In recent years, there has been growing interest in using acoustic emission (AE) time series data to develop fracture precursors for predicting imminent failure in cementitious materials. In this context, natural time (NT) analysis used in seismology has proven to be a useful tool, offering insights into the critical stage, namely the region of criticality, that precedes the mainshock event. Therefore, in the present study, the occurrence of impending macroscopic fracture in cementitious composites is predicted using the NT analysis of acoustic emission. To achieve this, the parameters of natural time, namely the variance, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\kappa _{1}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>κ</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>, the change in entropy, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\Delta S$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Δ</mi> <mi>S</mi> </mrow> </math></EquationSource> </InlineEquation>, and the complexity measure, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\Lambda _{i}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="normal">Λ</mi> <mi>i</mi> </msub> </math></EquationSource> </InlineEquation>, were utilized as precursors. Furthermore, the Tsallis q-index, obtained from the non-extensive statistical mechanics framework, was used in conjunction with the NT parameters. It was observed that the NT parameters, <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\kappa _{1}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>κ</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation> reached a critical value of 0.07, <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\Delta S$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Δ</mi> <mi>S</mi> </mrow> </math></EquationSource> </InlineEquation> attained a global minimum, and <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\Lambda _i$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="normal">Λ</mi> <mi>i</mi> </msub> </math></EquationSource> </InlineEquation> exhibited an abrupt increase before the mainshock event, similar to that observed in seismicity prior to major earthquakes. Furthermore, a sudden drop in Tsallis q-index was observed before the mainshock event. In addition, the behavior of the cementitious composite material closely resembled that of the Olami–Feder–Christensen earthquake model, as evidenced by the significant increase in cumulative AE energy observed after the region of criticality. Therefore, <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$\kappa _{1}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>κ</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$\Delta S$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Δ</mi> <mi>S</mi> </mrow> </math></EquationSource> </InlineEquation>, and <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$\Lambda _i$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="normal">Λ</mi> <mi>i</mi> </msub> </math></EquationSource> </InlineEquation> in combination with the q-index could be utilized as precursors for detecting impending macroscopic fracture in cementitious composites.

Predicting fracture precursors in cementitious materials using natural time analysis coupled with non-extensive statistical mechanics

期刊论文
发表日期：

2026年1月19日

查看全文

Kashif Naukhez,
R. Vidya Sagar,
J. M. Chandra Kishen

摘要

In recent years, there has been growing interest in using acoustic emission (AE) time series data to develop fracture precursors for predicting imminent failure in cementitious materials. In this context, natural time (NT) analysis used in seismology has proven to be a useful tool, offering insights into the critical stage, namely the region of criticality, that precedes the mainshock event. Therefore, in the present study, the occurrence of impending macroscopic fracture in cementitious composites is predicted using the NT analysis of acoustic emission. To achieve this, the parameters of natural time, namely the variance, $\kappa _{1}$ $κ_{1}$ , the change in entropy, $\Delta S$ $Δ S$ , and the complexity measure, $\Lambda _{i}$ $Λ_{i}$ , were utilized as precursors. Furthermore, the Tsallis q-index, obtained from the non-extensive statistical mechanics framework, was used in conjunction with the NT parameters. It was observed that the NT parameters, $\kappa _{1}$ $κ_{1}$ reached a critical value of 0.07, $\Delta S$ $Δ S$ attained a global minimum, and $\Lambda _i$ $Λ_{i}$ exhibited an abrupt increase before the mainshock event, similar to that observed in seismicity prior to major earthquakes. Furthermore, a sudden drop in Tsallis q-index was observed before the mainshock event. In addition, the behavior of the cementitious composite material closely resembled that of the Olami–Feder–Christensen earthquake model, as evidenced by the significant increase in cumulative AE energy observed after the region of criticality. Therefore, $\kappa _{1}$ $κ_{1}$ , $\Delta S$ $Δ S$ , and $\Lambda _i$ $Λ_{i}$ in combination with the q-index could be utilized as precursors for detecting impending macroscopic fracture in cementitious composites.