Constrained Modulus of Crushed Rock for Pipeline Embedment

The constrained modulus (M_s) of soil has been used to predict the deflection and the buckling potential of buried flexible pipe. Since the constrained modulus (M_s) of soil increases with depth, M_s could have significant value in calculations for deep burial conditions. The standard laboratory test used to determine the constrained modulus is limited to sand size particles and smaller for practical reasons. Gravel size crushed rock is a desirable material for buried pipe support. However, large scale tests to measure strength properties of gravel particles are impractical because of the expense and lack of standard procedures for cohesionless soils. Thus, only presumptive values of the constrained modulus (Ms) for crushed rock are available. As discussed in a companion paper (Gemperline and Gemperline 2011), a large-scale confined modulus laboratory test was developed to quantify M_s values for gravel size particles. The test was performed on different clean, uniform samples of crushed rock. Each sample was tested at low, medium, and high densities. The tests were incrementally loaded to a pressure simulating about 150 feet of fill. The stress-strain curve was found to be linear with load, resulting in a constant value of constrained modulus for each soil at a specific density. The constrained modulus was also found to be directly dependent on placement density. The constrained modulus ranged between approximately 2000 lb/in² and 10,000 lb/in². The low density tests had constrained modulus values between 2000 lb/in² and 4000 lb/in². The high density tests had constrained modulus values between 5000 lb/in² and 10,000 lb/in². The constrained modulus values representing compacted crushed rock compare favorably with published empirical and presumptive values. The constrained modulus values representing dumped conditions are 200 to 400 percent higher than published empirical and presumptive values. Higher M_s values may be possible using rounded to sub-rounded particles with a wider range of particle sizes. Further testing should verify this assumption.