I think it should also be explained that 13.8v (as typical on older caravans) WILL eventually fully recharge the battery, though it may well take quite a few days. Modern, so called 'smart', chargers will charge at a higher voltage (typically 14.4v - 14.8v) until the battery reaches a terminal voltage in that range. They then maintain that voltage for typically 1 to 2 hours, before reducing to a maintenance 'float' charge of around 13.8v. This considerably reduces the time it takes to recharge a depleted battery.
The precise ideal charging characteristics for a given situation will vary depending on a multitude of factors, and some sophisticated chargers (and also PV controllers) will allow you to create a charging profile customised to your particular circumstances.