Structural health monitoring refers to the evaluation of the health condition of engineering structures through real-time or periodic monitoring. Deep learning methods have gained attention due to their ability to extract high-level features from raw data. However, the diversity of damage types in practical applications and the lack of quantitative analysis for damage states remain challenging. In this paper, a partial skip-connected convolutional autoencoder-based approach for damage assessment and quantification is proposed. This method utilizes a convolutional autoencoder to process structural responses, reducing high-dimensional data to a low-dimensional feature space. A damage index is defined based on reconstruction error to assess health status, while a damage coefficient constructed from the low-dimensional features enables quantitative damage assessment. The effectiveness of the algorithm in damage detection and quantification is validated using the IASC-ASCE Benchmark Structures I and II datasets. Experimental results demonstrate that the damage index achieves 100% accuracy in identifying most damage states, with 96% accuracy in certain specific cases, and that the quantification aligns well with expected values across different damage states.