Log-based fault diagnosis is crucial for runtime debugging and maintenance. Existing fault diagnosis methods use language models pre-trained on natural language (PLMs) for log representation. However, system faults are reflected in the multi-level structure of system logs. PLMs pre-trained on natural language struggle to comprehensively capture multi-level fault information, failing to meet the requirements of fault diagnosis. We refer to this information as fallibility representations. To address this problem, we propose a novel log representation learning method, Bifrost. It draws inspiration from the log analysis experience of Site Reliability Engineers and meticulously designs strategies based on self-supervised contrastive learning to learn the fallibility representations of logs. Across three public systems and one industrial ML-as-a-Service system, the log representations produced by Bifrost outperform existing PLMs by average margins of 9.83% in F1 for anomaly detection, 18.28% in HR@k for root cause localization, and 20.88% in Macro-F1 for fault identification.