# Geometric factor for backfill

The geometric factor for the calculation of the external thermal resistance transforms the rectangular backfill area into an equivalent circle.

The following equation according to IEC 60287-2-1 Ed.2.0 is limited to ratios of $b_y/b_x$ of less than 3 and ratios of $L_b/r_b$ of more than 1.

When choosing 'El-Kady/Horrocks 1985' as calculation method, the extended values given in the list below are used.

Reference: M.A. El-Kady and D.J. Horrocks, Ontario Hydro, Toronto, Canada, 'Extended Values for Geometric Factor of External Thermal Resistance of Cables in Duct Banks', IEEE Transactions on Power Apparatus and Systems, Vol. PAS-104, No. 8, August 1985.

Symbol
$G_b$
Formulae
$\ln\left(u_b+\sqrt{{u_b}^2-1}\right)$
Related
$b_x$
$b_y$
$h_b$
$w_b$
Used in
$T_{4db}$
Choices
$\frac{h_b}{w_b}$ \ $\frac{L_b}{h_b}$0.61.02.03.04.05.06.07.08.09.010.011.012.013.014.015.016.017.018.020.0
0.050.080.320.390.590.770.931.081.211.341.451.561.671.771.871.962.052.142.232.312.47
0.10.10.360.650.941.181.391.571.721.872.02.132.252.372.472.572.662.762.852.943.12
0.21.140.451.01.371.681.932.122.242.392.532.662.792.93.013.123.213.313.413.513.69
0.30.180.561.261.682.022.292.482.62.752.893.023.153.273.383.493.593.693.83.894.08
0.40.220.681.431.862.192.452.662.82.953.093.223.353.473.583.693.793.883.954.024.12
0.50.250.811.511.922.212.462.672.832.993.133.253.383.53.613.713.813.914.014.114.29
0.60.290.91.622.042.342.592.812.983.153.293.423.553.683.83.914.024.134.244.354.56
0.70.320.971.712.142.442.72.923.13.273.433.573.723.863.994.124.244.374.494.624.86
0.80.351.041.812.262.582.873.123.343.553.743.924.114.294.474.644.815.05.195.395.79
0.90.391.111.92.392.743.073.373.643.914.164.44.654.95.155.395.635.896.146.416.94
1.00.421.172.02.522.933.313.674.014.354.685.015.345.686.016.356.687.017.347.678.33
1.20.471.242.062.582.983.353.74.034.364.685.025.345.675.986.36.616.937.257.578.21
1.40.521.312.122.643.033.43.754.084.414.735.055.375.696.06.316.626.927.257.578.2
1.60.561.372.182.73.13.473.824.154.484.815.145.465.786.096.46.717.037.347.668.29
1.80.61.432.242.763.173.553.914.244.584.925.265.595.926.246.566.877.197.527.858.5
2.00.641.482.312.833.253.644.014.364.725.075.435.786.126.456.787.117.457.798.138.82
2.20.671.522.392.93.353.774.174.554.945.325.716.096.476.847.217.587.968.338.719.46
2.40.71.562.462.983.443.894.324.745.165.586.06.426.837.247.658.058.468.879.2810.11
2.60.731.592.533.053.544.024.494.945.395.846.296.747.197.638.088.528.979.419.8610.75
2.80.761.622.63.133.654.154.655.135.626.16.587.067.558.038.518.999.479.9610.4411.41
3.00.791.642.663.23.744.284.815.335.856.376.887.47.928.438.959.479.9910.5111.0212.06
3.20.821.672.723.273.844.414.975.536.086.637.187.738.298.849.399.9510.511.0611.6112.72
3.40.841.72.773.353.954.555.145.736.326.97.488.078.669.259.8410.4311.0211.6112.213.38
3.60.861.722.813.424.054.685.315.946.567.17.798.419.049.6610.2910.9211.5412.1712.7914.04
3.80.881.752.853.494.164.825.485.146.87.458.18.769.4210.0810.7411.4112.0712.7313.3914.71
4.00.91.772.893.564.264.965.666.357.047.738.429.119.8110.511.211.912.613.2913.9915.38
4.50.941.832.963.744.535.316.16.887.668.449.2210.010.7911.5712.3513.1413.9314.7115.517.08
5.00.971.883.03.914.795.676.557.428.299.1710.0410.9111.7912.6613.5314.415.2816.1517.0318.79