Characteristics of Deformation and Energy Evolution of Roadbed Medium-Grained Sandstone under Differential Fatigue Loading

doi:10.16552/j.cnki.issn1001-1625.2025.0773

Abstract

Abstract:

In order to reveal the mechanical response mechanism of medium-grained sandstone under differential fatigue load， this paper studied the deformation characteristics and energy evolution law of sandstone under three loading modes （slow loading and rapid unloading， constant speed loading and unloading， rapid loading and slow unloading） through laboratory tests. The dynamic changes of peak strain， residual strain and energy dissipation of the samples were analyzed by MTS 322 rock mechanics test system. The results show that under varying loading modes， the strain exhibited by sandstone remains consistent， with the residual strain approximating the deformation discrepancy between successive cyclic stages. The peak strain is observed to be largest in the slow and fast unloading mode， and smallest in the fast and slow unloading mode. Furthermore， the residual strain exhibits a logarithmic growth at the initial stage due to the compression and density of the internal defects， and increases linearly with the maximum cyclic stress in subsequent stages. The input energy and elastic energy increase stepwise with the number of cycles， and the dissipation energy increase rate is significantly higher in the slow-plus-slow unloading mode than in the other modes. The dissipation energy of the first cycle of a single cyclic stage is elevated， and the mean dissipation energy is exponentially associated with the maximum cyclic load. The dissipated energy ratio fluctuates and converges with the number of cycles， a phenomenon that is closely related to the internal damage inhomogeneity of material damage and the fluctuation of loading stress. The present study elucidates the influence mechanism of loading rate on the fatigue performance of sandstone， thereby providing a theoretical basis for the selection of road base layer materials and structural optimization.

Key words: medium-grained sandstone, differential fatigue loading, mechanical property, peak strain, residual strain, energy dissipation

CLC Number:

TU45

LIU Gaoxi, WU Yunfeng, LIU Yongliang, LIU Yong. Characteristics of Deformation and Energy Evolution of Roadbed Medium-Grained Sandstone under Differential Fatigue Loading[J]. BULLETIN OF THE CHINESE CERAMIC SOCIETY, 2026, 45(2): 712-724.

Figures/Tables 12

Fig.1 Specimen pre-treatment

Fig.2 MTS322 rock mechanics test system

Table 1 Explanation of three loading modes

Loading mode	Loading time t₁/s	Unloading time t₂/s	Sample No.	Total duration of a single cycle/s	Loadfrequency/Hz
Mode 1： slow loading and rapid unloading	4.0	1.0	S1， S2	5	0.2
Mode 2： constant speed loading and unloading	2.5	2.5	S3， S4	5	0.2
Mode 3： rapid loading and slow unloading	1.0	4.0	S5， S6	5	0.2

Fig.3 Test path design

Fig.4 Schematic diagram of three energy calculation principles

Fig.5 Stress-strain curves in three loading modes

Table 2 Physical parameters of samples

Sample No.	Diameter/mm	Height/mm	Mass/g	Density/（g·cm^-3）	Longitudinal wave velocity/（m·s^-1）	Breaking strength/MPa
S1	49.75	100.30	503.3	2.58	4 238	67.9
S2	50.01	100.50	522.1	2.64	4 387	142.8
S3	50.10	100.25	520.0	2.63	4 066	108.6
S4	50.20	99.60	517.5	2.63	4 099	87.7
S5	50.05	99.55	516.7	2.64	4 547	148.6
S6	50.05	100.75	524.7	2.65	4 167	123.5

Fig.6 Relationship between peak axial strain and number of cycles

Fig.7 Relationship between axial residual strain and number of cycles

Fig.8 Variation of energy density with number of cycles

Fig.9 Relationship between mean dissipation energy and cyclic level

Fig.10 Relationship between dissipation energy ratio and number of cycles

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