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1.
We present measurements of the thermal conductance, G, and effective time constants, \(\tau \) , of three transition-edge sensors (TESs) populated in arrays operated from 80–87 mK with T \(_\mathrm{C}\)   \(\sim \)  120 mK. Our TES arrays include several variations of thermal architecture enabling determination of the architecture that demonstrates the minimum noise equivalent power, the lowest \(\tau \) , and the trade-offs among designs. The three TESs we report here have identical Mo/Cu bilayer thermistors and wiring structures, while the thermal architectures are: (1) a TES with straight support beams of 1 mm length, (2) a TES with meander support beams of total length 2 mm and with two phonon-filter blocks per beam, and (3) a TES with meander support beams of total length 2 mm and with six phonon-filter blocks per beam. Our wiring scheme aims to lower the thermistor normal state resistance R \(_{N}\) and increase the sharpness of the transition \(\alpha =\)  dlogR/dlogT at the transition temperature T \(_\mathrm{C}\) . We find an upper limit of \(\alpha \) given by ( \(25\pm 10\) ), and G values of 200 fW/K for (1), 15 fW/K for (2), and 10 fW/K for (3). The value of \(\alpha \) can be improved by slightly increasing the length of our thermistors.  相似文献   

2.
An ozone (O \(_{3})\) oxidation process was introduced for Nb/Al-based superconducting tunnel junctions (STJs) in order to form defect-free tunnel barriers at high critical current and to improve the energy resolution ( \(\Delta E\) ) for X-rays. The dependence of critical current ( \(J_\mathrm{C})\) and leak current ( \(I_\mathrm{leak})\) on the O \(_{3}\) exposure was measured to optimize the oxidation condition. The 50-square- \(\upmu \) m STJs produced by the O \(_{3}\) oxidation process exhibited an extremely small \(I_\mathrm{leak}\) of less than 50 pA. As expected, the lower or shorter the O \(_{3}\) exposure, the higher \(J_\mathrm{C}\) and the smaller the normal resistance ( \(R_\mathrm{N})\) . However, the maximum \(J_\mathrm{C}\) was 8 A/cm \(^{2}\) at an O \(_{3}\) exposure of 0.72 Pa min, which is much smaller than those of STJs with the conventional O \(_{2}\) oxidation process. It is expected that the high \(J_\mathrm{C}\) of 1,000 A/cm \(^{2}\) , at which a 9-eV-energy resolution for 277 eV photons is predicted, can be reached by an O \(_{3}\) exposure of 3.5 \(\times \) 10 \(^{-4}\) Pa min.  相似文献   

3.
The data available for the thermodynamic properties of propane, \(n\) -butane, and isobutane at temperatures above 440 K are outdated and show significant discrepancies with each other. The ambiguity associated with these data could be limiting to the development of any understanding related to the effects of mixing of these substances with other materials such as \(\text{ CO}_{2}\) , ammonia, and non-flammable or lower-flammable HFC refrigerants. In this study, the (p, \(\rho \) , T) properties of propane, \(n\) -butane, and isobutane were measured at temperatures ranging from (360 to 600) K and pressures ranging from (50 to 200) MPa. Precise measurements were carried out using a metal-bellows variable volumometer with a thermostatted air bath. The expanded uncertainties \((k = 2)\) in the temperature, pressure, and density measurements were estimated to be \(<\) 5 mK, 0.02 MPa, and 0.88 kg  \(\cdot \)  m \(^{-3}\) ( \(T\le 423\)  K, \(p<100\)  MPa), 0.76 kg  \(\cdot \)   \(\text{ m}^{-3}\) ( \(T\le 423\)  K, \(p\ge 100\)  MPa), 0.76 kg  \(\cdot \)   \(\text{ m}^{-3}\) ( \(T>423\)  K, \(p < 100\)  MPa), and 2.94 kg  \(\cdot \)   \(\text{ m}^{-3}\) ( \(T>423\)  K, \(p \ge 100\)  MPa), respectively. The data obtained throughout this study were systematically compared with the calculated values derived from the available equations of state. These models agree well with the measured data at higher temperatures up to 600 K, demonstrating their suitability for an effective and precise examination of the mixing effects of potential alternative mixtures.  相似文献   

4.
The densities of solid and liquid Cu \(_{48}\) Zr \(_{52}\) and the viscosity of the liquid were measured in a containerless electrostatic levitation system using optical techniques. The measured density of the liquid at the liquidus temperature (1223 K) is (7.02 \(\pm \) 0.01) g \(\cdot \) cm \(^{-3}\) and the density of the solid extrapolated to that temperature is (7.15 \(\pm \) 0.01) g \(\cdot \) cm \(^{-3}\) . The thermal expansion coefficients measured at 1223 K are (6.4 \(\pm \) 0.1) \(\,\times \,10^{-5}\) K \(^{-1}\) in the liquid phase and (3.5 \(\pm \) 0.3) \(\,\times \,10^{-5}\) K \(^{-1}\) in the solid phase. The viscosity of the liquid, measured with the oscillating drop technique, is of the form \(A\exp \left[ \left( {{E}_{0}}+{{E}_{1}}\left( 1/T-1/{{T}_{0}} \right) \right) \times \left( 1/T-1/{{T}_{0}} \right) \right] \) , where \({{T}_{0}}=1223\) K, \(A= (0.0254 \pm 0.0004)\) Pa \(\cdot \) s, \({{E}_{0}}\) =  (8.43 \(\pm \) 0.26) \(\,\times \,10^3\) K and \({{E}_{1}}\) =  (1.7 \(\pm \) 0.2) \(\,\times 10^7\) K \(^{2}\) .  相似文献   

5.
We present thermogravimetric and differential scanning calorimetric studies of PtO \(_2\) powders measured in different atmospheres. In synthetic air a mass loss of 11.4 % is found at the decomposition temperature \(T_\mathrm {D}\)  = 595  \(^{\circ }\hbox {C}\) which can be attributed to the reduction of PtO \(_2\) . In a helium atmosphere the mass loss is 12.0 % and is found at 490  \(^{\circ }\hbox {C}\) . Subsequent heating in air leads to another oxidation process above \(T_\mathrm {D}\) and a reduction at 800  \(^{\circ }\hbox {C}\) . The second oxidation and reduction process is strongly suppressed when the powder is heated in He. The remaining mass above \(T_\mathrm {D}\) does not comply with a reduction path PtO \(_2 \rightarrow \) PtO \(\rightarrow \) Pt. Differential scanning calorimetry shows an endothermic reaction at \(T_\mathrm {D}\) in synthetic air as well as in helium which corresponds with the mass loss. These measurements imply that the powder can be assigned to be \(\beta \) -PtO \(_2\) . Furthermore, catalytic activity of the PtO \(_2\) powder is evidenced by mass spectrometry to be present below 460  \(^{\circ }\hbox {C}\) . Finally, the impact of these findings on the stability of platinum resistance thermometers is discussed.  相似文献   

6.
Let \(q\) be a power of a prime number \(p\) . Let \(n\) be a positive integer. Let \(\mathbb {F}_{q^n}\) denote a finite field with \(q^n\) elements. In this paper, we consider the existence of the some specific elements in the finite field \(\mathbb {F}_{q^n}\) . We get that when \(n\ge 29\) , there are elements \(\xi \in \mathbb {F}_{q^n}\) such that \(\xi +\xi ^{-1}\) is a primitive element of \(\mathbb {F}_{q^n}\) , and \(\mathrm{Tr}(\xi ) = a, \mathrm{Tr}(\xi ^{-1}) = b\) for any pair of prescribed \(a, b \in \mathbb {F}_q^*\) .  相似文献   

7.
At the National Metrology Institute of Japan (NMIJ), the triple points of \(^{20}\) Ne and \(^{22}\) Ne were realized using modular sealed cells, manufactured by the Istituto Nazionale di Ricerca Metrologica (INRiM) in Italy to measure the difference of the triple-point temperatures of \(^{20}\) Ne and \(^{22}\) Ne. Standard platinum resistance thermometers (SPRTs) were used that were calibrated by NMIJ on the International Temperature Scale of 1990 (ITS-90). In previous reports, sealed cells of \(^{20}\) Ne and \(^{22}\) Ne were mounted one at a time in a cryostat and their triple points were realized in separate cool-downs (the single-cell measurement). In this study, first, the triple point was realized using the single-cell measurement for \(^{20}\) Ne and \(^{22}\) Ne cells. Second, the \(^{20}\) Ne and \(^{22}\) Ne cells were mounted together on the same copper block and their triple points were realized subsequently one after the other in the same cool-down of the cryostat (the double-cell measurement). The melting curves observed by the single-cell and the double-cell measurements were almost identical for each cell. The difference of the triple-point temperatures between the two cells, \(^{22}T -^{20}\!T\) , was estimated, not only using the subrange of SPRTs defined in the ITS-90 from 13.8033 K to 273.16 K (subrange 1) but also that defined from 24.5561 K to 273.16 K (subrange 2). The difference in \((^{22}T-^{20}\!\!T)\) between the subranges 1 and 2 is within 0.06 mK, which is caused by the subrange inconsistency in the ITS-90. The standard uncertainty in \((^{22}T-^{20}\!T)\) due to the subrange inconsistency is estimated to be 0.017 mK. After correction for the effects of impurities and other isotopes in the \(^{20}\) Ne and \(^{22}\) Ne cells, the difference in the triple-point temperatures between pure \(^{20}\) Ne and pure \(^{22}\) Ne is estimated to be 0.146 64 (5) K on subrange 1, which is consistent within the uncertainty with the former studies. When \(^{22}T-^{20}\!T\) for pure \(^{20}\) Ne and pure \(^{22}\) Ne is estimated on subrange 2, \(^{22}T-^{20}\!\!T\) becomes 0.146 60 (5), which agrees very well with the former reports of INRiM evaluating \(^{22}T-^{20}\!T\) on subrange 2.  相似文献   

8.
The determination of the neutrino mass is still an open issue in particle physics. The calorimetric measurement of the energy released in a nuclear beta decay allows to measure all the released energy, except the fraction carried away by the neutrino: a finite neutrino mass m \(_\upnu \) causes the energy spectrum to be truncated at Q  \(-\)  m \(_\upnu \) , where Q is the transition energy. The electron capture of \(^{163}\) Ho (Q \(\sim \) 2.5 keV) results to be an ideal decay. In order to achieve enough statistics, a large number of detectors ( \(\sim \) 10 \(^4\) ) is required. Superconducting microwave microresonators are detectors suitable for large-scale multiplexed frequency domain readout, with theoretical energy and time resolution of \(\sim \) eV and \(\sim \!\upmu \) s. Our aim is to develop arrays of microresonator detectors applicable to the calorimetric measurement of the energy spectra of \(^{163}\) Ho. Currently, a study aimed to the selection of the best design and material for the detectors is in progress. In this contribution, a comparison between the measurements (critical temperature, gap parameter, quasiparticle recombination time and X-ray energy spectra) made with stoichiometric, sub-stoichiometric TiN and Ti/TiN multilayer films are presented.  相似文献   

9.
Qualitative and quantitative analysis of molecular interaction prevailing in glycine, l-alanine, l-valine, and aqueous solution of ionic liquid (IL) [1-ethylpyridinium tetrafluoroborate ( \(\mathrm{EPyBF}_{4})\) ] have been investigated by thermophysical properties. The apparent molar volume ( \(\phi _{V}\) ), viscosity \(B\) -coefficient, molal refraction ( \(R_{\mathrm{M}}\) ), and adiabatic compressibility ( \(\phi _{ K} )\) of glycine, l-alanine, and l-valine have been studied in 0.001 mol \({\cdot }\, \mathrm{dm}^{-3}\) , 0.003 mol \({\cdot }\, \mathrm{dm}^{-3}\) , and 0.005 mol  \({\cdot } \,\mathrm{dm}^{-3}\) aqueous 1-ethylpyridinium tetrafluoroborate [ \(\mathrm{EPyBF}_{4}\) ] solutions at 298.15 K from the values of densities \((\rho )\) , viscosities ( \(\eta \) ), refractive index ( \(n_{\mathrm{D}})\) , and speed of sound \((u)\) , respectively. The extent of interaction, i.e., the solute–solvent interaction is expressed in terms of the limiting apparent molar volume ( \(\phi _{V}^0 )\) , viscosity \(B\) -coefficient, and limiting apparent molar adiabatic compressibility ( \(\phi _{K}^0)\) . The limiting apparent molar volumes ( \(\phi _{V}^0 )\) , experimental slopes ( \(S_{V}^*)\) derived from the Masson equation, and viscosity \(A\) - and \(B\) -coefficients using the Jones–Dole equation have been interpreted in terms of ion–ion and ion–solvent interactions, respectively. Molal refractions ( \(R_{\mathrm{M}})\) have been calculated with the help of the Lorentz–Lorenz equation. The role of the solvent (aqueous IL solution) and the contribution of solute–solute and solute–solvent interactions to the solution complexes have also been analyzed through the derived properties.  相似文献   

10.
The microcalorimeter array for a rhenium experiment (MARE) project aims at the direct and calorimetric measurement of the electron neutrino mass with sub-eV sensitivity. The design is based on large arrays of thermal detectors to study the beta decay of \(^{187}\) Re and the electron capture of \(^{163}\) Ho. One of the activities of the project, MARE 1 in Milan, has started in Milan using one array of 6  \(\times \)  6 silicon implanted thermistors equipped with AgReO \(_4\) absorbers. The purposes of MARE 1 in Milan are to achieve a sensitivity on the neutrino mass of a few eV and to investigate the systematics of \(^{187}\) Re neutrino mass measurements, focusing on those caused by the beta environmental fine structure and the beta spectrum theoretical shape. In parallel, the MARE collaboration is performing an R&D work for producing absorbers embedded with radioactive metal \(^{163}\) Ho. We report here the status of MARE using Re as beta source and the preliminary results obtained with \(^{163}\) Ho.  相似文献   

11.
A thickness shear quartz resonator technique is described to measure the shear viscosity of low-viscosity liquids in the frequency range from 6 MHz to 130 MHz. Examples of shear-viscosity spectra in that frequency range are presented to show that various molecular processes are accompanied by shear-viscosity relaxation. Among these processes are conformational variations of alkyl chains, with relaxation times \(\tau _{\eta }\) of about 0.3 ns for \(n\) -pentadecane and \(n\) -hexadecane at 25  \(^{\circ }\) C. These variations can be well represented in terms of a torsional oscillator model. Also featured briefly are shear-viscosity relaxations associated with fluctuations of hydrogen-bonded clusters in alcohols, for which \(\tau _{\eta }\) values between 0.3 ns ( \(n\) -hexanol) and 1.5 ns ( \(n\) -dodecanol) have been found at 25  \(^{\circ }\) C. In addition, the special suitability of high-frequency shear-viscosity spectroscopy to the study of critically demixing mixtures is demonstrated by some illustrative examples. Due to slowing, critical fluctuations do not contribute to the shear viscosity at sufficiently high frequencies of measurements so that the non-critical background viscosity \(\eta _\mathrm{bg}\) of critical systems can be directly determined from high-frequency shear-viscosity spectroscopy. Relaxations in \(\eta _\mathrm{bg}\) appear also in the shear-viscosity spectra with, for example, \(\tau _{\eta }\,\approx \) 2 ns for the critical triethylamine–water binary mixture at temperatures between 10  \(^{\circ }\) C and 18  \(^{\circ }\) C. Such relaxations noticeably influence the relaxation rate of order parameter fluctuations. They may be also the reason for the need of a special mesoscopic viscosity when mutual diffusion coefficients of critical polymer solutions are discussed in terms of mode-coupling theory.  相似文献   

12.
The (p, \(\rho \) , T, x) properties of binary mixtures of CO \(_{2}\) (volume fraction purity 0.99999) and propane (mole fraction purity 0.9999) ( \(x_{1}\) CO \(_{2}+x_{2}\) propane; \(x_{1} = 0.1744\) , 0.3863, 0.5837, and 0.7732) were measured in the compressed liquid phase using a metal-bellows variable volumometer. Measurements were conducted from 280 K to 440 K and 3 MPa to 200 MPa. The expanded uncertainties ( \(k = 2\) ) were estimated to be temperature, \(<\) 3 mK; pressure, 1.5 kPa ( \(p\le 7\)  MPa), 0.06 % (7 MPa \(< p\le 50\)  MPa), 0.1 % (50 MPa \(< p\le 150\)  MPa), 0.2 % ( \(p> 150\)  MPa); density, 0.10 %; and composition, \(4.4\times 10^{-4}\) . At \(p >100\)  MPa and 280 K or 440 K, the uncertainties in density measurements increase to 0.14 % and 0.22 %, respectively. The data were compared with available equations of state. The excess molar volumes, \(v_\mathrm{m}^\mathrm{E}\) , of the mixtures were calculated and plotted as a function of temperature and pressure.  相似文献   

13.
It can be noted that the germanate glass–ceramic is a functional material with excellent thermal stability which can be used in optical devices. The temperature-dependent effective thermal conductivities of CaO–BaO–CoO–Al \(_{2}\) O \(_{3}\) –SiO \(_{2}\) –GeO \(_{2}\) glass–ceramics from 295.5 K to 780 K are determined using a \(3\omega \) method. One of the main advantages for the \(3\omega \) method is to diminish radiation errors effectively when the temperature is as high as 1000 K. Thermal conductivities of CaO–BaO–CoO–Al \(_{2}\) O \(_{3}\) –SiO \(_{2}\) –GeO \(_{2}\) increase with a rise in temperature. Effective thermal conductivities of a sample increase from \(1.55~\hbox {W}\cdot \hbox {m}^{-1}\cdot \hbox {K}^{-1}\) at 295.5 K to \(7.64~\hbox {W}\cdot \,\hbox {m}^{-1}\cdot \hbox {K}^{-1}\) at 698.1 K. The effective thermal conductivity of CaO–BaO–CoO–Al \(_{2}\) O \(_{3}\) –SiO \(_{2}\) –GeO \(_{2}\) glass–ceramic increases with a rise of temperature. This investigation can be used as a basis for the measurement of thermal properties of ceramic materials at higher temperature.  相似文献   

14.
Temperature coefficients of the refractive index ( \(\mathrm{d}n/\mathrm{d}T\) ) in the \(25\,^{\circ }\mathrm{C}\) to \(35\,^{\circ }\mathrm{C}\) temperature interval for hydrocarbon mixtures containing as many as 14 compounds were investigated in this work. The measured \(-\mathrm{d}n/\mathrm{d}T\) of the mixtures were compared with calculations based on the values for each compound and their concentrations. Differences of about 1 % between measured and calculated values were observed for all mixtures. The additivity of \(-\mathrm{d}n/\mathrm{d}T\) for these hydrocarbons enables preparation of surrogate fuels that are formulated to have properties like those of specific diesel fuels.  相似文献   

15.
We recently proposed the idea of a novel sort of superconducting detector, i.e., a current-biased kinetic inductance detector (CB-KID). This detector is different from a current-biased transition edge detector studied previously, and is able to sense a change in kinetic inductance \(L_k\) given by \(L_{k} = \Lambda _{k}l/S = m_{s}l/n_{s}{q_{s}}^{2}S\) ( \(\Lambda _{k}\) ; kinetic inductivity, \(m_s\) ; mass of Cooper pair, \(n_s\) ; density of Cooper pairs, \(q_s\) ; charge of Cooper pair, \(l\) ; length of device, \(S\) ; cross sectional area) under a constant dc bias current \(I_b\) . In the present work, we first extend this idea to construct a multi-channel CB-KIDs array made of 200-nm-thick MgB \(_2\) thin-film meanderline with 3- \(\upmu \) m thin wire. We succeeded in observing clear signals for imaging from the four-channel CB-KIDs at 4 K by irradiating focused pulsed laser. A scanning laser spot can be achieved by an XYZ piezo-driven stage and an optical fiber with an aspheric focused lens. We can see typical signals from all 4 channels at 4 K, and obtain the positional dependence of the signal as the contour in XY plane. Our CB-KIDs can be used as neutron detectors by utilizing energy released from a nuclear reaction between \(^{10}\) B and cold neutron.  相似文献   

16.
ATHENA+ is a space mission proposal for the next ESA L2-L3 slot. One of the focal plane instruments is the X-ray integral field unit (X-IFU) working in the energy range 0.3–10 keV. It is a multi-array based on TES detectors aimed at characterizing faint or diffuse sources (e.g. WHIM or galaxy outskirt). The X-IFU will be able to achieve the required sensitivity if a low background is guaranteed. The studies performed by GEANT4 simulations depict a scenario where the use of an active anticoincidence (AC) is mandatory to reduce the background expected in L2 orbit down to the goal level of 0.005 cts cm \(^{-2}\)  s \(^{-1}\)  keV \(^{-1}\) . This is possible using a cryogenic anticoincidence (CryoAC) detector placed within a proper optimized environment surrounding the X-IFU. We propose a 2  \(\times \)  2 array of microcalorimeter detectors made by silicon absorber (each of about 1 cm \(^{2}\) and 300 \(\upmu \) m thick) and sensed by an Ir TES. In order to better understand the involved physics and optimize the performance, we have produced several samples featured by different absorber areas, TES size, and QPs Al collectors. Here we will discuss, as a review, the obtained results and the related impact to the final detector design.  相似文献   

17.
The thermal expansion behavior and electrical resistivity of BaTiO \(_{3}\) ceramics with different grain sizes were investigated. When they were heated and subsequently cooled in the range from 25  \(^{\circ }\) C to 200  \(^{\circ }\) C, the expansion and contraction curves of BaTiO \(_{3}\) ceramics with grain sizes of 600 nm and 1500 nm were not matched well to each other, and abnormal contraction and expansion behaviors were observed. For 30 nm and 150 nm BaTiO \(_{3}\) ceramics, the expansion and contraction curves basically are straight lines during heating. The linear thermal expansion coefficients ( \(\alpha _\mathrm{L}\) ) and the electrical resistivity of BaTiO \(_{3}\) ceramics were also measured. Experimental results showed that the value of \(\alpha _\mathrm{L}\) increases and the electrical resistivity decreases gradually with reducing grain size. This phenomenon can be attributed to the combination effect of the grain boundary and oxygen vacancies.  相似文献   

18.
Ultra-highly-sensitive far-infrared detectors are developed for potential application to astronomy. The detectors exploit a novel mechanism called Charge Sensitive Infrared Phototransistors (CSIPs), in which an upper quantum well (QW) in GaAs/AlGaAs double QW structures is positively charged up by photo-excitation via inter-subband transition. This causes the conductance of the lower QW channel to increase. The device is effectively a phototransistor, in which the upper QW serves as a photo-sensitive gate to the source-drain channel provided by the lower QW. Resultant extraordinary high photoconductive gain makes CSIPs so sensitive as to detect single photons. CSIPs are well established in the mid-infrared ( \(\lambda \) = 12–20  \(\upmu \) m), achieving noise equivalent power around 1.9 \(\times \) 10 \(^{-19}\) W/Hz \(^{1/2}\) with a quantum efficiency of 7 %. CSIPs have been demonstrated to work in longer wavelengths up to 45  \(\upmu \) m, but the sensitivity was not as high as in the shorter wavelengths, probably due to lower quantum efficiency. Reported here is a remarkable improvement in the performance of longer wavelength CSIPs (45  \(\upmu \) m), achieved primarily by optimizing the doping concentration in the upper QW. This work indicates that longer wavelength CSIPs are promising detectors for the astronomical application.  相似文献   

19.
The non-isothermal thermogravimetric method was used to study the thermal decomposition of \(\hbox {KClO}_{4}, \hbox {KNO}_{3}\) , and \(\hbox {NaNO}_{3}\) at heating rates of (5, 10, 15, and 20)  \(\hbox {K}\cdot \hbox {min}^{-1}\) . The activation energy of thermal decomposition reactions was computed by isoconversional methods of Ozawa–Flynn–Wall, Kissinger–Akahiro–Sunose, and Friedman equations. Also, the kinetic triplet of the thermal decomposition of salts was determined by the model-fitting method of the modified Coats–Redfern equation. The activation energies of \(\hbox {KClO}_{4}, \hbox {KNO}_{3}\) , and \(\hbox {NaNO}_{3}\) of (293 to 307, 160 to 209, and 192 to 245)  \(\hbox {kJ}\cdot \hbox {mol}^{-1}\) , respectively, are obtained by non–isothermal isoconversional methods. The modified Coats and Redfern method showed that the most probable mechanism functions \(g(\alpha )\) of \([-\hbox {ln}(1 - \alpha )]^{1/3}\) (model A3: Arami–Erofeev equation) and \((1 - \alpha )^{-1}- 1\) (model F2: second order) can be used to predict the decomposition mechanisms of \(\hbox {KClO}_{4}\) , \(\hbox {KNO}_{3}\) , and \(\hbox {NaNO}_{3}\) , respectively.  相似文献   

20.
This paper presents an investigation on mechanism of the inclined cone penetration test using the numerical discrete element method (DEM). A series of penetration tests with the penetrometer inclined at different angles (i.e., \(0^{\circ },\,15^{\circ },\,30^{\circ },\,45^{\circ }\) and \(60^{\circ }\) ) were numerically performed under \(\mu =0.0\) and \(\mu =0.5\) , where \(\mu \) is the frictional coefficient between the penetrometer and the soil. The deformation patterns, displacements of soil particles adjacent to the cone tip, velocity fields, rotations of the principal stresses and the averaged pure rotation rate were analyzed. Special focus was placed on the effect of friction. The DEM results showed that soils around the cone tip experienced complex displacement paths at different positions as the inclined penetration proceeded, and the friction only had significant effects on the soils adjacent to the penetrometer side and tip. Soils exhibited characteristic velocity fields corresponding to three different failure mechanisms and the right side was easier to be disturbed by friction. Friction started to play its role when the tip approached the observation points, while it had little influence on rotation rate. The normalized tip resistance \((q_{c}=f/\sigma _{v0})\) increased with friction as well as inclination angle. The relationship between \(q_{c}\) and relative depth \((y/R)\) can be described as \(q_{c}=a\times (y/R)^{-b}\) , with parameters \(a\) and \(b\) dependent on penetration direction. The normalized resistance perpendicular to the penetrometer axis \(q_{p}\) increases with the inclination angle, thus the inclination angle should be carefully selected to ensure the penetrometer not to deviate from its original direction or even be broken in real tests.  相似文献   

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