Application of Benford’s Law in Analyzing Geotechnical Data

Document Type: Research Papers

Authors

1 Department of Mining and Metallurgical Engineering, Urmia University of Technology. Band road, Urmia, West Azerbaijan, Iran.

2 School of Computer Science, Institute for Research in Fundamental Sciences (IPM).

Abstract

Benford’s law predicts the frequency of the first digit of numbers met in a wide range of naturally occurring phenomena. In data sets, following Benford’s law, numbers are started with a small leading digit more often than those with a large leading digit. This law can be used as a tool for detecting fraud and abnormally in the number sets and any fabricated number sets. This can be used as an effective tool for processing data sets from laboratory tests, site investigation tests data, geotechnical design (both financial and technical) in engineering and specially included in geotechnical engineering and, etc. In this paper, data sets from geotechnical data are gathered and analyzed. It is shown that most of them follow Benford’s law. Therefore, we can use this observation for similar applications to detect the validity of data. Also, this can be assumed as an evidence for natural numbers that follow Benford’s law.

Keywords


 

Al-Ajmi, A.M. and Zimmerman, R.W. (2005). "Relation between the Mogi and the Coulomb failure criteria", International Journal of Rock Mechanics and Mining Sciences, 42(3), 431-439.

Alipour, A., Jafari, A. and Hossaini, S.M.F. (2012). "Application of ANNs and MVLRA for estimation of specific charge in small tunnel", International Journal of Geomechanics, 12(2), 189-192.

Alipour, A., Mokharian, M. and Chehreghani, S. (2018). "An application of fuzzy sets to the blastability index (BI) used in rock engineering", Periodica Polytechnica Civil Engineering, 62(3): 580-589.

Alipour, A., Mokhtarian, M. and Abdollahei Sharif,  J. (2012). "Artificial neural network or empirical criteria? A comparative approach in evaluating maximum charge per delay in surface mining, Sungun copper mine", Journal of the Geological Society of India, 79(6), 652-658.

Alves, A.D., Yanasse, H.H. and Soma, N.Y. (2016). "An analysis of bibliometric indicators to JCR according to Benford’s law", Scientometrics, 107(3), 1489-1499.

Ariznavarreta-Fernández, F., González-Palacio, C., Menéndez-Díaz, A. and Ordoñez, C. (2016). "Measurement system with angular encoders for continuous monitoring of tunnel convergence". Tunnelling and Underground Space Technology, 56, 176-185.

Arshadi, L. and Jahangir, A.H. (2014). "Benford's law behavior of Internet traffic", Journal of Network and Computer Applications, 40, 194-205.

Barkhordari, K. and Entezari Zarch, H. (2015). "Prediction of permanent earthquake-induced deformation in earth dams and embankments using Artificial Neural Networks", Civil Engineering Infrastructures Journal, 48(2), 271-283.

Benford, F. (1938). "The law of anomalous numbers", Proceedings of the American Philosophical Society, 551-572.

Broch, E. and Franklin, J. (1972). “The point-load strength test”, International Journal of Rock Mechanics and Mining Sciences and Geomechanics, Abstracts, 9(6), 669-676, Pergamon.

Chakraborty, A., Raina, A., Ramulu, M., Choudhury, P., Haldar, A., Sahoo, P. and Bandopadhyay,  C. (2004). "Development of rational models for tunnel blast prediction based on a parametric study", Geotechnical and Geological Engineering, 22(4), 477-496.

Díaz, J., Gallart, J. and Ruiz, M. (2014). "On the ability of the Benford’s Law to detect earthquakes and discriminate seismic signals", Seismological Research Letters, 86(1), 192-201.

Doostmohammadi, R. (2016). "Investigation of swelling pressure of weak rocks in vicinity of support systems", Journal of Mining Science, 52(3), 473-480.

Fewster, R.M. (2009). "A simple explanation of Benford's Law", The American Statistician, 63(1), 26-32.

Geyer, A. and Martí, J. (2012). "Applying Benford's law to volcanology", Geology, 40(4), 327-330.

Gong, Q., Zhao, J. and Jiang, Y. (2007). "In situ TBM penetration tests and rock mass boreability analysis in hard rock tunnels", Tunnelling and Underground Space Technology, 22(3), 303-316.

Hales, D.N., Chakravorty, S.S. and Sridharan, V. (2009). "Testing Benford's Law for improving supply chain decision-making: A field experiment", International Journal of Production Economics, 122(2), 606-618.

Hill, T. P. (1995). “Base-invariance implies Benford’s law”, Proceedings of the American Mathematical Society, 123(3), 887-895.

Joannes-Boyau, R., Bodin, T., Scheffers, A., Sambridge, M. and May, S.M.  (2015). "Using Benford’s law to investigate Natural Hazard dataset homogeneity", Scientific Reports, 5, 12046.

Judge, G. and Schechter, L. (2009). "Detecting problems in survey data using Benford’s Law", Journal of Human Resources, 44(1), 1-24.

Knuth, D.E., Saitou, H., Nagao, T.,  Matui, S., Matui, T. and Yamauchi, H. (2004). The art of computer programming, Vol. 2, Seminumerical algorithms, (Japanese Edition), ASCII.

Kohestani, V.R., Vosoghi, M., Hassanlourad, M. and Fallahnia, M. (2017). "Bearing capacity of shallow foundations on cohesionless soils: A random forest based approach", Civil Engineering Infrastructures Journal, 50(1), 35-49.

Ley, E. (1996). "On the peculiar distribution of the US stock indexes' digits", The American Statistician, 50(4), 311-313.

Mogi, K. (1971). "Fracture and flow of rocks under high triaxial compression", Journal of Geophysical Research, 76(5), 1255-1269.

Moosavi, M., Yazdanpanah, M. and Doostmohammadi, R. (2006). "Modeling the cyclic swelling pressure of mudrock using artificial neural networks", Engineering Geology, 87(3), 178-194.

Newcomb, S. (1881). "Note on the frequency of use of the different digits in natural numbers", American Journal of Mathematics, 4(1), 39-40.

Nigrini, M.J. (1996). "A taxpayer compliance application of Benford's law", The Journal of the American Taxation Association, 18(1), 72.

Nigrini, M.J. (1999). "Adding value with digital analysis", Internal Auditor, 56(1), 21-24.

Nigrini, M.J. and Wells, J.T. (2012). Applications for forensic accounting auditing, and fraud detection, Vol. 586, John Wiley & Sons.

Panthi, K. and Nilsen, B. (2007). "Uncertainty analysis of tunnel squeezing for two tunnel cases from Nepal Himalaya", International Journal of Rock Mechanics and Mining Sciences, 44(1), 67-76.

Pérez-González, F., Heileman, G.L. and Abdallah,  C.T. (2007). “Benford's law in image processing”, International Conference on Image Processing (ICIP 2007), IEEE.

Pérez-Romero, J., Oteo, C. and De la Fuente, P. (2007). "Design and optimisation of the lining of a tunnel in the presence of expansive clay levels", Tunnelling and Underground Space Technology, 22(1), 10-22.

Pinkham, R.S. (1961). "On the distribution of first significant digits", The Annals of Mathematical Statistics, 32(4), 1223-1230.

Sambridge, M., Tkalc̆ić, H. and Arroucau, P. (2011). "Benford’s law of first digits: From mathematical curiosity to change detector", Asia Pacific Mathematics Newsletter, 1(4), 1-6.

Sambridge, M., Tkalčić, H. and Jackson, A. (2010). "Benford's law in the natural sciences", Geophysical Research Letters, 37(22), 1-5.

Serrano, A. and Olalla, C. (2006). "Shaft resistance of piles in rock: Comparison between in situ test data and theory using the Hoek and Brown failure criterion", International Journal of Rock Mechanics and Mining Sciences, 43(5), 826-830.

Shahraki, M., Rafiee-Dehkharghani, R. and Behnia, K. (2018). "Three-dimensional Finite Element modeling of stone column-improved soft saturated ground", Civil Engineering Infrastructures Journal, 51(2), 389-403.

Suwansawat, S. and Einstein, H.H. (2006). "Artificial Neural Networks for predicting the maximum surface settlement caused by EPB shield tunneling", Tunnelling and Underground Space Technology, 21(2), 133-150.

Tseng, H.-C., Huang, W.-N. and Huang, D.-W. (2017). "Modified Benford’s law for two-exponent distributions", Scientometrics, 110(3), 1403-1413.

Wei, L., Sundararajan, A., Sarwat, A.I.,  Biswas, S. and Ibrahim, E. (2017). “A distributed intelligent framework for electricity theft detection using benford's law and stackelberg game”, 2017 Resilience Week (RWS).

Whyman, G., Ohtori, N., Shulzinger, E. and Bormashenko, E. (2016). "Revisiting the Benford law: When the Benford-like distribution of leading digits in sets of numerical data is expectable?", Physica A: Statistical Mechanics and its Applications, 461, 595-601.

Yin, L.J., Gong, Q.M. and Zhao, J. (2014). "Study on rock mass boreability by TBM penetration test under different in situ stress conditions", Tunnelling and Underground Space Technology, 43, 413-4