Landfill liners are constructed using clay layers to restrict leachates. Time after which leachates pass through the liners is called as breakthrough time (t) which is calculated using ____.
( T= Thickness of clay layer ( m ), η= Clay liner porosity, K= Hydraulic conductivity ( m/ year ), H= Depth of leachate above liner (m))

Correct option is B

Introduction

Landfill clay liners retard the downward migration of leachate, and the breakthrough time quantifies how long the liner delays contaminant passage.

It depends on liner thickness, porosity, hydraulic conductivity, and the leachate head above the liner.

Information Booster

The correct formula is t = (T²η)/(K(H+T)). The breakthrough time represents how long leachate takes to seep through a compacted clay liner under saturated flow governed by Darcy's law.

The derivation combines Darcy's law with the liner's storage (porosity) characteristics:
Darcy's law gives the seepage velocity through the liner as:
v = (K × hydraulic gradient) / η = K(H+T)/(T·η)
Here the total hydraulic head driving flow is the leachate depth plus the liner thickness (H+T), and this head is dissipated across the liner thickness T, giving the hydraulic gradient (H+T)/T.

Dividing the Darcy velocity by porosity η converts it to the actual (seepage) velocity of the fluid moving through the pore spaces.
The breakthrough time is then the liner thickness divided by this seepage velocity:
t = T / v = T / [K(H+T)/(T·η)] = (T²η)/(K(H+T))

The formula correctly places T² in the numerator (thickness squared, since thickness appears both as the travel distance and in the gradient), porosity η in the numerator (more pore space means longer travel time), and hydraulic conductivity K with the total head (H+T) in the denominator (higher conductivity and greater head speed up breakthrough).

Additional knowledge

· t = (H+T)/η — Incorrect. This is dimensionally inconsistent and omits both hydraulic conductivity K and thickness-squared dependence; it cannot yield a time unit and ignores the physics of Darcy flow.
· t = η/(K(H+T)) — Incorrect. This drops the T² term entirely, so it fails to account for liner thickness as the travel distance; a thicker liner must increase breakthrough time, which this formula cannot represent.
· t = (T²η)/KH — Incorrect. This uses only H (leachate depth) in the denominator instead of the full head (H+T), neglecting the contribution of the liner thickness itself to the total hydraulic head driving flow.