# Numerical Simulation on Backfilling of Buried Pipes Using Controlled Low Strength Materials
## 4 Results
### Circumferential Strain of Pipe under Different Backfill Conditions  
For the three backfill conditions, the annular strain of the pipeline under different surface pressures was recorded. Figure 15 shows the circumferential strain around the pipe during loose backfill. It can be seen from the figure that the circumferential strain of buried pipeline is mainly compressive strain, and the maximum strain is located at the top of the pipe. The surface pressure increases from 100 kPa and 150 kPa to 200 kPa. The circumferential strain around the pipe increases continuously. The circumferential strain of pipe top increased from 0.38% and 0.64% to 0.97%. The strains on the left and right sides of the pipe are basically symmetrical, and tensile strains appear in the range of 45-115\({}^{\circ}\) and 245-315\({}^{\circ}\) of the pipe. The compressive strain is below the pipe side and the strain is small.  
Figure 16 show the circumferential strain around the tube during dense backfill and CLSM backfill. The circumferential strain around the pipe increases with the increase of  
Figure 14: Radial Displacement of Pipe.  
Figure 15: Circumferential strain in loose backfill.  
surface pressure. The surface pressure increased from 100 kPa to 150 kPa and 200 kPa, and the circumferential strain of the pipe top increased from 0.11% to 0.21% and 0.29%. The tensile strain appears in the range of 45-65\({}^{\circ}\) and 280-295\({}^{\circ}\) of the pipeline, and the range of the pipeline is compressive strain. The range of pipeline compressive strain is smaller than that of loose backfill around the pipe.  
Figure 17 shows circumferential strain around the pipe when using CLSM backfill. The surface pressure increased from 100 kPa to 150 kPa and 200 kPa, and the circumferential strain of pipe top increased from 0.02% to 0.04% and 0.059%. Compared with loose backfill and dense backfill, the circumferential strain around the pipe is greatly reduced. When the surface pressure is 150 kPa, the circumferential strain at the pipe top is reduced by 84% and 81%, respectively, compared with loose backfill and dense backfill. The pipe within 360\({}^{\circ}\) is compressive strain without obvious maximum and minimum values, and the pipe is uniformly compressed.  
Figure 18 is the circumferential strain of a pipe under three backfill conditions, when the surface pressure is 200 kPa. The circumferential strain around the buried pipe is greatly reduced by using CLSM backfill. When the surface pressure is 200 kPa, the circumferential strain of the pipe top is 0.97%, 0.29% and 0.059% in the case of loose backfill, dense backfill and CLSM backfill, respectively. Compared with loose backfill and dense backfill, the circumferential strain of CLSM backfill is reduced by 98.9% and 79.7%, respectively. For loose backfill and dense backfill, there is tensile strain around the pipe. Using CLSM for  
Figure 16: Circumferential strain in dense backfill.  
Figure 17: Circumferential strain in CLSM backfill.  
pipe backfill, the pipeline is no tensile strain, and the compressive strain distribution is relatively uniform. The deformation of the pipe is very small.