For one, you are not using the term "biodegradable" correctly. Strictly speaking, biodegradability refers to the degradation (falling apart) of a material induced by, typically, microorganisms (the "bio" part). If water is inducing the chemical changes, this is not biodegradation. We might refer to this as hydrolysis.
Also. Water doesn't necessarily have to degrade the polymer in order to induce changes. Many polymers, including most biopolymers, absorb water (a process known as swelling). This can drastically change the physical properties of the polymer, without actually causing any chemical changes to the polymer backbone. Swelling is not the same thing as dissolution, mind.
So basically, there's a lot of processes and you need to be specific about what you're really looking for. Only then can we talk about methods to measure whatever process you need to measure.