Pipeline covers on the seabed are called near-bed structures which are generally made of rip rap. The crest height of a near-bed structure is such that waves do not break over it. Near-bed structures are used to protect pipelines against fishing equipment, ship anchors, dropped objects and preventing destabilizing of the pipeline. There are two ways of designing a near-bed structure. The first is to design a stable construction given the design conditions present in the lifetime of the structure. The second approach is to allow some damage during the lifetime of the structure, and is the approach which this research focuses on. Presently the Rock Manual advises to use a formula from Wallast and Van Gent [2002] to describe the damage development during a storm. In this formula the damage development in time is forced to a dependency found by Van der Meer [1988]. It is unknown if this time dependency based on the number of waves is valid for damage development with near-bed structures. Besides this, the way to include cumulative damage for several subsequent storm conditions is presently calculated as a first approximation with a method from Van der Meer [1999] designed for breakwaters. It is not verified that this method can also be applied for near-bed structures. The goal of this research is to determine the actual relation between damage and time, and to investigate the cumulative damage development for near-bed structures in multiple storm events. To answer the research questions which have been made from these goals, an investigation is performed which makes use of physical scale model testing. Tests are performed in the Environmental Fluid Mechanic Laboratory at Delft University of Technology. After the execution of the model tests, an extensive analysis is performed based on the results of the scale model tests and results of previous research from Lomónaco [1994], Wallast and Van Gent [2002], Saers [2005], Van den Bos [2006] and Tørum et al. [2008]. The analysis concluded that there is not 'one' parameter as assumed so far to describe the relation between damage to near-bed structures and the number of waves. This parameter is thought to be depended on wave height, water depth, stone size and actual damage that occurs after a certain time. Besides this, the damage development did not reach an equilibrium in time with a large number of waves, which was assumed to be the case in other research. The average value for the exponent which describes the relation between the number of waves and damage is used in this thesis. With this relation and more data a new and improved damage prediction formula is investigated. The new prediction found in this thesis calculates the damage to a higher degree of accuracy with less variation present. It includes more parameters than the current prediction formula from Wallast and Van Gent. The extra parameters in this formula are the relative width, structure slope and Keulegan-Carpenter number. The method to include cumulative damage for multiple storm events from Van der Meer was proven to be usable by using the formulas found in this research. An important conclusion from these tests is that damage development stops or reduces to a large degree when a low wave condition passes the near-bed structure when a high condition is already imposed to the near-bed structure.