Seismic, Wind & Temperature Effects on Metro Structures Notes

Last reviewed 30 Sept 2026 · 7 min read

Different structures, different earthquake behaviour

An elevated station stands above ground like a building or a bridge: an earthquake shakes its base and the inertia of its mass produces lateral forces. An underground box is surrounded by soil, so it moves with the ground; its danger is not its own inertia but the distortion of the surrounding soil that squeezes and shears the box. The design methods are therefore different.

Elevated stations and viaducts

Treated as buildings or bridges: response-spectrum or time-history analysis according to IS 1893 (or the project's seismic criteria) with the zone factor, importance factor (higher for metro), response reduction factor (depends on ductile detailing and system) and soil type.
Seismic weight: dead load + a fraction of live load (25 % or 50 % depending on the intensity — see the IS 1893 rule).
Design lateral force (equivalent static): $V_{B} = A_{h} W$ with $A_{h} = \frac{Z}{2} \frac{I}{R} \frac{S _{a}}{g}$ .
Ductile detailing of columns and joints (IS 13920) and capacity design so that the failure occurs in flexural hinges rather than shear.
Viaduct–station interaction: the different stiffness and mass of the viaduct and the station building can produce pounding or differential movement; seismic joints with adequate gaps, and restrainers at the bearings.
Bearings: elastomeric pot or spherical; seismic isolation bearings may be used for the viaduct.

Underground boxes — racking

During an earthquake shear waves travelling upward cause the soil to distort horizontally. The soil around the box is racked, and the box is forced to follow the deformation. The racking (shear distortion) of the box is a key design quantity:

Racking ratio R = \frac{Δ _{s t r u c t u r e}}{Δ _{f r ee f i e l d}}

The free-field soil deformation $Δ_{f f}$ between the roof and the base of the box is computed from a site response analysis (one-dimensional wave propagation) or from simplified formulas based on peak ground velocity or acceleration. A flexible structure follows the soil ( $R \approx 1$ ); a stiff structure in soft soil resists and takes higher forces. The racking is then imposed on the frame model as prescribed displacements, giving the shears and moments in slabs, walls and columns.

FormulaSimplified steps for a station box

Find the design ground motion at the depth of the box (peak ground acceleration/velocity, from the site response).
Compute the free-field shear deformation between roof and base levels.
Apply the deformation to the 2D frame model — either the prescribed-displacement method (pushing the frame by imposed distortion) or the soil–structure interaction model with springs.
Combine with static loads (earth and water pressure, dead and live load) in the seismic combination.
Check columns for shear and ductility (the columns are the vulnerable elements) and provide confinement and shear reinforcement.
Check joints between the box and the tunnels and between box sections for differential movement.

Dynamic earth pressure

Earthquake shaking increases the pressure on retaining walls: the Mononobe–Okabe method adds a dynamic increment to the active or passive pressure, computed with a horizontal seismic coefficient $k_{h}$ (and vertical $k_{v}$ ). The dynamic increment is usually taken to act at about 0.6 of the wall height from the base. For deep, rigid, embedded boxes the Wood or simplified methods for stiff walls are used, as Mononobe–Okabe may underestimate the force on a rigid, non-yielding wall.

Liquefaction

In loose saturated sand the pore pressure rises and the soil loses strength: the box may float or the walls may lose support; the column loads change. The design checks the liquefaction potential and uses ground improvement (stone columns, compaction, grouting) where necessary.

Wind on elevated stations

Design wind speed and pressure follow IS 875 (Part 3):

V_{z} = V_{b} k_{1} k_{2} k_{3} k_{4}, p_{z} = 0.6 V_{z}^{2} (N/m^{2}, V_{z} in m/s)

$V_{b}$ = basic wind speed for the location; $k_{1}$ = risk coefficient, $k_{2}$ = terrain, height and structure-size factor, $k_{3}$ = topography factor and $k_{4}$ = importance factor for cyclonic regions. The force on a surface is $F = (C_{p e} - C_{p i}) p_{z} A$ using external and internal pressure coefficients that depend on the shape of the roof and the openness of the station.

Worked ExampleExample — wind pressure

An elevated station roof in a region with $V_{b}$ = 44 m/s. Taking $k_{1} = k_{3} = k_{4} = 1.0$ and $k_{2} = 1.05$ (terrain category and height):

$V_{z} = 44 \times 1.05 = 46.2$ m/s; $p_{z} = 0.6 \times 46. 2^{2} = 0.6 \times 2134 = 1281$ N/m² = 1.28 kN/m².

With a net pressure coefficient of −1.0 (uplift on a canopy roof), the design uplift = 1.28 kN/m² — the roof, purlins and their connections and the bearing are designed for this uplift, which can exceed the dead load of a light steel roof.

Open platform canopies and long-span roofs are vulnerable to suction, flutter of thin sheeting, and dynamic effects; for large roofs wind-tunnel testing is used. Cladding fixings and glazing are designed for local pressure coefficients, which are larger than the overall coefficients.

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