Model tree approach for predicting uniaxial compressive strength and Young’s modulus of carbonate rocks

Bulletin of Engineering Geology and the Environment - The uniaxial compressive strength (UCS) and Young’s modulus (E) of rock are important parameters for evaluating the strength,...     

Application of differential evolution algorithm and comparing its performance with literature to predict rock brittleness for excavatability

ABSTRACT

The aim of this study was to estimate brittleness of intact rock by applying differential evolution (DE) algorithm and then to compare the results obtained from the optimum model with literature. For this aim, several models including linear and nonlinear were developed for predicting the brittleness via DE algorithm using the dataset obtained from 48 tunnel cases around the world. Each model were developed using 80% of the dataset as training and 20% of the dataset as testing in random. After that, developed models are compared according to the coefficient of correlations (r ²), computer process unit (CPU), mean-squared error (MSE) and number of function evaluation (NFE) values to choose the best accurate one among them. It is found that the values r ², MSE, NFE and CPU ranged between 0.9385–0.9501, 8.2616–9.938, 7217–11,176 and 4.91–36.22, respectively, with the quadratic model (QM) indicating the best performance. It is concluded that the DE algorithm is itself very powerful tool for estimating the brittleness; however, the QM is superior especially for simulations in which computational time and optimisation is a critical.     

Untersuchung der wirkenden Kräfte beim Entstehen und Ablösen von Einzelblasen mit einem Simulationsmodell

Verwendung eines früher entwickelten mathematischen Modells zur Simulierung der Vorgänge bei der Entstehung von Einzelblasen in Flüssigkeiten und Stahl. Berechnung der wirkenden Kräfte und ihrer Anteile.     

Untersuchung der Abhängigkeiten des Ablösevolumens einzelner Gasblasen mit einem Simulationsmodell

Mit einem früher¹) entwickelten, mathematischen Modell zur Simulierung der Vorgänge bei der Entstehung, Ablösung und Bewegung einzelner Blasen, die an Düsen gebildet werden, werden Abhängigkeiten des Ablösevolumens von den Flüssigkeitseigenschaften sowie von konstruktiven und operativen Parametern untersucht. Die Ergebnisse des Simulationsmodells werden mit experimentellen Daten aus dem Schrifttum verglichen. Die Übereinstimmung ist überraschend gut. Als Vorteil des Simulationsmodells stellte sich unter anderem heraus, daß bei der Untersuchung des Einflusses der physikalischen Eigenschaften der flüssigen Phase wie Dichte, Viskosität und Grenzflächenspannung der Einfluß der Veränderung eines einzelnen Parameters unter Konstanthalten aller übrigen untersucht werden konnte, was in Experimenten mit realen Flüssigkeiten nicht möglich ist. Das Blasenablösevolumen steigt (grob gesprochen) mit zunehmender Grenzflächenspannung sowie abnehmender Dichte und ist unabhängig von der dynamischen Viskosität, solange diese unter etwa 100 mPas bleibt. Bei kleinen Laplace-Kostanten ist es unabhängig von der Laplace-Konstanten, erst bei höheren Werten dieser Konstante hängt das Ablösevolumen deutlich von ihr ab. Die Tendenz zur Annäherung an ein Grenzgesetz ist deutlich. Der Düsenquerschnitt hat bei kleinen Gasdurchsätzen großen Einfluß auf das Ablösevolumen, sein Einfluß sinkt mit zunehmendem Gasdurchsatz, bei hohem Gasangebot wächst das Ablösevolumen deutlich mit dem Gasdurchsatz, auch hier ist die Annäherung an ein Grenzgesetz unverkennbar. Kleine Ablösevolumina bedeuten durch die damit verbundene feine Dispergierung des Gases eine große Grenzflächenentfaltung. Maßnahmen zur Erzielung kleiner Ablösevolumina werden angegeben.     

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.      

Application of several non-linear prediction tools for estimating uniaxial compressive strength of granitic rocks and comparison of their performances

Uniaxial compressive strength (UCS) of rock is crucial for any type of projects constructed in/on rock mass. The test that is conducted to measure the UCS of rock is expensive, time consuming and having sample restriction. For this reason, the UCS of rock may be estimated using simple rock tests such as point load index (I _s(50)), Schmidt hammer (R _n) and p-wave velocity (V _p) tests. To estimate the UCS of granitic rock as a function of relevant rock properties like R _n, p-wave and I _s(50), the rock cores were collected from the face of the Pahang–Selangor fresh water tunnel in Malaysia. Afterwards, 124 samples are prepared and tested in accordance with relevant standards and the dataset is obtained. Further an established dataset is used for estimating the UCS of rock via three-nonlinear prediction tools, namely non-linear multiple regression (NLMR), artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS). After conducting the mentioned models, considering several performance indices including coefficient of determination (R ²), variance account for and root mean squared error and also using simple ranking procedure, the models were examined and the best prediction model was selected. It is concluded that the R ² equal to 0.951 for testing dataset suggests the superiority of the ANFIS model, while these values are 0.651 and 0.886 for NLMR and ANN techniques, respectively. The results pointed out that the ANFIS model can be used for predicting UCS of rocks with higher capacity in comparison with others. However, the developed model may be useful at a preliminary stage of design; it should be used with caution and only for the specified rock types.     

Computer simulation on the hydrodynamics of gas injection process in liquid steel

It is shown that with the aid of digital simulation methods complex multiphase interrelated systems, such as gas-injection process can be analysed. Interdependencies can be revealed and quantitative evaluation of characteristic system quantities are provided. The method of digital system simulation is a very convenient tool for process analysis or system engineering. Results of the computer-aided process simulations (Caps) yield a better understanding of complex phenomena and better aimed engineering of gas dispersion techniques in metallurgical processes. A particular interest of this investigation is to reveal the effect of mass-transfer rate on the hydrodynamic behaviour of a gas-injection process. The combined effects of total flow rate of injected gas and mass-transfer rate on the system quantities such as mixing power, induced liquid flow rate, holdup, interfacial area and volumetric mass transfer coefficient are evaluated under steady state conditions of the investigated systems and illustrated in simulation plots. The liquid velocity has a minor effect on bubble size at some distance from the orifice but controls the location of bubble breakup. The frequency of bubble breakup and final bubble size depends on the intensity of mass transfer. Mixing power due to gas bubbles and circulation velocity of the steel bath increase appreaciably if there is a chance of bath reactions producing more gas. The integral mean values of mixing power, induced velocity of liquid and holdup in plume, specific interfacial area and volumetric mass-transfer coefficient increase with increasing total flow rate of injected gas and intensity of mass transfer.     

Digitale Simulation des Stofftransports in hintereinander aufsteigenden Gasblasen unter Berücksichtigung ihrer Entstehungsphase

Ein früher entwickeltes digitales Simulationsmodell für Entstehung, Ablösung und Aufsteigen einzelner Blasen an Düsen in flüssigen Metallen wird um den Stoffaustausch erweitert und ausgewertet. Die Modellrechnungen zeigen die Notwendigkeit der Berücksichtigung der Blasenentstehungsphase bei quantitativen Berechnungen der Gasbehandlungen; beispielsweise erhöhen alle Maßnahmen wie kleine Badhöhen, kleine Gasdurchsätze, kleine Düsen, die die Verweilzeit der Blasen an der Düse im Vergleich zu ihrer Aufstiegszeit verlängern, den Anteil des Stoffaustauschs während der Blasenbildung im Vergleich zum Blasenaufstieg. Die Modellrechnungen simulieren erstaunlich gut auch den Stoffaustausch in flüssigen Metallen, soweit die bekannten, spärlichen experimentellen Daten einen Vergleich erlauben.     

Brief note on the influence of shape and percentage of gravel on the shear strength of sand and gravel mixtures

The paper records the influence of the shape and the percentage of gravel on the shear strength/frictional angle of sand and gravel mixtures using direct shear tests. The shear strength is mainly derived from the frictional forces developed due to sliding and interlock; they depend on the maximum particle size and shape, the uniformity coefficient, density and the effective normal stress. As the size of material in a mixture is variable, the shear strength also depends upon the ratio of the specimen diameter to the maximum particle size. In this study, two different shapes of limestone were used, angular and rounded, and the maximum gravel size was 6.3 mm in diameter. Air-dried samples were used in the tests. It is concluded that the shape and percentage of gravel have an important influence on the shear strength properties. Electronic Publication