Abstract:

Aiming to enhance understanding of the measured strain by distributed fiber optic sensing, a universal fiber strain decomposition model and interpretation framework have been proposed according to tensor analysis. And then the strict solutions to strain decomposition equations within elastic small deformation situation have been also given that adopted to most problem scenario covering fiber deployment in plane and cylindrical surface. Specifically addressing the issue in rock mechanics where there is an unclear understanding of the decomposition of helical fiber strain in uniaxial and triaxial compression tests, starting from the geometric definition of strain and using the law of cosines, this study for the first time derived the elastic small-deformation solution of the fiber strain decomposition equation consistent with the tensor projection method, and dialectically discussed the currently published strain decomposition methods. In addition, it also proved the existence of a critical helical rising angle that can make the measured fiber strain zero, and pointed out that fiber deployment strategies near the critical helical angle can relax the measurement limits within the fiber strain range. Finally, starting from the engineering strain geometric definition and combining with the law of cosines, the study for the first time fully presented the fiber strain decomposition equation solution applicable to geometric large deformations. The work emphasizes that in actual fiber deployment and interpretation processes, it is necessary to clarify the problem scenario requirements and assumptions, and to adopt an appropriate fiber deployment geometry and corresponding strain decomposition method.

Key words: distributed fiber optic sensing, strain decomposition, helical fiber optic deployment, tensor projection, rock mechanics

摘要：

为了深化对分布式光纤监测到的应变的理解，基于张量分析，建立了通用的光纤应变分解模型与解释框架，给出了适用于平面布纤和圆柱面布纤等大多数问题场景中，弹性小变形情况下的应变分解方程严格解。特别针对于岩石力学中单、三轴压缩试验所面临的螺旋部署的光纤应变分解认知不清的问题，从应变的几何定义出发，利用余弦定理，首次推导出了与基于张量投影法一致的光纤应变分解方程的弹性小变形解，并对当前已发表的应变分解方法进行了辩证讨论。此外，还证明了能够使测得的光纤应变为零的临界螺旋升角的存在，并指出在临界螺旋升角附近的光纤部署策略可放松光纤应变量程范围内测量的限制。最后，从工程应变几何定义出发，结合余弦定理，首次完整给出了适用于几何大变形下的光纤应变分解方程解。本研究强调在实际的光纤部署和解释过程中，需要明确问题场景需求与假设条件，采用合适的布纤几何构型与匹配的应变分解方法。

关键词: 分布式光纤传感, 应变分解, 螺旋布纤, 张量投影, 岩石力学