More than twenty-five years ago Miller and Low reported the existence of a threshold pore pressure gradient below which water would not flow through clay. Recent experimental observations of the shear strength of structured water on biotite surfaces have provided a physical basis for understanding this threshold gradient. The existence of this phenomenon has profound implications for the rheological properties of mature fault zones, such as the San Andreas, that contain large thicknesses of fault gouge. For example, a clay-filled fault zone about 1 km wide at the base of the seismogenic zone decreasing to zero width at the surface could support core fluid pressure equal to the maximum principal stress over the entire seismogenic zone. As a result, the fault would have near-zero strength and the maximum principal stress measured on the flanks of the fault, would be oriented normal to the fault surface. Another consequence of the threshold gradient is that normal hydrostatic fluid pressure outside the fault zone could coexist with near-lithostatic fluid pressures in the interior of the fault zone without the need for continual replenishment of the overpressured fluid. In addition, the pore pressure at any point should never exceed the local minimum principal stress so that hydrofracture will not occur.