The correct answer is: A. effective stress with time.
An isochrone is a line on a map that connects points that have the same time of travel. In the context of soil mechanics, isochrones can be used to represent the rate of consolidation of a soil. The slope of an isochrone at any point indicates the rate of change of effective stress with time.
Effective stress is the stress that is carried by the soil particles, and it is equal to the total stress minus the pore water pressure. The rate of consolidation is the rate at which the pore water pressure in a soil dissipates. The slope of an isochrone is therefore a measure of the rate at which the effective stress in a soil is changing.
Option B is incorrect because the slope of an isochrone does not indicate the rate of change of effective stress with depth. The effective stress at any point in a soil is equal to the total stress minus the pore water pressure, and the total stress and pore water pressure are both functions of depth. The slope of an isochrone is therefore a measure of the rate at which the effective stress is changing at a particular point, not the rate at which it is changing with depth.
Option C is incorrect because the slope of an isochrone does not indicate the rate of change of pore water pressure with depth. The pore water pressure at any point in a soil is a function of the total stress, the effective stress, and the soil’s permeability. The slope of an isochrone is therefore a measure of the rate at which the effective stress is changing at a particular point, not the rate at which the pore water pressure is changing with depth.
Option D is incorrect because the slope of an isochrone does not indicate the rate of change of pore water pressure with time. The pore water pressure in a soil dissipates over time due to consolidation, but the slope of an isochrone is a measure of the rate at which the effective stress is changing at a particular point, not the rate at which the pore water pressure is changing with time.