The road crack detection remains a crucial task in the road maintenance and safety management. However, due to the diversity and complexity of cracks, achieving the fine-grained and accurate segmentation is still challenging. To this end, this paper proposes a novel physically informed prior-guided crack segmentation method. Specifically, we employ the dynamic snake convolution to enhance the segmentation continuity and consistency. Moreover, a prior information is injected to supplement the morphology and structural features of road cracks, aiming to mitigate the miss detection of the binary-branched and webbed cracks. To ensure the continuity and completeness of cracks, a cross-correlation constraint is further designed. The constraint leverages the semantic consistence of the crack regions to promote the network to capture and segment small and complex cracks. Experimental validations on two datasets demonstrate that the proposed approach significantly outperforms state-of-the-art methods, achieving substantial improvements in the fine-grained detail and the continuity of the road crack segmentation.