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Despite demonstrating superior rate-distortion (RD) performance, learning-based image compression (LIC) algorithms have been found to be vulnerable to malicious perturbations in recent studies. However, the adversarial attacks considered in existing literature remain divergent from real-world scenarios, both in terms of the attack direction and bitrate. Additionally, existing methods focus solely on empirical observations of the model vulnerability, neglecting to identify the origin of it. These limitations hinder the comprehensive investigation and in-depth understanding of the adversarial robustness of LIC algorithms. To address the aforementioned issues, this paper considers the arbitrary nature of the attack direction and the uncontrollable compression ratio faced by adversaries, and presents two practical rate-distortion attack paradigms, i.e., Specific-ratio Rate-Distortion Attack (SRDA) and Agnostic-ratio Rate-Distortion Attack (ARDA). Using the performance variations as indicators, we evaluate the adversarial robustness of eight predominant LIC algorithms against diverse attacks. Furthermore, we propose two novel analytical tools for in-depth analysis, i.e., Entropy Causal Intervention and Layer-wise Distance Magnify Ratio, and reveal that hyperprior significantly increases the bitrate and Inverse Generalized Divisive Normalization (IGDN) significantly amplifies input perturbations when under attack. Lastly, we examine the efficacy of adversarial training and introduce the use of online updating for defense. By comparing their advantages and disadvantages, we provide a reference for constructing more robust LIC algorithms against the rate-distortion attacks.