南京大学冀胤霖研究员等:从滚轴链条到滚珠链条——岩石环向变形测量方法的改进

标       题：Advancing from Roller‑Chain to Ball‑Chain to Measure RockCircumferential Deformation 

期       刊：Rock Mechanics and Rock Engineering 

第一作者：Dehao Meng (南京大学;  德国GFZ地学研究中心)

通讯作者：Yinlin Ji 冀胤霖研究员 (南京大学; 德国GFZ地学研究中心); Honghu Zhu 朱鸿鹄教授(南京大学)

DOI：https://doi.org/10.1007/s00603-026-05450-x

发表日期：2026.03.24

岩石变形的准确测量在地球物理与岩土工程研究中具有重要意义。然而，在大变形条件下，传统滚轴链条易受样品局部轴向位移影响而发生倾斜，导致与其配套的引伸计可能高估环向变形。为克服这一局限性，本文开发了一种可与引伸计配合使用的新型滚珠链条装置。该装置采用可在全方向自由滚动的球形滚动元件，能够同时适应样品的轴向与环向变形，从而在变形过程中更好地保持链条的圆形构型。通过对花岗岩试样开展一系列单轴压缩试验，对该装置的性能进行了系统评估，并在不同伺服控制模式下与传统滚轴链条引伸计及应变片测量结果进行了对比。结果表明，滚珠链条引伸计在弹性阶段能够提供准确的环向应变测量，并在非弹性阶段表现出更高的测量稳定性与保真度。由于其对链条倾斜的敏感性较低，该装置在涉及既有裂隙激活及高度局部化变形的室内试验中具有良好的应用前景，有望克服传统测量方法在大变形条件下面临的局限性。

Fig.1 Experimental setup for the uniaxial compression test and detailed views of the chain extensometers, as well as circumferential strain calculation method. a Uniaxial compression test setup (middle) with detailed views of the roller-chain (left) and ball-chain (right) extensometers. The roller rotates around a central axis that connects adjacent links, while the ball is seated in a spherical void allowing free rotation in all directions. Both chain extensometers are mounted simultaneously on the same sample to compare the accuracy of circumferential deformation measurements, with strain gauges serving as a reference. The arrow on the upper loading cap indicates the loading direction. A linear variable differential transformer (LVDT) is used to monitor axial deformation. In separate tests, the positions of the two extensometers are swapped to avoid positional bias. b Under vertical compressive loading, lateral expansion due to the Poisson effect causes a change in chord length captured by the extensometer, while the chain length remains unchanged and the rollers allow lateral expansion (MTS 2004). c Local vertical displacement leads to chain inclination associated with ellipticity. Here, r is the radius of the rolling element of the extensometer chain; R_i and R_f denote the initial and final sample radii, respectively; θ_i and θ_f are the angles (in radians) subtended by the initial and final chord lengths (l_i and l_f)

Fig. 2 Stress–strain curves for Beishan granite samples subjected toaxial compressive loading servo-controlled by (a and b) LVDT-measured axial displacement, (c and d) ball-chain extensometer measuredcircumferential deformation, and (e and f) roller-chain extensometermeasured circumferential deformation. In each pair of tests, the positions of the extensometers are swapped to exclude positional bias. gCircumferential strain at failure (red triangles) and Poisson’s ratio(black circles) calculated from circumferential strain measurementsobtained using different methods

Fig. 3 Evolution of axial stress (black line) and circumferential strainmeasured by ball-chain extensometer (blue line), roller-chain extensometer (red line), and horizontal strain gauges (orange, green, andcyan lines) during the axial LVDT-controlled tests. Servo controlmode transitions from load rate control to axial LVDT-measureddisplacement control at approximately 75 MPa. The positions of theextensometers are swapped to exclude positional bias. Circumferential strain evolution in dashed rectangles is zoomed in and shown onthe right

Fig. 4 Evolution of axial stress (black line) and circumferential strainmeasured by ball-chain extensometer (blue line), roller-chain extensometer (red line), and horizontal strain gauges (orange, green, andcyan lines) during the ball-chain circumferential extensometer-controlled tests. Servo control mode transitions from load rate control toball-chain extensometer-measured circumferential deformation control at approximately 75 MPa. The positions of the extensometers areswapped to exclude positional bias. Circumferential strain evolutionin dashed rectangles is zoomed in and shown on the right

Fig. 5 Evolution of axial stress (black line) and circumferential strainmeasured by ball-chain extensometer (blue line) and roller-chainextensometer (red line) during the roller-chain circumferential extensometer-controlled tests. Servo control mode transitions from loadrate control to roller-chain extensometer-measured circumferentialdeformation control at approximately 75 MPa. The positions of theextensometers are swapped to exclude positional bias. Circumferential strain evolution in dashed rectangles is zoomed in and shown onthe right 

Fig. 6 Two typical experimental configurations for large-deformationregimes: a inclined fracture (Ji et al. 2022b) and b parallel fracture,both prone to chain inclination. a In the inclined fracture configuration, accurate measurement of both axial displacement and circumferential deformation is required to resolve fracture dilation duringshear slip. b In the parallel fracture configuration, dilation is primarily reflected in circumferential deformation. In both cases, slip alongthe fracture induces relative block movement, distorting the chainand introducing ellipticity, which compromises the accuracy of circumferential strain measurements. The performance of the ball-chainextensometer can be further improved by mechanically constrainingits axial position to reduce inclination effects

本研究提出了一种新型滚珠链条引伸计，其设计旨在减弱链式引伸计装置在样品局部轴向变形过程中因链条倾斜引起的椭圆化效应。通过一系列单轴压缩试验验证了其有效性，结果表明该装置在弹性阶段具有良好的测量准确性，在非弹性阶段能够提供更高的测量保真度。主要结论如下：

1）伺服控制模式对破坏行为具有显著影响。轴向位移控制试验表现为I类峰后响应，而基于环向变形控制的试验则呈现II类峰后行为。

2）应变局部化可在宏观弹性阶段内发生，这一点可由应变片测量结果的非均匀性体现。滚珠链条与滚轴链条引伸计测得的泊松比接近，差异小于5%，表明两者均能反映整体响应下的平均环向应变。此外，多组试验均观察到加载方向效应，即靠近加载端布置的引伸计记录到更高应变，其对应泊松比平均高出约17%，可能与加载端较弱的端部约束效应有关。尽管如此，两类链式引伸计在弹性阶段均能够可靠表征平均环向变形。

3）在非弹性阶段，滚珠链条引伸计相较于传统滚轴链条对局部轴向变形引起的链条倾斜及测量畸变敏感性更低。裂纹扩展过程中，滚轴链条引伸计与应变片测量结果分别受链条椭圆化与应变局部化影响而产生偏差，而滚珠链条引伸计则表现出更稳定的应变演化和更高的测量一致性。在峰值应力处，滚轴链条测得的环向应变平均高出滚珠链条约25%，且该差异在峰后阶段进一步扩大。

4）滚珠链条引伸计能够在适应轴向变形的同时保持近似圆形构型，使其适用于裂隙滑移等大变形条件下的实验研究。在此类条件下，准确监测环向变形对于理解裂隙剪胀行为及渗透率演化至关重要，而该装置为解决相关测量难题提供了有效手段。

综上，滚珠链条引伸计是一种实用且可靠的环向变形监测工具，尤其适用于存在大变形与应变局部化的实验岩石力学研究。

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