ANS:E - all the above.

1. Load is applied in one direction: Terzaghi's theory deals with the consolidation of soils under vertical loading, so it assumes that the load is applied primarily in one direction, vertically downward.
2. Coefficient of permeability is constant: The theory assumes that the coefficient of permeability, which represents the ability of soil to transmit water, remains constant throughout the consolidation process. While this assumption simplifies calculations, it may not hold true in all cases, especially for soils with varying properties or under changing conditions.
3. Excess pore water drains out only in the vertical direction: Terzaghi's theory assumes that excess pore water drains primarily in the vertical direction during consolidation, perpendicular to the direction of the applied load. This assumption simplifies the analysis of consolidation and is reasonable for many practical engineering applications.
4. Time lag in consolidation is due entirely to permeability: The theory attributes the time lag in consolidation, which is the delay between the application of load and the initiation of consolidation settlement, primarily to the permeability of the soil. This assumption implies that the rate of consolidation is controlled by the rate at which water can flow out of the soil mass.