• Progress in Medical Physics
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• v.9 no.4
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• pp.195-200
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• 1998

Purpose: When an elongated x-ray field is used for treating a patient, the equivalent- field method is commonly used for the output calculation. This study is intended for investigating potential factors such as, beam quality, field elongation ratio, and depth of measurement, which might effect on the applicability of the equivalent square technique for output calculation. The derivation of a 'rule of thumb' for the application criteria of the equivalent-field method is also aimed. Materials and Methods: Three x-ray beams, 4-, 6- and 10-MV, were employed for this study. Width of the rectangular field was ranged from 5-40 cm and the elongation ratio (length/width) 1:0 to 10:0. An elongation effect was measured in a water phantom at three different depths, dmax, 5-cm, and 10-cm. For an elongated field and its equivalent square field, the output factor was measured and the difference in the output factor were examined between two fields. Results and Discussions: As the elongation ratio increases, a larger discrepancy in outputs is observed between the elongated rectangular field and its corresponding equivalent square field. Output was measured larger for an elongated field than for its corresponding equivalent square field and the maximal difference over 10 % was found. The difference was found larger for the smaller field with the same elongation ratio. The effect of the beam quality and the depth of measurement on the output difference was minimal. Conclusion: Based on the study, there is criteria for the application of the method for output calculation. For the combination of long axis and elongation ratio whose relationship satisfies Elongation ratio < (0.48) (Long axis) - 0.5, the equivalent-field method is valid for output calculation within 2 % for the field whose long axis < 25-cm. For other combinations, instead of using the equivalent-field method, direct output measurement is recommended. This criteria can be applied for 4-10 MV x-ray beams up to 10-cm depth.

• Tunnel and Underground Space
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• v.19 no.2
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• pp.158-166
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• 2009

As a basic study for investigating the development of the stress-induced crack in Hoek-Brown rock, a homogenization technique of elastic cracks is proposed. The onset of crack is monitored by Hoek-Brown empirical criterion, while the orientation of the crack is determined by the critical plane approach. The concept of volume averaging in stress and strain component was invoked to homogenize the representative rock volume which consists of intact rock and cracks. The formulation results in the constitutive relations for the homogenized equivalent anisotropic material. The homogenization model was implemented in the standard FEM code COSMOSM. The numerical uniaxial tests were performed under plane strain condition to check the validity of the propose numerical model. The effect of friction between the loading plate and the rock sample on the mode of deformation and fracturing was examined by assuming two different contact conditions. The numerical simulation revealed that the homogenized model is able to capture the salient features of deformation and fracturing which are observed commonly in the uniaxial compression test.