In the field of offshore engineering, subsea rock installation has emerged as a pivotal technique. As offshore operations extend to greater water depths, the deployment of a versatile fallpipe has become a cornerstone for precise rock particle placement. A comprehensive determination of the overall rock material volume required for installation entails accounting for geometric factors, operational losses, and seabed displacements. To ensure effective project management and cost estimation, a precise grasp of volume loss during installation proves indispensable. Against this backdrop, the current thesis delves into the intricate domain of volume loss stemming from rock penetration within sand substrates.

The core endeavor of this research is the development of a model that quantifies volume loss due to rock penetration within sandy seafloors. The investigation combines theoretical modeling with empirical validation through lab testing. Through analysis, it is revealed that the complex behavior of granular media necessitates an in-depth understanding of the theory, together with assumptions and simplifications to create an effective penetration depth model. The literature study outlines the various forces exerted on a rock as it impacts the seafloor and commences its penetration into the sand. Within the summation of forces, one component to consider is the bearing force exerted by the sand. This force can be calculated using two distinct approaches: the Terzaghi formula for shallow foundations and the Brinch Hansen formula, also applicable to shallow foundations. In this thesis, both formulas are employed to assess their applicability to the dynamic penetration of spherical particles in a sandy seafloor. Once these forces have been aggregated within the equation, two distinct methods to resolve the equation and determine the penetration depth of a spherical rock in sand are employed. The first method is rooted in the principle of a work-energy balance, stating that the cumulative work done by the sum of forces matches the change in the rock's kinetic energy. In contrast, the second method is based on the impulse-momentum balance, underlining the concept that the summation of forces multiplied by a specific duration in time, is equivalent to the change in the rock's momentum during that defined time interval. The work-energy method is preferred over the impulse-momentum method because of the specific objective of the single stone model, which centers on determining penetration depth, a distance measurement. The work-energy method inherently incorporates the distance variable within its formula, aligning directly with the desired outcome. In contrast, the impulse-momentum method necessitates calculating penetration depth by multiplying time with velocity for each discrete time step, introducing a less efficient computational process. \\
Following a comparison between the results derived from laboratory tests and the computed penetration depths using both the Terzaghi and Brinch Hansen-based models, it becomes evident that the Terzaghi formula offers a closer approximation to the behavior of the bearing force.

Further insights are drawn from multi-stone penetration testing, wherein assumptions and simplifications are strategically employed. The intersection of the multi-stone model with a three-dimensional normal distribution delineates the positions of rocks post-fallpipe discharge, bridging theoretical modeling with practical subsea rock installation scenarios. Although a somewhat unrealistic scenario of centric rock-rock collisions and perfect stacking of rocks on top of each other is assumed, the model provides a valuable worst-case scenario in terms of volume loss.

Though the model's validation is confined to sandy seafloors, its implications extend beyond. The study underscores the need for real-world data integration to refine the model.