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Top1. Introduction
Predictability of a structural design’s performance is one of many important aims of structural analysis. Elastic analysis of structures requires that very specific conditions at all points within the structure and on its boundary are satisfied. Action and reaction forces must be in equilibrium, deformations of adjacent points within and on the boundaries of a structural element must be compatible, and only appropriate stress-strain laws may be employed. To enhance performance, structures and structural elements are often designed as composites of multiple materials. The buried pipe-soil structural composite requires properly selected and compacted soils surrounding the pipe to reinforce it at a manner that favorably minimizes the pipe’s bending stress and maximizes ring compression. It is the performance of the pipe-soil composite structure that must be predicted by engineering design.
A steel pipe is buried at a shallow depth beneath a roadway. An analysis is required to evaluate the effect of wheel loading on the deformation at the road surface, the deflection and stresses in the pipe. For unburied or unsupported pipes of elastic materials, and for unburied or unsupported pipes of plastic materials, at the instant of load application as shown in Figure 1, the relationship between load and deflection is given by:
Top2. Interaction Of A Soil Envelope With A Flexible Pipe
Flexibility of buried pipes is a desired attribute. A buried pipe and its adjacent soil elements will attract earth embankment loads and live loads in accordance with a fundamental principle of structural analysis: stiffer elements will attract greater proportions of shared load than those that are more flexible.
This principle is illustrated in Figure 2 where, given the same well-compacted soils surrounding the pipe, the more flexible pipe attracts less crown load than the rigid pipe of the same outer geometry. The surrounding soil is of greater stiffness than the flexible pipe and of lesser stiffness than the rigid pipe.
Top3. Numerical Models
3.1 Problem Statement
The top of the pipe is 1.5m beneath the road surface. The pipe has an outer diameter of 4m and is 0.12m thick. The pipe excavation is 15m wide and 6m deep. The pipe is situated on a 0.4m-thick layer of soil back fill, and then soil is compacted around the pipe. The wheel load is applied to four grid points on the surface. If the load is assumed to be carried by ½ of each zone connected to the grid points, then the wheel are a can be assumed to be 1.275m. The wheel load is increased until failure mechanism occurs in the soil. The analysis determines the failure load and the resulting soil settlement, pipe displacement and stresses.
3.2 Modeling Procedure
A Mohr-Coulomb was selected from those available in FLAC 3D to describe the soil behavior in this research. FLAC 3D incorporates a fully automatic mesh generation procedure, in which the geometry is divided into elements of the basic element type, and compatible soil-structural elements.
The x=0 plane corresponds to the vertical plane through the center of the pipe, and the y=0 plane corresponds to the plane mid way between wheel loads. The model contains 600 zones, with finer zoning in the vicinity of the applied wheel load. A full model of the pipe is required if buckling along the pipe is expected. Table 1 is shown material properties used by FLAC 3D.
Table 1. Soil parameters used in FLAC 3D analysis
| Parameters | Soil |
| Density (kg/m3) | 2200 |
| Shear modulus (Pa) | 40000000 |
| Bulk modulus (Pa) | 75000000 |
| Friction angle (°) | 35 |
| Dilation angle(°) | 22 |
| Tensile strength | 1000 |
| Cohesion, c (Pa) | 6000 |
The FLAC3D model assumes symmetric conditions about a vertical plane through the center of the pipe and a vertical plane mid way between the wheel loads. The model grid is shown in Figure 3.