^aLaw Engineering Testing Company, Washington, D.C. (U.S.A.)

^bLaw Engineering Testing Company, Atlanta, Ga. (U.S.A.)

To illustrate the applicability of the freezing method, various considerations in the design of an 8-ft. diameter tunnel in upstate New York, a 75-ft. diameter tunnel in Georgia, and a 12 1/2-ft. diameter tunnel in Washington, D.C. are discussed. All three of the tunnels were to pass immediately beneath mainline railroad tracks. A laboratory testing program was implemented to determine the effects of the repetitive train loads on the zone of frozen soil around the tunnel perimeter. Stress-controlled repeated load triaxial tests were performed on both undisturbed and remolded samples frozen from temperatures of −7°C for the New York tunnel to −10°C for the Atlanta and Washington tunnels. Static testing consisted of both quick triaxial tests and creep tests on frozen samples of the various soil types.

It was found that there was little difference between the cumulative strain response from repeated load tests and static tests for the low frequencies investigated (one-quarter to one-half cycles per minute). Hyperbolic stress—strain functions were developed to simulate the stress—strain relationship for various cumulative loading times.

The stresses and strains in the frozen soil tunnel configuration were computed by the finite element method, using both linear and hyperbolic stress—strain functions. Tangent modulus values were varied to reflect the decreasing modulus with increasing loading time. The analyses indicated that zones of frozen soil of approximately 3 ft. thick were required for both the New York and Washington tunnels. However, high tensile stresses were calculated for the Atlanta tunnel, precluding the use of the freezing method.