Estimating uniaxial compressive strength of rocks using genetic expression programming

The aim of this paper is to estimate the uniaxial compressive strength(UCS) of rocks with different characteristics by using genetic expression programming(GEP).For this purpose,five different types of rocks including basalt and ignimbrite(black,yellow,gray,brown) were prepared.Values of unit weight,water absorption by weight,effective porosity and UCS of rocks were determined experimentally.By using these experimental data,five different GEP models were developed for estimating the values of UCS for different rock types.Good agreement between experimental data and predicted results is obtained.     

Estimation of uniaxial compressive strength from point load strength,Schmidt hardness and P-wave velocity

Uniaxial compressive strength is considered one of the most important parameters in the characterization of rock material in rock engineering practice. The study investigated correlations between uniaxial compressive strength and point load index, P-wave velocity and Schmidt hardness rebound number together with the effects of core diameter size. A total of 150 core samples at five different diameters (54, 48, 42, 30 and 21 mm) were obtained from sandstone, limestone and cement mortar. Ten saturated samples at each diameter (length:diameter ratio 2:1) were prepared from each of the three materials. The best correlations were found between uniaxial compressive strength and point load or Schmidt hammer values. The closest relationship was observed for the 48 mm diameter cores.      

Application of machine learning in predicting the rate-dependent compressive strength of rocks

Accurate prediction of compressive strength of rocks relies on the rate-dependent behaviors of rocks, and correlation among the geometrical, physical, and mechanical properties of rocks. However, these properties may not be easy to control in laboratory experiments, particularly in dynamic compression experiments. By training three machine learning models based on the support vector machine (SVM), back-propagation neural network (BPNN), and random forest (RF) algorithms, we isolated different input parameters, such as static compressive strength, P-wave velocity, specimen dimension, grain size, bulk density, and strain rate, to identify their importance in the strength prediction. Our results demonstrated that the RF algorithm shows a better performance than the other two algorithms. The strain rate is a key input parameter influencing the performance of these models, while the others (e.g. static compressive strength and P-wave velocity) are less important as their roles can be compensated by alternative parameters. The results also revealed that the effect of specimen dimension on the rock strength can be overshadowed at high strain rates, while the effect on the dynamic increase factor (i.e. the ratio of dynamic to static compressive strength) becomes significant. The dynamic increase factors for different specimen dimensions bifurcate when the strain rate reaches a relatively high value, a clue to improve our understanding of the transitional behaviors of rocks from low to high strain rates.     

Estimating the uniaxial compressive strength of pyroclastic rocks from the slake durability index

Because the preparation of standard samples may not always be possible for weak or soft rocks, the prediction of uniaxial compressive strength (UCS) from indirect methods is widely used for preliminary investigations. In this study, the possibility of predicting UCS from the slake durability index (SDI) was investigated for pyroclastic rocks. For this purpose, pyroclastic rocks were collected from 31 different locations in the Cappadocian Volcanic Province of Turkey. The UCS and SDI tests were carried out on the samples in the laboratory. The UCS values were correlated with the SDI values and a very strong exponential relation was found between the two parameters. Since some data were scattered over the UCS values of 20 MPa, the correlation plot was redrawn for above and below the UCS values of 20 MPa, respectively. Very strong linear correlations were developed for two cases. Our concluding remark is that the UCS of pyroclastic rocks can be estimated from the SDI.

     

Nail penetration test for determining the uniaxial compressive strength of rock

We offer a new and practical index test method, the nail penetration test (NPT), to estimate the UCS of intact rocks, to be used as alternative to the point load test (PLT) or Schmidt rebound hammer test (SRH). The major tools used in the investigation include a gasnailer with 130 J power and its nails ranging from 25 to 60 mm in length. The study material covers 65 rock blocks of gypsum, tuff, ignimbrite, andesite, sandstone, limestone, and marble. For the NPT, five nail shots were performed on each block sample and the average value was obtained. Two to three uniaxial compression tests were carried out on each specimen. Ten impacts were applied on rock blocks by using both the L- and N-types of SRH. Regarding the PLT, either 10 axial or 10 block tests was applied on each rock type.The average nail penetration depths were correlated with the UCS, I_S(50) and rebound number for both types of the SRH. Also, the measured UCS values were compared with those obtained from the empirical relationships using the data from the NPT, PLT, and SRH. It was found that the NPT provides better estimates for UCS than the PLT or SRH. Particularly applicable to weak to very weak rocks, the NPT is capable of indirectly estimating the UCS of intact rocks up to 100 MPa. The test is proposed for use in mainly in situ applications.     

Utilizing the strength conversion factor in the estimation of uniaxial compressive strength from the point load index

The strength conversion factor (k) is the ratio between the uniaxial compressive strength (UCS) and the point load index (PLI). It has been used to estimate the UCS from the PLI since the 1960s. Many researchers have investigated the relationship between UCS and PLI for various rock types of different geological origins, such as igneous, sedimentary, and metamorphic rocks. In this study, the k values for subclasses of igneous (pyroclastic, volcanic, and plutonic), sedimentary (chemical and clastic), and metamorphic (foliated and nonfoliated) rocks were evaluated. For this purpose, UCS and PLI data for a total of 410 rock samples extracted from literature published around the world as well as UCS and PLI data obtained in this work for 80 rock samples taken from the Eastern Black Sea Region in Turkey were evaluated together to determine the k values of different rock classes. Strength conversion factors were obtained using zero-intercept regression analysis, formulation, and a graphical approach. This study confirmed that there is no single k value that is applicable to all rock classes. According to statistical analyses, k varied between 12.98 and 18.55 for the rocks studied. These findings demonstrate that the k values derived in this work can be reliably used to estimate the strengths of rock samples with specific lithologies.     

The effect of rock classes on the relation between uniaxial compressive strength and point load index

Uniaxial compressive strength and point load tests were carried out on 17 igneous, 16 metamorphic and 19 sedimentary rocks and the values correlated with their I _s values. The influence of the different rock type was investigated using regression analysis and the derived equations were statistically tested. Although the derived equation for all data is significant, the data points are scattered and the coefficient of correlation is not strong. However, when the regression analysis was repeated for igneous, metamorphic and sedimentary rocks respectively, the data were less scattered and stronger correlation coefficients were obtained.      

Predicting uniaxial compressive strength,modulus of elasticity and index properties of rocks using the Schmidt hammer

The Schmidt hammer test is a non-destructive method which can be used in both laboratory and field to provide a quick and relatively inexpensive measure of rock hardness. The study investigated the relationship between the Schmidt hardness and modulus of elasticity, uniaxial compressive strength and index properties of nine types of rock including travertine, limestone, dolomitic limestone and schist. The empirical equations developed indicated the Schmidt hardness rebound values have a reliable relationship with the uniaxial compressive strength of rock (r = 0.92). Comparing the results with those reported by other researchers, it is concluded that no single relationship can be considered reliable for all rock types. Whilst the equations developed in this study may be useful at a preliminary stage of design, they should be used with caution and only for the specified rock types.      

Dynamic failure analysis on granite under uniaxial impact compressive load

High strain-rate uniaxial compressive loading tests were produced in the modified split Hopkinson pressure bar (SHPB) with pulse shaper on granite samples. It was shown that the failure of the granite cylinder was typical tensile splitting failure mode by sudden splitting parallel to the direction of uniaxial compressive loading at different strain rates. Besides, it was concluded that not only the strength of granite increased, but also the fragment size decreased and the fragment numbers increased with the increasing strain rate. To quantitatively analyze the failure phenomena, the numerical calculation based on a dynamic interacting sliding microcrack model was adopted to investigate the influence of microcrack with the different initial crack length, crack angle, crack space and friction coefficient on the macro-mechanical properties of granite under different strain rates. Accordingly, the strain-dependency of the compression strength and the fragmentation degree of granite was explained reasonably.     

花岗岩在单轴冲击压缩荷载下的动态断裂分析

利用脉冲整形器改进后的分离式Hopkinson压杆(SHPB)系统,对新加坡Bukit Timah地区的花岗岩圆柱形试样进行了高应变率下的单轴压缩实验。实验结果发现:随着应变率的增加,不仅花岗岩材料的抗压强度增大,而且以轴向拉伸劈裂为主要破坏形式的破碎程度也有所提高,表现为碎块的尺寸减小和数量增加。针对上述花岗岩的动态特性,采用多裂纹相互作用的动态滑移型裂纹模型定量的分析了不同应变率下,材料的微裂纹的初始长度、角度、初始裂纹间距以及裂纹面的摩擦系数等微裂纹特征对材料动态强度及破碎的影响,将岩石类材料的宏观动力学特性与其细观微结构联系起来,合理地解释了花岗岩的动态强度及破碎程度的应变率相关性。     

Dynamic failure analysis on granite under uniaxial impact compressive load

High strain-rate uniaxial compressive loading tests were produced in the modified split Hopkinson pressure bar (SHPB) with pulse shaper on granite samples. It was shown that the failure of the granite cylinder was typical tensile splitting failuremode by sudden splitting parallel to the direction of uniaxial compressive loading at different strain rates. Besides, it was concluded that not only the strength of granite increased, but also the fragment size decreased and the fragment numbers increased with the increasing strain rate. To quantitatively analyze the failure phenomena, the numerical calculation based on a dynamic interacting sliding microcrack model was adopted to investigate the influence of microcrack with the different initial crack length, crack angle, crack space and friction coefficient on the macro-mechanical properties of granite under different strain rates. Accordingly, the strain-dependency of the compression strength and the fragmentation degree of granite was explained reasonably. __________ Translated from Chinese Journal of Geotechnical Engineering, 2007, 29(3): 385–390 [译自: 岩土工程学报]     

The effect of length to diameter ratio of test specimens on the uniaxial compressive strength of rock

One of the parameters which affect the uniaxial compressive strength (UCS) of rock materials is the length to diameter ratio (L/D) of test cores. ASTM recommends a ratio of between 2 and 2.5, and ISRM suggests 2.5–3:1. Research has shown that high UCS values are obtained for L/D ratios <2, a very slight difference in values between 2 and 2.5, and they remain effectively constant with a L/D ratio >2.5:1. In this study, the shape effect on the UCS of seven rocks was investigated by testing dry cores with L/D ratios from 1 to 2.5:1. Based on the results, a decrease in UCS with increasing L/D ratios up to 2.5:1 was measured for all the rocks except the tuff. By omitting the data from the tuff sample, a correction formula was determined for the rocks tested in this study and results obtained from the literature. However, further work is required on different types of rock to verify or modify this formula.     

混凝土强度对其动态抗压强度的影响

简述了混凝土建筑材料的性能特点,介绍了不同强度混凝土静、动态单轴压缩试验,通过分析其试验结果,表明混凝土静态抗压强度对其动态抗压强度具有重要影响。     

Specimen shape and cross-section effects on the mechanical properties of rocks under uniaxial compressive stress

Uniaxial compressive properties of rocks are very important for designing and constructing engineering projects. Based on the available standards for determining these properties, high quality core specimens with proper geometry are needed. In many cases, the standard specimens, especially in clay-bearing, fractured, and weathered rocks, are always not able to be prepared. On the other hand, in some natural conditions, rocks with different size, shape, and cross-section are undergoing uniaxial compressive loading. Therefore, in order to evaluate the uniaxial compressive strength dependency behaviors of rocks on the shape and cross-section of tested specimens, some marble specimens with three different cross-sections, including circular, square, and rectangular, as well as four different shape ratios (height to diameter/width ratio) of 0.5, 1, 2, and 3 were prepared and tested. Axial and lateral strains, acoustic emission (AE), and camera photographs were recorded during the tests. Rock strength behavior was evaluated based on several stress thresholds, including crack closure stress (σ_cc), crack initiation stress (σ_ci), damage stress (σ_cd), and peak stress (σ_ucs). The results indicated that σ_cc was not dependent on the cross-sectional shape of specimens. With increasing shape ratio, σ_cc gradually increased, while σ_cd and σ_ucs greatly decreased, and σ_ci remained at a constant value. The cross-sectional shape effect became operative when r was less than or equal to 1. Moreover, the values of σ_cd and σ_ucs of rectangular prism specimens and square prism specimens are lower than those of cylindrical specimens, indicating that the unstable crack propagation of prism specimens occurs earlier. The difference gap of σ_cd and σ_ucs between specimens with different cross-sectional shapes was dramatically decreased with increasing shape ratio. The AE and camera recorded data indicated that the fracture modes of rectangular and square prism specimens are more likely to change from shearing to slabbing fracture when the shape ratio decreased from 3 to 0.5. The main crack developed surface turned from wide surface to narrow surface with the shape ratio of rectangular prism specimens changing from 3 to 1 and 0.5. The research results are of referential meaning to the design of pillars in underground hard rock mines.

     

高强橡胶混凝土单轴受压力学性能的试验研究

对高强橡胶混凝土进行了单轴受压试验,得到了含不同掺量、不同粒径的高强橡胶混凝土的应力-应变曲线.分析了橡胶掺量、胶粉粒径对高强橡胶混凝土的单轴抗压强度、极限应变、初始弹性模量和破坏形态的影响.研究结果表明:橡胶掺量对高强橡胶混凝土的单轴抗压强度、极限应变、初始弹性模量和破坏形态的影响都比较明显;胶粉粒径对高强橡胶混凝土的强度、初始弹性模量和破坏形态有一定的影响,对极限应变的影响不明显.