The SRBs, like most big solid rocket motors, has an internal geometry different from what many people think. The propellant has a hollow core to expose more surface area, increasing thrust. You can see the hollow core in one of the lower photos on this page. Once ignited, all of the core surface area is burning.

Thrust on a solid rocket motor is controlled by the propellant geometry. An end burning unit with no hollow core (I suspect that's what you though was happening in the Shuttle SRBs) would have an essentially level thrust level throughout the burn. This is relatively uncommon. For most rockets, you want a higher thrust level for initial acceleration. Engineers can cast the propellant with a hollow core to increase thrust, varying the core geometry to control the thrust level. I've seen cores that are star shaped (more surface area than a simple circle) and a variety of other geometries.

Propellant geometry errors, such as cracks or bubbles in the propellant, are one of the leading causes for solid rocket motor failures. The extra surface area of the crack causes the internal pressure to be higher than what the casing or the nozzle can handle, causing an explosion. This paper discusses nondestructive means of detecting propellant errors.