For an overconsolidated clay layer subjected to a new load that keeps the stress below its pre-consolidation pressure, which consolidation parameter, Compression Index (C_c) or Recompression Index (C_r), primarily governs the settlement?

For an overconsolidated clay layer subjected to a new load that keeps the stress below its pre-consolidation pressure, the Recompression Index (C_r) primarily governs the settlement. An overconsolidated clay is a clay that has previously experienced a higher effective stress in its past than it currently experiences. This maximum past effective stress is termed the pre-consolidation pressure (often denoted as σ'p or p'c). It represents the stress level at which the clay's stress-strain behavior transitions from a relatively stiff, recompression response to a more compressible, virgin compression response. When a new load is applied to an overconsolidated clay, and the resulting effective stress remains below its pre-consolidation pressure, the clay is said to be undergoing recompression. During this phase, the soil particles are primarily moving closer together in a somewhat recoverable, elastic-like manner, resulting in relatively small changes in void ratio and thus smaller settlements. The Recompression Index (C_r) is a geotechnical parameter that specifically quantifies this compressibility during recompression. It is determined from the slope of the recompression curve on a plot of void ratio (e) versus the logarithm of effective stress (log σ'). In contrast, the Compression Index (C_c) represents the compressibility of the clay when it is either normally consolidated or when an overconsolidated clay is loaded beyond its pre-consolidation pressure, entering the virgin compression range. This virgin compression involves significant, largely irreversible rearrangement of the soil structure, leading to much larger changes in void ratio and greater settlements. Since the given condition specifies that the stress remains below the pre-consolidation pressure, the clay does not enter the virgin compression range, making C_c irrelevant for this specific settlement calculation. The value of C_r is typically much smaller than C_c, reflecting the significantly lower compressibility of the clay in its overconsolidated state during recompression compared to its virgin compression behavior.