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ADE	can provide more practical outputs. The successful application of these algorithms has been reported by other researchers in mining and geotechnical engineering fields (Armaghani et al. 2016; Salimi et al. 2016; Hasanipanah et al. 2017b; Khandelwal et al. 2017). Hence, it is necessary to use state-of-the-art modelling ...
ADE	horizontal in-situ stress in the face to be unloaded; 𝜎 : vertical in-situ stress; 𝜎 : rockburst 𝑣 𝑅𝐵 maximum stress; 𝐼 : rockburst risk index; 𝐷: depth, 𝜌: density, 𝐾: horizontal pressure 𝑅𝐵 coefficient (ratio of average horizontal stresses to the vertical stress due to overburden), 𝑀𝐿𝑅: multiple linear ...
ADE	Taheri 2019) The AHC is the most common type of clustering techniques which is used in earth sciences (Hudaverdi 2012). The AHC follows a bottom-up procedure that iteratively creates the single object clusters and then these clusters are merged into the larger clusters based on the similarity or dissimilarity criteria....
ADE	5.3. Methods and Results 5.3.1. Stepwise Selection and Elimination Process This section aims to do a systematic stepwise selection and elimination (SSE) analysis to identify the most important parameters on the outputs and reduce the complexity of the developed models. The process of parameter reduction also is carried...
ADE	correlating with 𝜎 (i.e. 𝑆𝑖𝑔.(2−𝑡𝑎𝑖𝑙𝑒𝑑) ≤ 0.05), while 𝐷 (depth) with the 𝑆𝑖𝑔.> 0.05 𝑅𝐵 and low correlation coefficient (𝑟 = −0.128) was removed from the input parameters for further modelling of 𝐼 . The elimination of parameters does not show that they have not any 𝑅𝐵 influence on the output, but s...
ADE	and from 0.754 (model 1) to 0.821 (model 5) for 𝐼 , respectively. In other words, the 𝑅𝐵 parameters of 𝑈𝐶𝑆, 𝐸, and 𝜎 can explain 82.8% (𝑅2 = 0.828) variations in 𝜎 . As such, the 𝑣 𝑅𝐵 parameters of 𝜎 , 𝐾, 𝐸, 𝜈, and 𝜌 can explain 67.4% (𝑅2 = 0.674) variations in 𝐼 . Thus, 𝑅𝐵 𝑅𝐵 these parameters w...
ADE	5.3.2. Non-linear Regression Analysis Non-linear regression (NLR) attempts to find a function which is a non-linear combination of the input parameters using a method of successive approximation (Archontoulis and Miguez 2015; Bethea 2018). In geoscience, most of the dependent parameters show a non-linear relationship w...
ADE	user (Alavi and Gandomi 2011). By inspiring from the Darwinian principle of “Survival of the Fittest” (Nazari and Pacheco Torgal 2013) and the natural evolution, a new subset of soft computing was introduced as the evolutionary algorithm (EA). Generally speaking, EAs work with a randomly generated population of individ...
ADE	in Ferreira.(Ferreira 2006) In the current study, the selected inputs from the SSE analysis were considered as terminal sets to formulate the rockburst parameters nonlinearly as follows: 𝜎 = 𝑓(𝑈𝐶𝑆,𝐸,𝜎 ) (5.4) 𝑅𝐵 𝑣 𝐼 = 𝑓(𝜎 ,𝐾,𝜐,𝐸,𝜌) (5.5) 𝑅𝐵 𝑅𝐵 The rockburst database was divided randomly into traini...
ADE	𝑅𝑀𝑆𝐸′′ = 𝑅𝑀𝑆𝐸′ ×(1+ 1 × 𝑆𝑚𝑎𝑥−𝑆 𝑖 ) (5.8) 𝑖 𝑖 5000 𝑆𝑚𝑎𝑥−𝑆 𝑚𝑖𝑛 where 𝑆 is the size of the GEP program, 𝑆 and 𝑆 are the maximum and minimum 𝑖 𝑚𝑎𝑥 𝑚𝑖𝑛 program sizes which are calculated by the following equations: 𝑆 = 𝐺(ℎ+𝑡) (5.9) 𝑚𝑎𝑥 𝑆 = 𝐺 (5.10) 𝑚𝑖𝑛 where 𝐺 is the number of g...
ADE	𝜎 and 𝐼 versus the predicted ones by the constructed GEP models for training and testing 𝑅𝐵 𝑅𝐵 data groups. As seen, the data points have almost a uniform distribution around the fitted lines in both GEP-based models which show the goodness-of-fit of the models. The developed models and their performance are disc...
ADE	Fitness function RMSE′′ RMSE′′ i i Parsimony pressure Yes Yes Mutation rate 0.01 0.04 Inversion rate 0.1 0.1 Transposition 0.1 0.1 One-point recombination 0.3 0.3 Two-point recombination 0.3 0.3 Gene recombination 0.1 0.1 CART parameter Setting σ I RB RB Initial inputs UCS,E,σ σ ,K,υ,E,ρ v RB Excluded parameter - ρ Min...
ADE	assumption is made with the distribution of values of the independent parameters. On the other hand, CART can handle the highly skewed (multimodal) quantitative data as well as the qualitative parameters with ordinal or non-ordinal structures (Breiman et al. 1984; Salimi et al. 2016). In this algorithm, it is not neces...
ADE	classified in sub-node 𝑡 (𝑥𝜖{𝑅,𝐿}), 𝑦 is the value of the objective parameter for the case 𝑖, 𝑥 𝑖 𝑦̅(𝑡) is the mean value of parent node, and 𝑦̅(𝑡 ) is the mean value of the sub-node 𝑡 . 𝑥 𝑥 The best split is obtained by maximizing the Φ showing the reduction of impurity of an RT (𝑡) model. This splitt...
ADE	sensitivity of the problem. Furthermore, to assess the performance of the developed models in depth, new validation indices have been proposed by other researchers. Golbraikh and Tropsha (2002) defined two indices of 𝑘 and 𝑘′ to validate the models on testing datasets. In addition, Roy and Roy (2008) proposed an indi...
ADE	Table 5.7 Statistical indices for the external validation of the developed models Item Formula Threshold 𝜎 𝐼 𝑅𝐵 𝑅𝐵 GEP CART GEP CART 1 ∑𝑛 (ℎ −ℎ̅)(𝑡 −𝑡̅) 𝑅>0.8 0.969 0.957 0.972 0.943 𝑅= 𝑖=1 𝑖 𝑖 𝑖 𝑖 √∑𝑛 (ℎ −ℎ̅)2∑𝑛 (𝑡 −𝑡̅)2 𝑖=1 𝑖 𝑖 𝑖=1 𝑖 𝑖 2 ∑𝑛 (ℎ𝑡) 0.85<𝑘<1.15 0.934 0.931 0.962 0.981 𝑘= 𝑖=...
ADE	component in a combination of other parameters in a non-linear form. As mentioned in the GEP modelling section, during the modelling procedure, by applying the variable pressure coefficient, excluding any of the selected three parameters (i.e. 𝑈𝐶𝑆, 𝐸, and 𝜎 ) from the 𝑣 modelling procedure did not improve the acc...
ADE	2 1 y = -0.0186x3+ 0.2124x2-0.7981x 1.5 0.8 + 1.1997 R² = 0.9521 y = 1.2524x-0.244 B 1 B0.6 R² = 0.9859 R R I I 0.5 0.4 0 0.2 0 2 4 6 0 100 200 300 K σ (MPa) RB Figure 5.14 (Continued) 5.6. Summary and Conclusions As a catastrophic geohazard, rockburst threatens the safety of workers and infrastructures in deep geotech...
ADE	29 If E in [36.05, 71) and K in [1.721, 5.866) and 𝜎 in [56.8, 255.5) then 𝐼 = 0.185 in 12.8% of cases 𝑅𝐵 𝑅𝐵 30 If E in [14.1, 29.7) and K in [1.721, 5.866) and 𝜎 in [56.8, 255.5) then 𝐼 = 0.292 in 12.8% of cases 𝑅𝐵 𝑅𝐵 31 If E in [29.7, 36.05) and K in [1.721, 5.866) and 𝜎 in [56.8, 255.5) then 𝐼 = 0.547 ...
ADE	Cai M, Kaiser P (2018) Rockburst support reference book—volume I: rockburst phenomenon and support characteristics. Laurentian University Chen G, Li T, Wang W, et al (2019) Weakening effects of the presence of water on the brittleness of hard sandstone. Bulletin of Engineering Geology and the Environment 78(3):1471–148...
ADE	Golbraikh A, Tropsha A (2002) Beware of q2! Journal of Molecular Graphics and Modelling 20(4):269–276 Hasanipanah M, Faradonbeh RS, Amnieh HB, et al (2017a) Forecasting blast-induced ground vibration developing a CART model. Engineering with Computers 33(2):307-316 Hasanipanah M, Faradonbeh RS, Armaghani DJ, et al (201...
ADE	model development using gene expression programming. Powder Technology 308:61-69 Hudaverdi T (2012) Application of multivariate analysis for prediction of blast-induced ground vibrations. Soil Dynamics and Earthquake Engineering 43:300–308 Jahed Armaghani D, Faradonbeh RS, Momeni E, et al (2017) Performance prediction ...
ADE	Liu X, Liang Z, Zhang Y, et al (2018) Experimental study on the monitoring of rockburst in tunnels under dry and saturated conditions using AE and infrared monitoring. Tunnelling and Underground Space Technology 82:517–528 Mahjoobi J, Etemad-Shahidi A (2008) An alternative approach for the prediction of significant wav...
ADE	Saharan MR, Mitri H (2011) Destress blasting as a mines safety tool: Some fundamental challenges for successful applications. In: Procedia Engineering. Elsevier 26(37-47) pp 37–47 Salimi A, Faradonbeh RS, Monjezi M, Moormann C (2016) TBM performance estimation using a classification and regression tree (CART) technique...
ADE	Su G, Chen Z, Ju JW, Jiang J (2017a) Influence of temperature on the strainburst characteristics of granite under true triaxial loading conditions. Engineering Geology 222:38–52 Su G, Jiang J, Zhai S, Zhang G (2017b) Influence of Tunnel Axis Stress on Strainburst: An Experimental Study. Rock Mechanics and Rock Engineer...
ADE	Title of Paper Post-peak behaviour of rocks under cyclic loading using a double-criteria damage-controlled test method Publication Status Published Accepted for Publication Submitted for Publication U npublished and Unsubmitted work written in manuscript style Publication Details Shirani Faradonbeh R, Taheri A, Karakus...
ADE	Post-Peak Behaviour of Rocks Under Cyclic Loading Using a Double-Criteria Damage- Controlled Test Method Abstract Cyclic loading-induced hazards are severe instability problems concerning surface and underground geotechnical projects. Therefore, it is crucial to understand the rock failure mechanism under cyclic loadin...
ADE	excavation and mining seismicity, which threaten their long-term stability (Taheri et al. 2016; Munoz et al. 2016a). Therefore, it is necessary to evaluate the time-dependent behaviour of rocks under cyclic loading. In rock engineering, understanding the fatigue response of rocks is of particular interest since rock st...
ADE	rockburst phenomenon near underground excavation in deep underground conditions, post- peak analysis of the rocks in terms of strain energy evolution is required. In other words, the rockburst hazard in deep underground openings is associated with not only internal strain energy accumulation but also seismic disturbanc...
ADE	stress is reversed when a certain amount of axial or lateral displacement is achieved in a loading cycle. Munoz et al. (2016b) showed that under uniaxial loading conditions, soft, medium-strong and strong rocks demonstrate either class II or a combination of class I and class II post-peak behaviours. As a result, the p...
ADE	cyclic loading load-controlled test (Li et al. 2019), d multi-level systematic cyclic loading axial displacement-controlled test (Liu et al. 2014), e load-based damage controlled cyclic loading load-controlled test (Guo et al. 2018), f load-based damage controlled cyclic loading axial displacement-controlled test (Heap...
ADE	tests to capture the rock behaviour before and after peak stress. The axial load (acquired by a load cell), axial strain (acquired by a pair of LVDTs), and lateral strain (acquired by a chain extensometer) were recorded simultaneously during the tests by a data acquisition system at a rate of 10 data points per second ...
ADE	(here, 6 MPa) is reached. In this stage, the axial stress and lateral strain feedback signals received from the load cell and the chain extensometer, respectively, are continuously compared with the program signals (i.e., the user-defined values) and the errors, if any, are adjusted by the servo-controller. By doing so...
ADE	stress level (i.e., 6 MPa) is reached. Afterwards, the specimen is unloaded monotonically, and then cyclic loading is applied under a constant lateral strain rate of 2×10-4/s. At the first step of cyclic loading, the amplitude of lateral strain, 𝐴𝑚𝑝.(𝜀 ), is relatively low (6×10-4/s after 200 𝑙 cycles), and the fi...
ADE	10 SL 1= 6 MPa SL 2= 6.5 MPa 10 0 0.07 MPa de/d=0.02 l t -20 de/d=0.02 l t 6 MPa 6 MPa -40 6.5 MPa Failure point de/d= 2 l t -60 Amp. (e l)= 6 de l/d t= 2 -4 de/d= 2´10 L t Time Amp (e)= 16 l Amp (e)= 17 l Amp (e)= 17 l Time -80 0 2000 4000 6000 8000 Time, t (s) Figure 6.8 Typical time-history of axial stress and later...
ADE	6.3.2. Fatigue Damage Evolution Damage can be characterised by the process of generation, propagation and coalescence of mesoscopic defects and voids through solid materials. Damage can be described by the degradation of some material properties, such as stiffness, residual strength, and P-wave velocity. Additionally, ...
ADE	Fig. 6.11 summarises the evolution of the damage variable (𝐷), elastic modulus (𝐸), and energy dissipation ratio (𝐾 = 𝑈 /𝑈 ) as damage parameters for specimen TL6. A similar trend was 𝑑 𝑡 observed for the other tested specimens. As demonstrated in Fig. 6.11, the total behaviour of damage parameters under multi-l...
ADE	constant and very close to the maximum stress in each cycle. When transitioning to the higher stress levels using a monotonic loading, 𝜎 increases to reach a stationary state at each stress 𝑐𝑑 level. The results presented in Fig. 6.9 show that by applying 400 cycles at each stress level, the closed microvoids and mi...
ADE	cyclic loading (see Fig. 6.9). As explained in section 3.3, specimen TL8, which experienced more loading and unloading cycles in the pre-peak region than the other specimens did, is mostly in the compaction-dominated stage; dilation occurs at the failure point, followed by the sudden decrease in 𝜎 . This, in turn, res...
ADE	6.5. Conclusions An innovative testing methodology considering two criteria was proposed in this study to describe the post-peak behaviour of rocks subjected to systematic cyclic loading. Regarding this, the Tuffeau limestone was selected to evaluate the capability of the proposed testing method in capturing the full s...
ADE	4. An increase in strength with an increase in fatigue life was observed for the highly porous Tuffeau limestone. According to the variation in the damage parameters, stiffness and crack damage threshold stress during the systematic cyclic loading tests, this hardening behaviour can be due to the further compaction of ...
ADE	Beck K, Al-Mukhtar M (2014) Cyclic wetting–drying ageing test and patina formation on tuffeau limestone. Environmental Earth Sciences 71(5):2361–2372 Burdine NT (1963) Rock Failure Under Dynamic Loading Conditions. Society of Petroleum Engineers Journal 3(1):1–8 Cardani G, Meda A (2004) Marble behaviour under monotonic...
ADE	fractured rock under cyclic loading based on energy dissipation principle. Engineering Fracture Mechanics 206:330–341 Liu J, Xie H, Hou Z, Hou Z, Yang C, Chen L (2014) Damage evolution of rock salt under cyclic loading in unixial tests. Acta Geotechnica 9(1):153–160 Ma L, Liu X, Wang M, Xu H, Hua R, Fan P, Jiang S, Wan...
ADE	Taheri A, Tatsuoka F (2012) Stress–strain relations of cement-mixed gravelly soil from multiple-step triaxial compression test results. Soils and Foundations 52(4):748–766 Taheri A, Tatsuoka F (2015) Small- and large-strain behaviour of a cement-treated soil during various loading histories and testing conditions. Acta...
ADE	Chapter 7 Failure Behaviour of a Sandstone Subjected to the Systematic Cyclic Loading: Insights from the Double-Criteria Damage-Controlled Test Method Abstract The post-peak behaviour of rocks subjected to cyclic loading is very significant to appraise the long-term stability of underground excavations. However, an app...
ADE	List of Symbols 𝐸 Tangent Young’s modulus 𝜀𝑖𝑟𝑟 Irreversible axial strain 𝑡𝑎𝑛 𝑎 𝜈 Poisson’s ratio 𝜀𝑖𝑟𝑟 Irreversible lateral strain 𝑙 𝜎 Major principal stress Σ𝜀𝑖𝑟𝑟 Cumulative irreversible axial strain 1 𝑎 𝜎 Axial stress Σ𝜀𝑖𝑟𝑟 Cumulative irreversible lateral strain 𝑎 𝑙 𝜎 Indicator stress 𝑈 E...
ADE	place in the pre-peak or post-peak regime (Munoz and Taheri 2019). For instance, as depicted in Fig. 7.1, a pillar may experience cyclic loading due to blasting operation or other seismic activities beyond the limit in uniaxial conditions. Under such loading conditions, rock materials may still keep some loadings even ...
ADE	Shirani Faradonbeh et al. (2020) categorised the cyclic loading methods based on the loading histories and load control variables into two main groups of systematic cyclic loading (single- level or multi-level) (Figs. 7.2a and b) and damage-controlled cyclic loading (load-based or displacement-based) (Figs. 7.2c and d)...
ADE	Figure 7.2 Classification of cyclic loading tests, a single-level systematic cyclic loading path, b multilevel systematic cyclic loading path, c load-based damage controlled cyclic loading path and d displacement-based damage controlled cyclic loading path, Amp. (𝜎 ) refers to 𝑎 loading amplitude, Amp. (𝜀 ) refers t...
ADE	strain behaviour of rocks in the post-peak regime, the local strain measurement tools such as strain gauges are not effective. To characterise the post-peak instability of rocks in terms of brittleness, the complete stress-strain curves of rocks are required, and therefore, external LVDTs were used to measure the large...
ADE	ratio (𝜎 /𝜎 ) and crack damage stress ratio (𝜎 /𝜎 ) are approximately similar, 𝑐𝑖 𝑎−𝑝𝑒𝑎𝑘 𝑐𝑑 𝑎−𝑝𝑒𝑎𝑘 which indicates a small discreteness of the tested specimens. As such, in the post-failure regime, the sudden drops and recoveries of the load-bearing capacity can be observed for all specimens which can...
ADE	(b) GS-1 50 GS-2 ) a GS-3 P M 40 GS-4 ( GS-5 a GS-6 , s 30 s e r t s l a 20 i x A 10 0 0 20 40 60 80 Axial strain, e (´10-4) a Figure 7.4 (Continued) 7.3. Systematic Cyclic Loading Tests As discussed earlier, the single-criterion load-based and displacement-based loading methods are not sufficient to control the axial ...
ADE	a) the pre-defined maximum axial stress level (𝜎 /𝜎 ) is reached; 𝑎 𝑚 b) the pre-defined maximum lateral strain amplitude, 𝐴𝑚𝑝.(𝜀 )= 32×10-4 is 𝑙 reached; 3. Reverse the axial load to 𝜎 = 0.07 MPa, and repeat steps 1 and 2 until 1500 loading 𝑎 and unloading cycles are completed. 4. If the specimen did no fai...
ADE	7.4. Stress-Strain Relations In total, 17 single-level systematic cyclic loading tests (see Table 7.2) were carried out at different stress levels (𝜎 /𝜎 ) ranging from 80% to 96% of the average monotonic strength 𝑎 𝑚 following the proposed double-criteria damage-controlled testing method. As listed in Table 7.1, th...
ADE	curves of Gosford sandstone specimens subjected to the systematic cyclic loading. Furthermore, like the monotonic tests, a combined class I-II behaviour at different extents can be seen in the post-peak regime for both hardening and fatigue cyclic loading tests. Generally, the variation of hysteretic loops along with t...
ADE	(c) (d) ) a 50 AOI 50 Dilation Compaction P ) M a P ( 40 M 40 a ( , a s s 30 30 e , r t s s s e l a 20 r t s 20 i x l A 10 a i x 10 A 0 0 -600 -400 -200 0 100 -100 -80 -60 -40 -20 0 20 100 Volumetric strain, e (´10-4) Volumetric strain, e (´10-4) vol vol Figure 7.7 (Continued) 7.5. Rock Behaviour During Hardening Cycli...
ADE	incurring irreversible deformations in the specimen by doing more cycles, 𝐸 and 𝐾 remained 𝑡𝑎𝑛 fairly constant, and no considerable energy was dissipated until 1500 cycles were completed (i.e. a quasi-elastic behaviour). This quasi-elastic behaviour can be further investigated using AE results. Fig. 7.8c shows the...
ADE	(c) 2000 6000 (1) Initial monotonic loading stage (2) Systematic cyclic loading stage (3) Final monotonic loading until peak stress (4) Post-peak stage 1500 (5) Pre-peak stage s 5 t i ) 4000 h s e 10 14 E m 4 A s t i h Ei At ( 1000 1 stis he Em Ai () t 2468 246811 02 stih E A evitalum uC 3 2000 e v i t a l u m u 500 C ...
ADE	behaviour. In other words, when the stress level that cyclic loading is applied is not high enough to fail the specimen during cyclic loading, the cyclic loading has a negligible effect on the post- failure behaviour. This can be further investigated based on the variation of rock brittleness. Although there is no cons...
ADE	for several cycles, a quasi-elastic behaviour dominated the damage evolution during the pre- peak cyclic loading. This behaviour was accompanied by the progressive rock compaction (see Fig. 7.6) and strength improvement up to 8%. It should be noted that rock strength improvement induced by cyclic loading also has been ...
ADE	(b) m 1.08 GS-13 / h GS-8 ,o GS-10 i 1.06 t a r g n i 1.04 n e d r a h h 1.02 GS-11 GS-12 t g n GS-7 e GS-9 r 1.00 t S 0.98 80 82 84 86 88 Applied stress level, s/s (%) a m Figure 7.11 a The variation of axial peak stress for all monotonic and hardening cyclic loading tests and b strength hardening ratio vs. applied st...
ADE	(b) 1.0 I B0.8 ,x e d n0.6 i s s e n e0.4 l t t i r B 0.2 0.0 86 88 90 92 94 96 Applied stress level, s /s (%) a m Figure 7.13 (Continued) 7.6.2. Damage Evolution in the Post-Peak Regime The irreversible deformations are not accumulated at a constant rate in the rock specimen during the pre-peak cyclic loading but foll...
ADE	mechanism explained above. The loose behaviour at the end of the pre-peak systematic cyclic loading extends to the post-peak regime and then accelerates. In Fig. 7.14e and f the cumulative irreversible axial (∑𝜀𝑖𝑟𝑟) and cumulative irreversible lateral strains (∑𝜀𝑖𝑟𝑟) measured after full 𝑎 𝑙 unloading of each ...
ADE	7.7. Conclusions In this study, a series of systematic cyclic loading tests were conducted on Gosford sandstone specimens using an innovative double-criteria damage-controlled testing method. A comprehensive evaluation was carried out on the experimental results in terms of damage evolution, post-peak instability and s...
ADE	of brittleness index (𝐵𝐼) with 𝜎 /𝜎 for the fatigue cyclic loading tests. Therefore, 𝑎 𝑚 rocks may behave in a more brittle/violent manner when the cyclic loading is applied at stress levels close to their monotonic strength. 5. The evolution of hysteretic loops for fatigue cyclic loading tests showed that the ro...
ADE	interpretation and research perspectives. Rock Mechanics and Rock Engineering 51(2):391–414 Erarslan N, Alehossein H, Williams DJ (2014) Tensile Fracture Strength of Brisbane Tuff by Static and Cyclic Loading Tests. Rock Mechanics and Rock Engineering 47(4):1135– 1151 Fairhurst CE, Hudson JA (1999) Draft ISRM suggested...
ADE	Li T, Pei X, Wang D, et al (2019) Nonlinear behavior and damage model for fractured rock under cyclic loading based on energy dissipation principle. Engineering Fracture Mechanics 206:330–341 Liu J, Xie H, Hou Z, et al (2014) Damage evolution of rock salt under cyclic loading in unixial tests. Acta Geotechnica 9(1):153...
ADE	Development and Brittleness Quantification by Pre-peak Strength Parameters in Rock Uniaxial Compression. Rock Mechanics and Rock Engineering 49(12):4587–4606 Munoz H, Taheri A, Chanda EK (2016b) Pre-peak and post-peak rock strain characteristics during uniaxial compression by 3D digital image correlation. Rock Mechanic...
ADE	Taheri A, Zhang Y, Munoz H (2020) Performance of rock crack stress thresholds determination criteria and investigating strength and confining pressure effects. Construction and Building Materials 243:118263 Tarasov B, Potvin Y (2013) Universal criteria for rock brittleness estimation under triaxial compression. Interna...
ADE	Statement of Authorship Title of Paper Fatigue Failure Characteristics of Sandstone Under Different Confining Pressures Publication Status Published Accepted for Publication Submitted for Publication U npublished and Unsubmitted work written in manuscript style Publication Details Shirani Faradonbeh R, Taheri A, Karaku...
ADE	Chapter 8 Fatigue Failure Characteristics of Sandstone Under Different Confining Pressures Abstract Rock fatigue behaviour including the fatigue threshold stress (FTS), post-peak instability and strength weakening/hardening during cyclic loading, is of paramount significance in terms of safety and stability assessment ...
ADE	List of Symbols 𝑀 Post-peak modulus 𝑞 Peak deviator stress 𝑚 𝐸 Pre-peak modulus 𝑞 Residual deviator stress 𝑟𝑒𝑠 𝑁 Number of cycles before failure 𝑞 /𝑞 Deviator stress level 𝑢𝑛 𝑚−𝑎𝑣𝑔 𝑅 Strain gauge resistance 𝑞 /𝑞 Fatigue threshold stress 𝑓 𝑚−𝑎𝑣𝑔 𝑞 Deviator stress 𝜎 /𝑈𝐶𝑆 Confinement level 3 ...
ADE	different researchers have made many attempts to unveil the rock fatigue mechanism under different loading conditions using laboratory experiments (Cerfontaine and Collin 2018). In other words, the damage evolution mechanism in rocks can be characterised more efficiently using cyclic loading tests as it is straightforw...
ADE	From the viewpoint of the post-peak domain, due to difficulties in capturing the complete stress-strain relations of rocks under cyclic loading, especially for brittle rocks which show a class II post-peak behaviour (Wawersik and Fairhurst 1970), very few studies have investigated the influence of the pre-peak cyclic l...
ADE	8.2. Experimental Profile 8.2.1. Gosford Sandstone In this study, Gosford sandstone (Fig. 8.1a) extracted from the massive Triassic Hawkesbury sandstone of the Sydney Basin, New South Wales, Australia, was chosen as the testing material (Ord et al. 1991; Masoumi et al. 2017). X-ray powder diffraction (XRD) analysis of ...
ADE	Figure 8.1 Gosford sandstone used in this study: a prepared specimens and b SEM photograph 8.2.2. Testing Equipment A fully digital closed-loop servo-controlled hydraulic compressive machine, i.e. Instron-1282 with the maximum loading capacity of 1000 kN, was employed to conduct the triaxial monotonic and cyclic loadin...
ADE	Through a high-pressure wire and a feed-through connector fitted to the Hoek cell, the feedback signal is sent to the control unit of the testing machine to adjust the loading rate. By doing so, the membrane gauges are protected from damage during loading, and finally, the complete lateral deformation of rocks can be r...
ADE	(b) High-pressure wire Strain gauges R R 1 2 + Wheatstone Bridge - + V V ex o - R 4 R 3 Figure 8.2 (Continued) 8.3. Test Scheme and Conditions 8.3.1. Uniaxial and Triaxial Monotonic Loading Tests Before conducting the triaxial monotonic and cyclic loading tests at different confining pressures, the uniaxial compressive...
ADE	The tests were conducted in a way that the axial load and confining pressure were applied simultaneously to the rock specimen under a constant axial strain rate of 𝑑𝜀 /𝑑𝑡= 0.03 mm/min 𝑎 until the desired confining pressure level is achieved. Thereafter, the confining pressure and axial load were kept constant for ...
ADE	8.4. Confining Pressure Effect on Fatigue Threshold Stress As mentioned earlier, fatigue threshold stress (FTS) is a critical parameter, that can be used as an effective compressive strength of the intact rock subjected to static, dynamic and cyclic loads. Depending on the rock type, testing method and loading history,...
ADE	8.5. Confining Pressure Effect on Post-Peak Instability As mentioned earlier, the post-peak instability of rocks can be characterised as class I and class II, representing the stable and unstable rock fracturing process under a specific loading history, respectively. Brittleness is an appropriate intact rock property t...
ADE	𝐵𝐼 ≈ 1 and 𝐵𝐼 ≈ 0) to more class II/brittle behaviour. By increasing the confining pressure 1 2 to a certain amount (i.e. 𝜎 /𝑈𝐶𝑆 =50%), the maximum rock brittleness was achieved, and 3 𝑎𝑣𝑔 then, the 𝐵𝐼 values showed a decremental trend. A drastic drop in 𝐵𝐼 was observed for 𝜎 /𝑈𝐶𝑆 > 65%, specifically...
ADE	8.6. Confining Pressure Effect on Fatigue Damage Evolution 8.6.1. Hardening and Weakening Cyclic Loading Tests Rock specimens usually experience deformation under external forces, and a part of this deformation can be recovered by withdrawing the applied force, representing elastic characteristics. However, owing to in...
ADE	reduction and rock compaction under consecutive loading and unloading cycles. For specimen GS-C-31 (i.e., weakening test), although no failure was recorded during the cycles, a different trend for variations of 𝜔𝑖𝑟𝑟 was observed (see Fig. 8.10). For the weakening test, 𝜔𝑖𝑟𝑟 increased 𝑎 𝑎 rapidly, first for se...
ADE	8.6.1.1. Acoustic Emission Characteristics Acoustic emission (AE) is a well-known non-destructive technique that can monitor the micro and macrocrack evolution in rocks during loading in real-time. Due to the local micro-scale deformations, small fracturing events corresponding to the immediate release of strain energy...
ADE	(𝜎 /𝑈𝐶𝑆 =100% and 𝑞 /𝑞 =80%) in phase B. According to Fig. 8.11b, after a slight 3 𝑎𝑣𝑔 𝑢𝑛 𝑚−𝑎𝑣𝑔 increase in AE hits during the initial monotonic loading, the microcracking increased with a higher rate by increasing loading and unloading cycles in phase B, which is manifested by a higher number of AE hits...
ADE	(b) 4000 35000 A: Initial monotonic loading pahse 3500 B C: : S Fy ins ate l m ma ot nic o c toy nc il cic l olo aa dd inin gg p p hh aa ss ee 30000 3000 s 25000 t i h 2500 E s t i h 2000 A B C 20000 A e v E A 15000 i t a 1500 l u m 10000 u 1000 C 500 5000 0 0 0 100 200 300 Time, t (min ) (c) 3000 30000 A: Initial mono...
ADE	8.6.3. Applied Stress Level Effect on Damage Evolution As stated earlier, systematic cyclic loading was applied to the specimens at different stress levels (𝑞 /𝑞 ). To evaluate the effect of the applied stress level on damage evolution of 𝑢𝑛 𝑚−𝑎𝑣𝑔 rocks under different confining pressures, the axial strain at t...
ADE	Figure 8.14 Variation of axial strain at failure point for monotonic and cyclic loading tests under different confinement levels: a 0%, b 10%, c 20%, d 35%, e 50%, f 65%, g 80% and h 100% ) 4 -0 Damage cyclic loading tests 1 (´ 480 Hardening/weakening cyclic loading tests g v Monotonic loading tests a -a 400 ,e y=57.40...
ADE	rock types under various loading conditions, such as Gosford sandstone (up to 7.82% increase) under uniaxial systematic cyclic loading (Shirani Faradonbeh et al. 2021b), Tuffeau limestone under uniaxial multi-level systematic cyclic loading (up to 28.55% increase) (Shirani Faradonbeh et al. 2021a), hard graywacke sands...
ADE	8.7.2. An Empirical Model for Strength Prediction As discussed above, the study on strength variation of rocks under the coupled influence of cyclic loading and confining pressure is rare and limited to some specific confining pressures. Therefore, no empirical model can be found in the literature to predict strength v...
ADE	) % ( 8 n o i t a i r a 4 v h t g n e 0 r t s k a e p -4 y=0.8996x+0.2625 d e R2= 0.90 t c i d e -8 r P -8 -6 -4 -2 0 2 4 6 8 Measured peak strength variation (%) Fig. 8.18 The comparison of the measured and predicted values of peak strength variation 8.8. Conclusions Triaxial monotonic and cyclic loading tests were un...
ADE	rock brittleness, while for 𝜎 /𝑈𝐶𝑆 = 80% and 100%, the weakening effect of 3 𝑎𝑣𝑔 systematic cyclic loading history on rock brittleness was more significant. 3. Fatigue damage evaluation of rocks using different parameters (i.e. 𝐸 , 𝜔𝑖𝑟𝑟and AE 𝑡𝑎𝑛 𝑎 hits) showed that for hardening cyclic loading tests, n...
ADE	Sciences 42(2):237–250 Breiman L, Friedman J, Stone CJ, Olshen RA (1984) Classification and Regression Trees. CRC press Bruning T, Karakus M, Nguyen GD, Goodchild D (2018) Experimental Study on the Damage Evolution of Brittle Rock Under Triaxial Confinement with Full Circumferential Strain Control. Rock Mechanics and R...
ADE	microstructure on fatigue behavior of intact rocks under completely reversed loading. Analytical and Numerical Methods in Mining Engineering 6:55–62 Khandelwal M, Armaghani DJ, Faradonbeh RS, et al (2017) Classification and regression tree technique in estimating peak particle velocity caused by blasting. Engineering w...
ADE	damage zones of rocks under cyclic loading. Geotechnical Testing Journal 42(6), 1663- 1684 Nejati HR, Ghazvinian A (2014) Brittleness effect on rock fatigue damage evolution. Rock Mechanics and Rock Engineering 47(5):1839–1848 Ord A, Vardoulakis I, Kajewski R (1991) Shear band formation in Gosford sandstone. In: Intern...
ADE	Taheri A, Tatsuoka F (2015) Small- and large-strain behaviour of a cement-treated soil during various loading histories and testing conditions. Acta Geotechnica 10(1):131–155 Tarasov B, Potvin Y (2013) Universal criteria for rock brittleness estimation under triaxial compression. International Journal of Rock Mechanics...
ADE	Chapter 9 Conclusions and Recommendations 9.1. Conclusions In this thesis, state-of-the-art methodologies comprising machine learning (ML)- and experimental-based approaches were employed to investigate the rockburst phenomenon in detail. The significant findings and major contributions of the conducted research projec...
ADE	• The results of the sensitivity analysis conducted on the developed GEP-based binary model for rockburst status prediction revealed that the input parameters of maximum tangential stress (𝜎 ), elastic energy index (𝑊 ), uniaxial tensile strength (𝜎 ) and uniaxial 𝜃 𝑒𝑡 𝑡 compressive strength (𝜎 ) have the highe...
ADE	modulus, and Poisson’s ratio) represented a significant effect on the failure mechanism (i.e., squeezing, slabbing, and strain burst) of the competent overs-stressed rock masses. The initial assessment of the compiled database from different underground mining projects showed that the failure mechanisms cannot be predi...

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