###### Abstract
Geological CO\({}_{2}\) storage also involves a range of geomechanical risks associated with associated physical phenomena. These risks arise from the interaction between the injected CO\({}_{2}\) and the geological formations, leading to changes in rock mechanics, fluid dynamics, and chemical reactions. Key concerns include induced seismicity due to subsurface stress alterations, caprock integrity challenges from pressure-induced deformation, and changes in rock and fault strength owing to CO\({}_{2}\)-related geochemical reactions. Furthermore, the integrity of wells is at risk due to CO\({}_{2}\) corrosion, and the long-term effects of mineral dissolution or precipitation add complexity to the stability and safety of storage sites [21]. Among these, excessive ground displacement emerges as a critical issue. For onshore projects, such ground displacement can lead to considerable damage to houses and buildings, as in the case of the Groningen gas field in The Netherlands [22]. In offshore environments, the primary concern lies with the impact on subsea infrastructure and surface facilities, such as the Ekofisk oil field in the North Sea [23], where substantial subsidence led to significant engineering interventions to mitigate the adverse effects. This paper specifically focuses on ground deformation as the principal risk under investigation. During the injection process and even afterward, the injection of large volumes of CO\({}_{2}\) into deep geological formations can cause significant pressure buildup and change stresses on the reservoir and the surrounding rocks. The pressure buildup induced by fluid injection can lead to expansion of the storage formation in proportion to the pressure increase. This expansion pattern can cause an uplift of the caprock, as observed in some actual GCS projects [24; 25]. Additionally, the dissolution of CO\({}_{2}\) into water forms carbonic acid, which lowers the pH and can result in the dissolution of rock. Furthermore, vaporization of water can also lead to the precipitation of minerals [26; 27; 28; 29]. These geochemical reactions have the potential to alter the geomechanical properties of rocks and faults, which depends on the position of the displacement fronts [30; 31]. Therefore, injection conditions that may initially appear geomechanically stable could become unstable in the long term if geochemical reactions weaken the strength of the rocks or faults [32]. Furthermore, in the event of fault reactivation, induced seismicity is possible, which has been associated with the risk of generating seismic activity due to stress changes caused by CO\({}_{2}\) injection [33; 34]. In the pursuit of advancing GCS technologies, the importance of conducting comprehensive uncertainty analyses on key geomechanical parameters cannot be overstated. These analyses are essential for accurately characterizing the behaviors of geological formations under CO\({}_{2}\) injection scenarios. The variability inherent in rock properties, coupled with the dynamic nature of CO\({}_{2}\) injection processes, introduce uncertainties that must be addressed to ensure the efficacy and safety of CO\({}_{2}\) sequestration efforts. By evaluating the sensitivity of model outcomes to changes in rock mechanical properties, caprock permeability, and injection rates, researchers can identify critical thresholds and optimize monitoring and mitigation strategies. For instance, a study [35; 36] on sensitivity analysis of geomechanical constraints in CO\({}_{2}\) storage highlights the significant impact of rock properties and injection rate on pressure buildup and CO\({}_{2}\) plume migration, underscoring the importance of accurately characterizing these parameters to predict storage site performance. Similarly, work on minimizing geomechanical risks under geological uncertainty through controlled CO\({}_{2}\) injection into storage reservoirs [37] demonstrates the critical role of understanding and managing uncertainties in geomechanical properties to ensure caprock integrity and minimize leakage risks.