests were performed to verify the results of the proposed analytical model, in which good agreements were observed for tests conducted at different soil/burial conditions, displacement rates and pipe properties. Considering the similarities in the axial pullout mechanism, the analytical model was extended to explain the pullout response of geotextiles buried in reinforced soil structures.
Another analytical model was derived for the case of a pipe that is subjected to combined loading from axial tension and bending when the initial soil loading is acting perpendicular to the pipe axis. With the direct account of the axial tensile force development, more realistic pipe performance behaviors were obtained as compared to the results obtained from traditional numerical formulations.
TABLE OF CONTENTS
COVER PAGE
TITLE PAGE
APPROVAL PAGE
DEDICATION
ACKNOWELDGEMENT
ABSTRACT
NOMENCLATURE
CHAPTER ONE
1.0 INTRODUCTION
1.1 BACKGROUND OF THE PROJECT
1.2 OBJECTIVES OF THE STUDY
1.3 SCOPE OF THE STUDY
1.4 PROJECT ORGANISATION
CHAPTER TWO
- LITERATURE REVIEW
- OVERVIEW OF THE STUDY
- PERFORMANCE OF THE PIPES SUBJECT TO AXIAL SOIL LOADING
- EXPERIMENTAL STUDIES TO DETERMINE RESPONSE OF BURIED PIPES SUBJECT TO AXIAL SOIL LOADING
- PULLOUT TESTS PERFORMED AT CORNELL UNIVERSITY
- FIELD PIPE PULLOUT TESTING
- FIELD PIPE MONITORING
- ANALYTICAL MODELS TO DETERMINE PIPE RESPONSE FROM AXIAL SOIL LOADING
- INTERFACE FRICTION BETWEEN SOIL AND PIPE
- COMPARISON OF EXISTING ANALYTICAL MODELS TO DETERMINE THE RESPONSE OF PE PIPES
- DETERMINING THE DISPLACEMENT CORRESPONDING TO PEAK FRICTIONAL RESISTANCE
- INTERFACE FRICTIONAL BEHAVIOR OF PIPES BURIED IN FINE-GRAINED MATERIALS
- STRESS-STRAIN BEHAVIOR OF THE PIPE MATERIAL
- ANALYTICAL APPROACHES TO DETERMINE THE LATERAL SOIL RESISTANCE OF PIPE
- EXPERIMENTAL APPROACHES TO DETERMINE THE LATERAL SOIL RESISTANCE PER UNIT LENGTH
- ACCIDENTS IN NATURAL GAS PIPELINES
- ACCIDENTS CAUSED BY GROUND MOVEMENTS
- DETERMINATION OF THE PIPE RESPONSE DUE TO GROUND MOVEMENTS
- FRAMEWORK FOR UNDERSTANDING THE PIPE-SOIL INTERACTION
- MODEL-SCALE AND ELEMENT-LEVEL TESTS ON PIPES
CHAPTER THREE
3.0 METHODOLOGY
3.1 CHARACTERIZATION OF MATERIAL PROPERTIES
3.2 FRICTION ANGLE OF SAND
3.3 PROPERTIES OF THE PIPE MATERIAL (MDPE)
3.4 CHARACTERIZATION OF STRESS-STRAIN PROPERTIES OF MDPE PIPES
3.5 EXPERIMENTAL DETAILS OF FIELD PIPE PULLOUT TESTS
3.6 TRENCH AND OTHER SUPPORTING STRUCTURES
3.7 DATA ACQUISITION SYSTEM
3.8 PREPARATION OF TEST SPECIMENS
CHAPTER FOUR
4.0 ANALYTICAL MODEL FOR PIPE RESPONSE FROM AXIAL SOIL
4.1 INTRODUCTION
4.2 SLIDE GEOMETRY
4.3 ANALYTICAL MODEL TO DETERMINE PIPE PERFORMANCE
4.4 DEVELOPMENT OF ANALYTICAL MODEL FOR INTERFACE FRICTION
4.5 IMPACT OF THE MEAN EFFECTIVE STRESS ON SOIL DILATION
- ANALYTICAL FORMULATION OF THE PIPE–SOIL INTERACTION RESPONSE
- DETERMINATION OF THE INTERFACE FRICTION ANGLE (d)
- DETERMINATION OF THICKNESS OF SHEAR ZONE (DTD)
- DETERMINATION OF SHEAR MODULUS DEGRADATION (G)
4.10 SELECTION OF INPUT PARAMETERS FOR THE ANALYTICAL SOLUTION
4.11 AXIAL PULLOUT TESTS PERFORMED ON DENSE SAND
4.12 AXIAL PULLOUT TESTS PERFORMED ON LOOSE SAND
4.13 COMPARISON OF RESULTS OBTAINED FROM ANALYTICAL SOLUTION AND FIELD PULLOUT TESTS
4.14 SELECTION OF INPUT PARAMETERS FOR THE ANALYTICAL SOLUTION
4.15 IMPACT OF DIFFERENT OF PIPE SIZE AND BURIAL DEPTH ON PIPE DISPLACEMENT CAPACITY
4.16 IMPACT OF DIFFERENT SDR VALUES ON PIPE PERFORMANCE
CHAPTER FIVE
5.1 SUMMARY AND CONCLUSIONS
5.2 FUTURE WORK AND RECOMMENDATIONS
5.3 REFERENCES
NOMENCLATURE
Ap The cross sectional area of the pipe
a, b, c,d Constants that can be determined by fitting the stress-strain responses obtained from uniaxial extension or compression tests
aˆ, bˆ
Constants to represent the variation of mobilized frictional length (non dimensional)
a and b Hyperbolic constants to represent the degradation of non-dimensionalized shear modulus ratio (non dimensional)
bGTX
Width of the geotextile (m)
C0 , C0¢ Constants to be determined from boundary conditions in pre-peak zone (non dimensional)
Cn , Cn¢ Constants to be determined from boundary conditions in post peak region, for the
nth geotextile/pipe element (m).
D Diameter of Pipe
d50 The average grain size of the soil.
E
ini
Initial modulus of the geotextile/pipe (N/m2)
G0 Initial/ small strain soil shear modulus (N/m2)
G(g ) Shear modulus of soil at a shear strain of g (N/m2)
H Burial depth of the geotextile or depth to pipe springline (m)
ID Relative density of the soil (non dimensional)
IR Relative dilatancy index (non dimensional)
K 0 Lateral earth pressure coefficient (non dimensional)
P Pullout force measured in the geotextile/pipe (N)
Q, R Constants used in Bolton’s (1986) relationship to link effective stress to dilatancy (non dimensional).
T Frictional force developed along a unit length geotextile/pipe (N/m)
T1 Peak frictional resistance developed along a unit length of geotextile/pipe (N/m)
Td Net increase in friction along a unit length of geotextile due to soil dilation (N/m)
tGTX
Thickness of the geotextile (m)
u Relative displacement of the geotextile/pipe at any given point x (m)
ue Relative displacement in the pre-peak zone (m)
u ‘ Tensile strain in the geotextile/pipe at any given point x (%)
Wp Weight of the pipe and its content
x Distance to any point along the geotextile/pipe, and represents the mobilized frictional length (m)
z Constant used to simplify the expression for relative displacement (non dimensional)
G Constant used to simplify the expression for interface friction (non dimensional)
d Interface Friction Angle
g Shear strain (%)
g Effective unit weight of soil (N/m3)
Dsdc Increase in normal stress due to soil dilation (N/m2)
h Hyperbolic constant used to represent the nonlinear stress-strain response of geotextile/pipe (non dimensional)
l Constant that represents the interface and geotextile/pipe material properties (1/m)
n Poisson’s ratio of the soil (non dimensional)
- ¢ Normal effective stress due to soil overburden (N/m2)
- u ¢ Stress in geotextile/pipe corresponding to a strain level of
t Shear stress at the geotextile- soil interface (N/m2)
u ‘ (N/m2)
fS¢ / GSY
fm¢ ax
fc¢v
y max
Interface friction angle between soil and geotextile (°) Peak friction angle of the soil (°)
Constant volume friction angle (°)
Maximum angle of dilation (°)
CHAPTER ONE
1.0 INTRODUCTION
1.1 BACKGROUND OF THE STUDY
Plastic pipes have been employed in gas, oil, potable water, sewer, marine, landfill, electrical and telecommunication lines due to their many advantages over rigid steel or concrete pipes. One of the main attractions is the cheaper material cost of plastic pipes compared to metallic pipes. Additionally, the lightweight and flexibility offered by the plastic pipes are likely to reduce the costs relating to pipe installation. It has been suggested that, compared to steel pipes, plastic pipes require less maintenance during their operation life-time if the pipes are properly designed and installed (PIPA 2001). A greater deformation tolerance and stress-relaxation in plastic pipes is another key advantage when considering the plastic pipes response to external loading. Owing to these benefits, plastic pipes have been employed in rugged terrain, in the presence of aggressive chemicals and in extreme climates.
Sowing to the aforementioned advantages, polyethylene (PE) pipes in particular have become vastly popular in natural gas distribution industry since its introduction in late 1960’s. In North America, more than 90% of the natural gas distribution systems use plastic pipes, of which 99% are PE pipes (PIPA 2001) in which MDPE (Medium Density Polyethylene) pipes account for 2/3rdof the usage in gas distribution industry. MDPE pipes have the added advantage of having a higher ductility and fracture toughness together with long-term strength and stiffness that is comparable to that of HDPE (Stewart et al., 1999). These gas pipes are manufactured in different sizes ranging from 12.5 mm (½”) conduits to 610 mm (24”) diameter pipes, and are available in wide range of pipe thicknesses. In contrast to these small diameter plastic pipes used in the distribution systems, large diameter steel pipes are used in gas transmission pipelines. These high–capacity transmission lines are designed to transmit natural gas from the source to refineries and distribution locations.
1.2 OBJECTIVES OF THE STUDY
The objectives of this thesis are:
- Develop an analytical solution to model the friction at the pipe-soil interface, incorporating the influence of soil dilation and frictional degradation. These factors need to be accounted through proper analytical models to calculate the frictional resistance at pipe element
- Determine a stress-strain model to simulate the strain rate dependant nonlinear stress- strain behavior for the pipe material and validate using independent experimental findings.
- Develop an analytical model to represent the overall pipe performance by combining the interface frictional forces with nonlinear stress-strain behavior of the pipe
- Conduct a numerical model (soil-spring based) to simulate the pipe response using the proposed frictional resistance model and a viscoelastic model to represent the stress- strain behavior of the pipe
- Perform large-scale field axial pipe pullout tests to overcome the limitations (e.g., limited burial length) in laboratory-scale pullout tests. The experiments should be designed to investigate the response of pipes at different rates of loading, the impact of stress- relaxation in viscoelastic pipes, the impact of the overburden stress and the pipe response at large strain Compare the experimental results obtained from the field and laboratory pullout tests with the results obtained from the analytical and numerical models.
- Extend the analytical solution to explain the observed pullout response of planar geotextiles in reinforced earth structures, and verify the analytical approach by comparing with published results from different scholars. In this analytical model for geotextiles, it is required to develop a separate interface frictional model to account for the soil dilation and frictional degradation aspects in planar
Develop an analytical approach to determine the pipe response accounting for the combined effect of tension and bending moments in pipes when the initial ground movement is perpendicular to the pipe axis.
1.3 SCOPE OF THE STUDY
To accomplish the aforementioned research objectives, the following scope of work was conducted in this research project.
- Conduct a field pipe pullout testing program to study axial pullout response of pipes. This included the design and construction of the self-reacting loading mechanism and wooden shores to retain the trench material. As a part of this work, conduct of five axial pipe pullout tests with different burial depths, pullout rates and loading regimes. The pipe performance is directly measured through strain gauges, string potentiometers and the load cells.
- Develop of a new analytical model to determine the response of a pipe due to axial soil loading. The model is derived using an advanced interface friction model to account for the soil dilation and interface friction aspects and combined with the nonlinear stress-strain response for the pipe material. This also includes model validation by comparing the strain, pullout resistance, displacement and mobilized frictional length with experimental data obtained from laboratory and the field pullout tests [a total of ten pullout tests]. A numerical model based on soil-spring analysis is also compared with the experimental findings.
- Develop a similar analytical solution to explain the pullout response observed in planar geotextiles. The analytical model includes a new interface friction model for planar geotextiles. The proposed model is validated by comparing with twenty four pullout tests performed by nine different scholars. A simplified performance chart and equations are proposed to estimate the strain and mobilized frictional length along a
- Develop an analytical solution to explain the pipe performance when the pipe is subject to bending and tensile loading arising due to ground movement occurring perpendicular to the pipe axis.
1.4 PROJECT ORGANISATION
The work is organized as follows: chapter one discuses the introductory part of the work, chapter two presents the literature review of the study, chapter three describes the methods applied, chapter four discusses the results of the work, chapter five summarizes the research outcomes and the recommendations.
CHAPTER TWO
2.0 LITERATURE REVIEW
2.1 OVERVIEW OF THE STUDY
Over the last few decades, several studies have been undertaken to determine the response of the buried pipelines subject to ground movement. These studies include laboratory tests that spans from full-scale pipe pullout tests to centrifuge tests, field pipe testing, and pipe system monitoring. Based on these experimental results, several numerical and analytical models have been developed to determine the response of buried pipes subject to ground movements. However, most of the research has been focused on large diameter steel pipes, and it is believed that the findings on steel pipes can contribute to the understanding of more complex interaction in plastic pipes. In addition, considering the similarities in the interaction aspects, the studies conducted on piles, soil nails and planar geotextiles will further facilitate the understanding of buried pipes under different soil loading conditions
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