According to Sample Problem 15-3, 89.6% of an iceberg is submerged. Yet occasionally icebergs turn over, with possibly disastrous results to nearby shipping. How can this happen considering that so much of their mass is below sea level?

When the center of gravity and the center of buoyancy of a floating body are not lying on the same vertical line of the object, there is a net torque act on the body. This makes to tip the body to bring in its equilibrium position.
There is a continuous formation of ice on the ice bergs. When this happens, submerged icebergs occasionally have center of gravity and their center of buoyancy not lying on the same vertical line. So, there is net torque acting on it. This torque tends to tip the icebergs to bring in its equilibrium position. Therefore, submerged icebergs occasionally turn over.