Cone Factor Research Articles

SU‐FF‐T‐94: Analytical Calculations of Dosimetry Data for a 6‐MV Narrow Radiosurgery Beam with Cones

Purpose: To analytically derive narrow beam dosimetry data for a 6 MV radiosurgery beam with cones from broad beam measurements. Method and Materials: currently radiosurgery dosimetry calculation is commonly done using a radiosugery treatment planning system. Such a planning system is typically commissioned using output factors, TMR, and off‐axis ratio measured in water for narrow beams. The experimental measurements in water for small radiosurgery beams are difficult and with large uncertainty due to lack of lateral electronic equilibrium and finite detector size. In this work, an analytical model was used to calculate the cone factors, TMR, and off‐axis ratio (OAR) for various cone sizes for a 6 MV radiosurgery unit. The model is parameterized with the measured broad beam cax beam data where lateral dose equilibrium exists and accurate measurement can be performed without much of difficulties. The calculated results were benchmarked with the experimental measurements. The cone size ranged from 4 mm to 20 mm in diameter in this study. Results: Compared the calculated dosimetry data with those from measurements, the agreement for cone factor was within 1 %, and within 4 %for TMR beyond dmax. The agreements for OAR are within typical experiment uncertainties. Conclusion: The analytical method described here can be used to calculate narrow cone beam dosimetry data in place of the arduous in‐water narrow beam measurements. Alternatively, it can be used to validate narrow beam dosimetry measurements if the direct measurements are prefered.

SU-FF-T-396: Analytical Derivation of 6 MV Radiosurgery Cone Factors

Purpose: To derive cone factors analytically for 6 MV radiosurgery beams Method and Materials: Lack of lateral electronic equilibrium and finite detector size make experimental measurements of stereotactic radiosurgery cone factors a difficult task. In this work, cone factors for 6 MV radiosurgery beams of various cross sections are determined using an analytical model for absorbed dose in narrow photon beams and validated by means of experimental measurements in water. The model allows one to calculate absorbed dose under electronic disequilibrium conditions using measured broad‐beam data. For each cone ranging from 4 mm to 20 mm in diameter, cone factor is derived analytically and compared to that measured in water experimentally using a high resolution diode and a computerized data acquisition system. Results: The agreement between the analytical and measured cone factors is within 2.5 % of local value. Conclusion: Based on the results of this study for 6 MV x‐rays, the analytical method described here can be employed to determine radiosurgery cone factors. It provides a viable alternative to experimental methods where measurements in water are arduous. It can be used as an independent method or to validate experimental results.

SU‐FF‐T‐188: Correlation Between in Vivo Electron Diodes Response and Nominal Surface Dose for Broad Electron Beams

Purpose: To establish correlation between in vivo diodes response and nominal surface dose Ds for broad electron beams, thus simplifying the calibration process for electron diodes. Method and Materials: The nominal surface dose Ds defined by TG25 was extracted from electron PDD data that were measured by cylindrical ion chamber (RK chamber, Scanditronix‐Wellhofer) on a Varian 2100C Linac at 100 cm SSD. Cone factors were measured using ion chamber (Capintec PR‐06) at dmax. A QED p‐type electron diode with Model 1131 dosimeter (Sun Nuclear Corp.) was calibrated to the dose at dmax for 9 MeV electron beam at 100 cm SSD using 10×10 cone. Diode readings using this calibration factor were then obtained with 10×10 cone and 15×15 cone for 6, 9, 12, 16 and 20 MeV electron beams delivering 200 MUs. The same diode was then re‐calibrated to the dose at dmax for 12 MeV electron beam. The above measurements were repeated with 10×10 cone and 25×25 cone to reconfirm our hypothesis. Results: The diode readings were first divided by cone factors, and then the corrected readings were plotted against nominal skin dose. For diodes calibrated by 9 MeV electrons, the correlation coefficient R‐squared value were 0.9954 and 0.9796 for 10×10 cone and 15×15 cone respectively. For diodes calibrated by 12 MeV electrons, the R‐squared value were 0.9967 and 0.9980 for 10×10 cone and 25×25 cone respectively. Conclusion: The correlation between in vivo p‐type diode response and nominal surface dose Ds for broad electron beams has been empirically established and confirmed. The diode response corrected by cone factor demonstrated a clear correlation with nominal surface dose Ds. This correlation can significantly simplify the electron diode calibration process. It can also be potentially used to monitor relative skin dose along with dmax dose at the same time.

SU-FF-T-327: Comparison of Characteristics of Electron Beams Generated by Siemens and Varian Linear Accelerators

Purpose: To compare the electron beam data for Siemens and Varian accelerators. Method and Materials: Beam data for the electron beams for at least 4 linear accelerators are compared in seven categories: (1) percent depth dose for open beam and small circular cutouts, (3) phantom scatter factor, (4) head scatter factor as a function of cone size and SSD, (5) cone factors, (6) distance factor and (7) virtual source position. Results: PDD for broad beams is in good agreement among all accelerators. However, PDD for small circular cutouts of the two Siemens Oncor accelerators are different from the other accelerators with their mean energy shifted by 2 MeV. The phantom scatter factor, defined as the ratio of blocking factor in water at reference depth and head scatter factor in air, for the same cone size and radius, is a function of radius and nominal electron energy only, regardless of linac makers with a maximum and standard deviation of 10% (for the smallest cutout of 1cm) and 2.3%, respectively. The head scatter factor H is defined as the ratio of in-air energy fluence between circular cutout with radius r and open cone for the same cone size and source-to-detector distance. The renormalized H is a function of electron energy and cutout radius. The cone factor for all energies, among all accelerators agreed within 1.9% among the Varian accelerators and 1.7% within the Siemens accelerators. The distance factors varied up to 10% for the smallest energy (6e) and up to 3.4% for the 21e. The virtual position varied by 3.8cm and 6.5cm for the Siemens and Varian accelerators, respectively. Conclusion: Accelerators from the same manufacturer, with the same nominal energy, can be treated as “identical” for conventional treatment except for small circular cutouts and large SSDs, where variations of 10% are observed.

A numerical study of cone penetration in clay

This paper presents results from large-displacement finite-element analysis of cone penetration into clay. The soil is idealised as a homogeneous elastic-perfectly plastic material obeying a Tresca yield criterion, and the analysis is carried out using an ‘arbitrary Lagrangian–Eulerian’ technique, with periodic remeshing and interpolation of all field values. This allows the cone to be advanced by several diameters, thus achieving steady-state conditions. A full parametric study has been undertaken, quantifying the influences of the rigidity index, in situ stress anisotropy and the cone roughness. A theoretical correlation for the cone factor, Nkt, is developed from this study, and compared with previous correlations developed using the strain path method. Characteristics of the stress distribution around the cone, the extent of the plastic zone and apparent incremental movements are discussed, allowing new insights into this problem.

On the Electronic Cone Factor Nkt for Saturated Clays

On the Electronic Cone Factor <I>N<SUB>kt</SUB></I> for Saturated Clays

Development of a New Cone Penetrometer and its Application to Great Depths of Pleistocene Clays

A new piezocone was developed and applied to Osaka Pleistocene clay layers as deep as 250 m. Its geometry is the same as that of the reference procedure defined by the ISSMFE and standard of JGS: i.e., the projected cross sectional area is 10 cm2; the angle of the cone is 60°; the pore water pressure is measured at the shoulder. This piezocone does not measure the skin friction. Due to great depth at the investigated site, the capacity of the point resistance (qt) and the pore water pressure is as large as 30 MPa and 20 MPa, respectively. The test was carried out, using a borehole drilled prior to the penetration, because of stiff sand or gravel layers and large skin friction between the rod and the ground. The qt measured by the cone penetration test (CPT) was correlated to the yield consolidation pressure (py) measured by the Constant Rate of Strain (CRS) oedometer test for the soil sample recovered near the point of the CPT investigation. The cone factor for the py value (Npc) was defined by (qt -pvo)/py, where pvo is the in situ total overburden pressure. The range of observed Npc value is relatively narrow and between 2.5 and 2.8, which is in the middle of the range of Npc factors measured in Holocene clays in the various areas in the world as well as Japan. The overconsolidation ratio (OCR) was also derived by CPT. Variation of the OCR estimated by the CPT is nearly equivalent to that measured by the CRS oedometer. It may be concluded from this investigation that the consolidation properties, especially the py value, derived from samples recovered from great depths, are quite reliable as design parameters.

CPTu로부터 구한 시화지구 해성점토의 비배수 전단강도

Estimation of undrained shear strength <TEX>$(S_u)$</TEX> of clayey soils from piezocone penetration test (CPTu), which has widely been known as one of very promising in situ test methods, requires piezocone factors. Empirical correlations are generally utilized to derive piezocone factors, but previous studies on the empirical piezocone factors are site-specific and in some cases need engineering characteristics, which should be obtained from additional laboratory tests. In this study, empirical cone factors were evaluated by comparing 6 CPTu results at Shihwa region in Korea with reference <TEX>$S_u$</TEX> values obtained from field vane test (FVT). From previous CPTu results of other regions in Korea as well as the results herein, the correlations between piezocone factor, <TEX>$N_{kT}$</TEX> and CPTu results were investigated and three simplified evaluation methods of <TEX>$S_u$</TEX> using only CPTu results were presented. The <TEX>$S_u$</TEX> values estimated by <TEX>$(q_T-{\sigma}_v)/{\sigma}'_v$</TEX> method shows better matches with those obtained from laboratory tests for marine clays at Shihwa region.

Influence of Strength Anisotropy on Piezocone Resistance in Clay

Since different undrained shear strengths may be obtained from different laboratory or field tests, different cone factors are needed to calculate the undrained shear strengths from the results of a piezocone test in clay. Based on the anisotropic undrained shear strength criterion, a set of cone factors for calculating undrained shear strength is proposed in this paper. These cone factors are interrelated with each other in terms of the strength anisotropy ratio of the clay. The suitability of the proposed cone factors has been verified using the test results generated from different tests and from clays with different origins. By comparing with the cone factor for isotropic clay, it was found that the effect of strength anisotropy on the cone factor is not always significant. In fact, the effect of strength anisotropy becomes significant only in lightly overconsolidated to normally consolidated clay with moderate to high strength anisotropy. Furthermore, the maximum difference in cone factor is not expected to exceed 20% with or without taking into account the strength anisotropy of clay.

THE INVESTIGATION OF LOAD CARRYING CAPACITY OF ELASTIC-PLASTIC STRAIN HARDENING BISTEEL I-SECTION BEAMS

In the present study, CPT is modelled by static elastic-plastic small strain finite element method (FEM) analysis of axi-symmetric problem. Undrained soil properties and Tresca yield criterion is used for determining cone resistance of clay. Sand is modelled by using drained soil properties and Mohr-Coulomb yield criterion. Cone penetration problem is formulated as a collapse load problem. Associated and non-associated flow rules were used for modelling. A number of numerical experiments were performed to determine rational size of discrete region. Received dimensions of region were used for further research. Cone factor&nbsp;Nc&nbsp;for clay was obtained and the comparison of&nbsp;Nc&nbsp;values with other theoretical solutions is presented. A conclusion may be made that the limit of the validity of geometrically linear systems has been reached. The evaluation of the effect of cone penetration requires the analysis of large strains to be made. First Published Online: 30 Jul 2012

Cavity expansion and cone penetration resistance in anisotropic clay

Due to strength anisotropy, the undrained shear strength of naturally deposited clay can vary with its position in the coordinate. When subjected to a spherical expansion, the undrained shear strength of clay yields the lowest value in the horizontal direction and the largest value in the vertical direction. To represent the nature of clay, a model based on the anisotropic undrained strength criterion has been developed in this paper to determine the anisotropic undrained shear strength under a spherical expansion condition. To simplify the model, the effects of in‐situ initial stresses, anisotropy, and the anisotropy of soil deformability are not taken into account here. Combining the spherical cavity expansion theory and the anisotropic undrained shear strength under spherical expansion conditions, a simplified limit pressure of spherical cavity expansion in anisotropic clay has been established. The magnitude of limit pressure is related to its position in the spherical cavity. Based on the limit pressure in spherical cavity expansion derived from anisotropic strength, the cone factor of an advancing cone has been derived to correlate the cone resistance and undrained shear strength of clay. The calculated cone factors uniquely correspond to the undrained shear strengths determined from different tests and are interrelated to each other in terms of strength anisotropy ratio Ar of clay. The accuracy of the calculated cone factors has been satisfactorily verified with laboratory and field CPTU results. However, it has also been found that the effect of strength anisotropy only becomes obvious when clay has a low rigidity and high strength anisotropy. If the strength anisotropy of clay is not considered, a less than 15% error on the value of the cone factor will result.

Theory and practice of the fall cone test

The fall cone is considered as a more reliable method for determining the liquid limit than the Casagrande method, and is standardised in many countries as the preferred liquid limit test method. In this paper the theory and practice of the fall cone test are described. First the penetration mechanism of a fall cone into clay is analysed, introducing the concept of dynamic strength to the static results. Next the applicability of dynamic analysis to the fall cone test is examined with regard to Hansbo's cone factor, K, for various cone angles. The theoretical K value for the 60° cone with a semi-rough surface is found to agree better with experimental results than is the case for the 30° cone. It is proposed that the liquid limit be redefined internationally as the water content at which a 60°, 60g fall cone penetrates 10 mm. Finally the applicability of the fall cone test as a device to relate the strength of a clay with the index properties is examined.

Theory and practice of the fall cone test

The fall cone is considered as a more reliable method for determining the liquid limit than the Casagrande method, and is standardised in many countries as the preferred liquid limit test method. In this paper the theory and practice of the fall cone test are described. First the penetration mechanism of a fall cone into clay is analysed, introducing the concept of dynamic strength to the static results. Next the applicability of dynamic analysis to the fall cone test is examined with regard to Hansbo's cone factor, K, for various cone angles. The theoretical K value for the 60° cone with a semi-rough surface is found to agree better with experimental results than is the case for the 30° cone. It is proposed that the liquid limit be redefined internationally as the water content at which a 60°, 60g fall cone penetrates 10 mm. Finally the applicability of the fall cone test as a device to relate the strength of a clay with the index properties is examined.

Choice of Radiation Detector in Dosimetry of Stereotactic Radiosurgery-Radiotherapy

Dosimetry of the small radiation fields used in radiosurgery is often difficult because of finite detector size and loss of lateral electronic equilibrium. However, small-field dosimetry is critical in radiosurgery where a relatively high dose in a single fraction is often delivered. Radiosurgery dosimetry varies significantly in small fields depending upon the choice of detector. Small-volume (0.015 cm3–0.125 cm3) cylindrical ion chambers, parallel-plate ion chamber, films (Kodak and CEA), thermoluminescent dosimeter (TLD), diamond detector, and Monte Carlo simulation were used to study the small-field (≤ 4 cm) dosimetry of a radiosurgery unit, which consists of Radionics hardware with cone sizes of 12.5 mm to 40 mm with a 6-MV linear accelerator. Results indicate that, in general, ion chambers and TLDs are not suitable for beam profiles. The diamond detector provides better resolution when faced parallel, rather than the perpendicular, to the beam axis. The dose profiles measured with laser-film densitometer are found to be moderately sensitive to the aperture sizes (200 μm–470 μm). The profiles generated using film and diamond detectors are nearly identical. The cone factors measured using film, diamond detectors, and TLD varies (+ 5%) depending upon the uncertainty of the measurements; however, the measured cone factors differ significantly (≤ 10%) among various ion chambers. The Pinpoint (0.015 cm3) ion chamber provides reliable data, which differs from other detectors. Monte Carlo data are in between all other measured data. The large variation in SRS dosimetry suggests that there should be a national protocol to review the dosimetry in small fields.

GEOTAIL observation of electron cyclotron harmonic waves near the dayside magnetopause

We have been studying electron cyclotron harmonic (ECH) waves observed in the magnetosphere with the Plasma Wave Instrument (PWI) onboard the GEOTAIL spacecraft. The dynamic spectra show various types of ECH waves particularly near the dayside magnetopause. Superimposed on weak ECH waves, intense bursts with multiple harmonic bands are observed intermittently and sporadically in time, which is called “Totem Pole” emission (TP emission). The present paper focuses on the relation between the ECH waves and the corresponding electron velocity distribution functions obtained by the GEOTAIL LEP. The electron velocity distributions consist of multiple components including hot electrons at energy of a few keV and warm electrones of about hundred eV. To correct the total density estimated from the velocity distribution, we added a cold Maxwellian below 70 eV. As studied in linear theory, the GEOTAIL LEP observation also shows that the density ratio between the hot and cold electrons determines unstable harmonic modes. Linear dispersion analysis with the observed velocity distributions modified with the cold component indicates that ECH waves are marginally stable for each case. With increased loss cone factors of the hot electrons, however, multiple harmonic modes become unstable.

Continuous Intrusion Miniature Cone Penetration Test System for Transportation Applications

The electronic cone penetrometer is an important investigation tool of choice for in situ site characterization. Application of this proven concept of the cone penetration test (CPT) to transportation applications is described. A miniature cone penetrometer with a projected cone area of 2 cm2 has been developed and implemented in a continuous intrusion miniature CPT system (CIMCPT). This device may be used for rapid, accurate, and economical characterization of sites as well as to determine engineering soil parameters needed in the design of pavements, embankments, and earth structures. The miniature CPT (MCPT) gives finer details than the standard 10-cm2 cross-sectional area reference cone penetrometer, which makes it attractive for subgrade characterization, quality control assessment, compaction control of embankments, and assessment of ground improvement effectiveness for transportation infrastructure. In situ calibration of the CIMCPT system was conducted at a highway embankment site in Baton Rouge, Louisiana. MCPT penetration profiles were compared with those obtained with the standard cone penetrometer at the same site. The tip resistance of the MCPT was 10 percent higher than that of the reference CPT. The sleeve friction and friction ratio of the reference CPT were higher than that of the MCPT by 12 and 23 percent, respectively. Calibration was also performed to determine empirical cone factors required for estimating undrained shear strength from MCPT data.

Monte Carlo dosimetry study of a 6 MV stereotactic radiosurgery unit

Small-field and stereotactic radiosurgery (SRS) dosimetry with radiation detectors, used for clinical practice, have often been questioned due to the lack of lateral electron equilibrium and uncertainty in beam energy. A dosimetry study was performed for a dedicated 6 MV SRS unit, capable of generating circular radiation fields with diameters of 1.25-5 cm at isocentre using the BEAM/EGS4 Monte Carlo code. With this code the accelerator was modelled for radiation fields with a diameter as small as 0.5 cm. The radiation fields and dosimetric characteristics (photon spectra, depth doses, lateral dose profiles and cone factors) in a water phantom were evaluated. The cone factor for a specific cone c at depth d is defined as , where is the reference cone. To verify the Monte Carlo calculations, measurements were performed with detectors commonly used in SRS such as small-volume ion chambers, a diamond detector, TLDs and films. Results show that beam energies vary with cone diameter. For a 6 MV beam, the mean energies in water at the point of maximum dose for a 0.5 cm cone and a 5 cm cone are 2.05 MeV and 1.65 MeV respectively. The values of obtained by the simulations are in good agreement with the results of the measurements for most detectors. When the lateral resolution of the detectors is taken into account, the results agree within a few per cent for most fields and detectors. The calculations showed a variation of with depth in the water. Based on calculated electron spectra in water, the validity of the assumption that measured dose ratios are equal to measured detector readings was verified.

Calibration of a Miniature Cone Penetrometer for Highway Applications

The electronic cone penetrometer is an important in situ investigation tool of choice for site characterization. Application of this proven concept of the cone penetration test (CPT) to highway design and construction control by miniaturization is described. A miniature cone penetrometer with a projected cone area of 2 cm2 has been developed and implemented in a continuous intrusion miniature cone penetration test system (CIMCPT). This device may be used for rapid, accurate, and economical characterization of sites and to determine engineering soil parameters needed in the design of pavements, embankments, and earth structures. The miniature cone penetration test (MCPT) gives finer details than the standard 10-cm2 cross-sectional area reference cone penetrometer. This makes the MCPT attractive for subgrade characterization, quality-control assessment, compaction control of embankments, and assessment of ground improvement effectiveness for transportation infrastructure. In situ calibration of the CIMCPT system was conducted at a highway embankment site in Baton Rouge, Louisiana. MCPT penetration profiles were compared with those obtained by using the standard cone penetrometer at the same site. The tip resistance of the MCPT was 10 percent higher than that of the reference CPT. The sleeve friction and friction ratio of the reference CPT were higher than that of the MCPT by 12 and 23 percent, respectively. Calibration was also performed to determine empirical cone factors required for estimating undrained shear strength from MCPT data.

Characteristics of a dedicated linear accelerator-based stereotactic radiosurgery-radiotherapy unit

A stereotactic radiosurgery and radiotherapy (SRS/SRT) system on a dedicated Varian Clinac-600SR linear accelerator with Brown-Roberts-Wells and Gill-Thomas-Cosman relocatable frames along with the Radionics (RSA) planning system is evaluated. The Clinac-600SR has a single 6-MV beam with the same beam characteristics as that of the mother unit, the Clinac-600C. The primary collimator is a fixed cone projecting to a 10-cm diameter at isocenter. The secondary collimator is a heavily shielded cylindrical collimator attached to the face plate of the primary collimator. The tertiary collimation consists of the actual treatment cones. The cone sizes vary from 12.5 to 40.0 mm diameter. The mechanical stability of the entire system was verified. The variations in isocenter position with table, gantry, and collimator rotation were found to be <0.5 mm with a compounded accuracy of ⩽1.0 mm. The radiation leakage under the cones was <1% measured at a depth of 5 cm in a phantom. The beam profiles of all cones in the x and y directions were within ±0.5 mm and match with the physical size of the cone. The dosimetric data such as tissue maximum ratio, off-axis ratio, and cone factor were taken using film, diamond detector, and ion chambers. The mechanical and dosimetric characteristics including dose linearity of this unit are presented and found to be suitable for SRS/SRT. The difficulty in absolute dose measurement for small cone is discussed.

Calibration Chamber Studies of Piezocone Test in Cohesive Soils

Results of miniature piezocone penetration tests (PCPT) on cohesive soil specimens in a calibration chamber system are presented. The influence of soil type, stress history, penetration boundary conditions, and filter locations on PCPT data are investigated. An increase in the strength of the soil around the cone penetrometer is observed when penetration is resumed after a dissipation test. The penetration depth required to attain a steady excess pore pressure value at the tip of the cone is influenced by the overconsolidation ratio and the lateral stress coefficient. The empirical values of the cone factor and the pore pressure factor are found to be strongly influenced by the lateral stress and the plasticity index. The tip resistance measured during the miniature quasi‐static friction cone penetration tests (QCPT) are consistently lower than the values obtained from the PCPT. Interpretation of the dissipation results to evaluate the radial coefficient of consolidation should be based on the initial dissipation values of the excess pore pressure, and not the penetration pore pressure.