Study of Stress Distribution in Concrete Tunnel LiningsProblem:

The problem deals with checking of stressconcentrations in the concrete lining runningalong a stretch of a tunnel excavated into asolid mass of sandstone. Sandstone is not abad rock mass and can hold a pretty decentshape when excavated, thus it does notrequire heavy supports such as steel ribs orpattern rock bolts. Spot rockbolts in placesthat are vulnerable are generally provided.There are chances, however, of the rocksshifting and releasing their in-situ pressuredirectly to the concrete lining exposing thelining to unanticipated loads.

Model:

- A two-dimensional (2D) plain-strain conditionwas chosen to simulate the response of thetunnel and surrounding rock-mass.

-The overall dimensions of the modelboundaries comprise a width of 4.5 timesthe tunnel width (B1) from the tunnel centerand a height of 8.6 times the tunnel height(H1). The rock above the tunnel is 4H1, andthe rock below the tunnel is 3.6H1. Thesedimensions were considered adequate toeliminate the influence of boundary effects.

Material : Sandstone RockDensity 25 KN/m3Elastic PropertiesYoung’s Modulus, E 5000,000 KN/m2Poisson’s Ratio 0.25Mohr-Coulomb PlasticityFriction angle 28˚Cohesion 70 KN/m2

Material : M-35 ConcreteDensity 24 KN/m3Elastic PropertiesYoung’s Modulus, E 28,000,000 KN/m2Poisson’s Ratio 0.2

Assumptions:- Concrete lining is considered a linear-

elastic material at all times,- For surrounding ground the Mohr-

Coulomb property is given.- The Interface between the Rock and the

Lining is considered as a full contactinterface

- The contact interaction propertytangential behavior friction formulationis “Rough”

- The normal behavior was given as “Hard”contact with no separation allowed.

Analysis Results:- Maximum deflection of 0.4728mm

downwards at the crown- Center of the vertical walls deflected by

about 0.411mm inwards- The Interface between the Rock and the

Lining is considered as a full contactinterface

- A deflection of 0.335mm upwardsobserved in the floor of the excavation

Stress Distribution in Lining:Top of slab of the lining resting on the excavation base is in tension. Tensile stress here is 214kN/m2 due to the heaving of the floor of the excavation. Highest compressive stress isobserved at the junction of the bottom slab and the side walls. The compressive stress here is1300 kN/m2 in the innermost corner and 300 kN/m2 at the outermost corner of the lining. Thiscorner region receives two different compressive forces one each from the side walls and thebase slab. Simply put it can be said that the concrete in the corners is being squished due tothe rock mass trying to release its stresses in the excavated region. At the crown compressivestress is more on the top of the lining, 290 kN/m2 than at the bottom of the lining 85 kN/m2.This is because of its direct contact to the rock mass. Moving towards the inner face of thelining at the top the compressive force decreases due to arch action.

Conclusion:If a rock mass is relatively good and does not undergo toomuch deformation, the concrete lining can easily take upany unanticipated loads coming from the deformation ofrock mass due to minimum support failure. The maximumtensile stress observed in the lining at the top of the bottomslab is 214 kN/m2 and is below the expected concrete tensilestrength of 2-5 MPa. The maximum compressive stress seenwas about 1300 kN/m2. This falls short of the permissiblecompressive strength of concrete used in linings rangingfrom 20-40 MPa.