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Robert A. Beeler, Teresa W. Haynes and Kyle Murphy

R eferences [1] R.A. Beeler, T.W. Haynes and K. Murphy, An introduction to t-restricted optimal rubbling , Congr. Numer., to appear. [2] C. Belford and N. Sieben, Rubbling and optimal rubbling of graphs , Discrete Math. 309 (2009) 3436–3446. doi:10.1016/j.disc.2008.09.035 [3] T.A. Clarke, R.A. Hochberg and G.H. Hurlbert, Pebbling in diameter two graphs and products of paths , J. Graph Theory 25 (1997) 119–128. doi:10.1002/(SICI)1097-0118(199706)25:2⟨119::AID-JGT3⟩3.0.CO;2-P [4] R. Feng and J.Y. Kim, Graham’s pebbling conjecture on

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Andrzej Batog and Elżbieta Stilger-Szydło

embankment, while its crown in the extreme case reached approx. 0.5 m above the crown of the old embankment. Due to savings, the substrate under the embankment was not reinforced. The old embankment was connected with the new one via shelves and the system of geosynthetics. Figure 1 Longitudinal crack in the surface as a result of uneven settlement of the embankment. Figure 2 shows the graph of the embankment’s settlement after 43 months of road exploitation. The forecasted final settlement of the embankment amounted to 41 cm, while the analysis of measurement

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Tadeusz Majcherczyk, Zbigniew Niedbalski and Łukasz Bednarek

kN. Insignificant values of compressive forces at the level of –8 kN were recorded at the initial part of the rock bolt. Every reading that followed later indicated a slight increase of axial forces in particular points of the rock bolt. Only during the last measurement, taken on the 623rd day after the installation, there was a slight decrease in the values of force in the rock bolt. The graph of axial forces acting on the instrumented rock bolt represents the fracture load pattern of the rock bolt. The initial length of the bolt can become subject to a small