The significant petroleum reserve in the Arctic drives the need for offshore facilities in the Arctic made of ferritic structural steels. Such steel materials often exhibit a brittle fracture mode without noticeable prior plastic deformations. This paper presents a combined experimental and numerical investigation to assess the cleavage fracture failure for high-strength steels used in offshore applications. The experimental program includes a set of non-conventional, special single-edge notched bend, SSE(B) specimens, tested under a lower ambient temperature of -90 °C. In contrast to the conventional through-thickness fracture specimens, which experience an approximately uniform crack driving force along the entire crack front, the specimens with a curved crack front indicates strong variations in both the crack driving forces and constraints along the crack front. This study therefore utilizes an average toughness value calculated from the η-approach to describe the scatter observed in the fracture toughness. This study also presents a numerical investigation using the local Weibull stress approach to estimate the probability of cleavage fracture in the fracture tests. A combination of the fracture initiation zone defined by the J-integral values with a local Weibull stress driving force predicts reasonably well the probability of fracture of the experimental specimens.