钻孔体应变与面应变观测模型是地壳岩石应变测量资料分析的理论基础，对揭示研究对象的物理本质有所帮助，因为都含有参数k(应变仪钢筒内壁面应变与空孔岩石面应变之比)，故k 的解算对模型的正确表述十分关键。考虑到外加应力需在岩石、膨胀水泥和仪器钢筒等3 层介质中传递的实际情况，根据弹性力学中的厚壁圆筒方程，推导出轴对称应力作用下k的计算式，该式与平面应力作用下基于双衬套理论(潘立宙、欧阳祖熙和陈沅俊等建立)的解算结果完全一致，公式的可靠性由此得到互证。又对k 的影响因素进行了系统研究，给出有关变化规律曲线和定量指标。最后，与Evertson 用2 层介质模型(岩石、钢筒)推导的k 值(0. 9)进行了比较，指出二者之间的明显差异和0. 9 的狭窄适用范围。

Borehole volumetric strain and area strain observation models are the theoretical basis of the analysis of crustal rocks in strain measurement data and can help to reveal the physical nature of the research objects． Because parameter k ( the ratio between the area strain of inner walls of the strain instrument probe steel tube and that of empty hole rock ) is involved，the correct interpretation of model in the solution of k value becomes important． Since the applied stress needs to pass in the three layer medium of rocks，expansive cement and instrument steel cylinder，the calculation formula of k in the axisymmetric stress is deduced on the basis of thick wall cylinder equations in elasticity． The results of the formula is completely consistent with double bushing theory ( Pan Lizhou，Ouyang Zuxi and Chen Yuanjun ) ． The reliability of the formula is thus mutually proved． The paper also studies the affecting factors of k and provides the change curve and quantitative indexes． Finally，a comparison is made between this model and Evertson's two layers medium model ( rock，steel tube) with its k value of 0. 9 (1977) ． Points out the obvious differences between the two and the narrow scope of application 0. 9． The paper points out the differences between these two models and the limited applications of k value of 0. 9．

国家科技支撑计划项目(2012BAK19B02-02)与地震行业科研专项(201108009)联合资助