To accurately measure muck volume during earth pressure balance shield tunneling, improve control of ground loss during excavation, and mitigate the risk of surface settlement in urban environments, a three-dimensional point cloud scanning method for a muck box is proposed. In addition, a volume calculation algorithm based on triangular meshing and slicing is developed using muck box point clouds acquired from the Chengdu metro line 10 shield tunneling project. The algorithm′s accuracy and computational efficiency are improved by constructing a virtual bottom surface and optimizing slice contour paths. Finally, indoor simulation tests are conducted to comprehensively verify the accuracy of the proposed volume-estimation methods and to analyze potential error sources. The results indicate that: (1) LiDAR is more suitable than structured-light cameras for muck box scanning, offering superior scanning range and measurement accuracy. Under both slicing and meshing approaches, the structured-light camera exhibits volume errors that are 1.79% and 1.82% higher than those obtained using LiDAR, respectively. (2) When complete point clouds are available, the slicing method achieves higher accuracy than the meshing method. For LiDAR point clouds corresponding to actual muck volumes of 133.68, 178.24, and 222.80 dm³, the slicing method reduces the volumeestimation error rate by 0.61%, 0.66%, and 0.25%, respectively, compared with the meshing method. In contrast, the meshing method demonstrates stronger robustness when point clouds are incomplete. (3) Field tests were conducted by manually measuring muck box loads during engineering operations and comparing them with point-cloud-based estimates. Statistical analysis of more than 100 excavation rings confirms that the proposed volume-measurement approach achieves an engineering calculation error of less than 3%.