A Universal Tunnel Design Method For Hand Calculation

INTRODUCTION This paper presents a method of calculation of internal moments and thrusts in tunnel liners of any material. The method is intended for hand calculation, but as it is numerical in nature it can be programmed for use in computers. The information required for design or analysis is presumed active internal and external pressures, the effective moment of inertia and cross-sectional area of the tunnel liner, the liner's modulus of elasticity, and the coefficient of subgrade reaction of the material surrounding the tunnel. Starting with active external and internal pressures and following the procedure described herein using the structural properties of the liner and surrounding medium, external passive reactions and internal moments and thrusts are calculated. The method is intended for use by design engineers. GENERAL Experience has shown that flexible tunnel liners have less internal bending stresses than those calculated using classical structural theory applied to free-standing arches. In fact, liners which are very flexible in relation to the surrounding soil or rock have virtually no bending moments when compared to free-standing arches supporting equal active loads. In order for this phenomenon to occur, the original active pressure diagram must be "modified" by additional external reactions (passive pressures) from the surrounding material, so that the thrust line within the lining follows the centroid of the tunnel arch more closely than that of a similar free-standing arch. These passive pressures are reactions developed through outward deflection of the tunnel liner. Thus, the outward moving portions of a