When analyzing seepage under a concrete dam, what critical condition at the downstream toe indicates a high risk of piping failure?

The critical condition at the downstream toe indicating a high risk of piping failure is when the exit hydraulic gradient approaches or exceeds the critical hydraulic gradient of the foundation soil. The downstream toe is the specific location where the concrete dam's structure meets the natural ground on the lower water level side, serving as the exit point for water seeping underneath the dam. Seepage refers to the underground flow of water through the permeable soil and rock pores beneath the dam, driven by the pressure difference between the upstream and downstream water levels. The hydraulic gradient is the rate at which the hydraulic head, or water pressure, changes with respect to distance along the path of flow, representing the driving force for water movement. Specifically, the exit hydraulic gradient is the gradient experienced by the water as it emerges from the soil at the downstream toe. The critical hydraulic gradient is a specific value of the hydraulic gradient where the upward seepage force exerted by the flowing water on the soil particles becomes equal to the submerged weight of those soil particles. When this condition is met, the effective stress, which is the stress carried by the contact points between soil grains and is responsible for the soil's shear strength, reduces to zero. With zero effective stress, the soil at the downstream toe loses its strength and cohesion, entering a fluid-like state often referred to as a quicksand condition or 'boiling'. In this state, individual soil particles become suspended in the upward-flowing water and are easily washed away. This removal of soil particles initiates piping failure, a progressive process where concentrated channels or 'pipes' are formed by erosion within the foundation, extending backward from the downstream toe towards the upstream side. As these pipes enlarge and propagate, they progressively undermine the dam's foundation, reducing its support and stability, which can ultimately lead to a catastrophic collapse of the structure.