Provided are a touch substrate and a method for driving the same, and a display apparatus. The touch substrate includes a base substrate, and a plurality of touch control units, gate lines and read lines disposed on the base substrate. Each touch control unit includes a first electrode plate, a piezoelectric material layer and a second electrode plate sequentially disposed on the base substrate. The gate lines are configured to provide a constant voltage to the first electrode plates during a touch control period. The read lines are configured to read out an amount of charges generated by the piezoelectric material layers so as to determine a position of a touch point.