Analiza trajnih deformacij ciklično obremenjenih Murskih prodov

Abstract

This contribution presents the results of the analysis of permanent deformations of gravel in the Mura region under repeated loading. The purpose of the analysis is to forecast the development of permanent normalised axial deformations ▫$/epsilon_1^{p*}$▫ regarding the number of loading cycles N and appurtenant stress states during cycling loading. The analysis used the results of tests performed by ZAG Ljubljana and Faculty of Civil Engineering and Geodesy (FGG) of the University of Ljubljana [1]. The analysis considers five types of stonematerials of different quantity of crushed grains in the mixture and of different water contents. Four types of stone materials are mixtures of different portions of crushed grains larger than 2 mm (Dcr = 87.7 %, 58.9 %, 32.6 % in 0 %), and of the water content around w = wopt - 2%. The stone material with portions of crushed grains larger than 2 mm Dcr= 58.9 % is analysed also for water content w = wopt + 0.7 %. The results of the analysis are deformations expressed as a function of the number of loading cycles N, and a spherical component of the repeated loading p and a distortional component of the repeated loading q. The results can be presentedas deformation surfaces in the ▫$/epsilon_1^{p*}$▫ - p - q space for an arbitrary number of cycles N. The relation between the spherical stress component p and the distortional stress component q, at arbitrary values of axial permanent deformations ▫$/epsilon_1^{p*}$▫, gives a failure envelope, and the so called deformation envelopes in the p - q space. The failure envelopes and deformation envelopes are given separately for five types of stone material. The deformation envelopes are low at small values of the axial permanent deformation ▫$/epsilon_1^{p*}$▫ When permanent axial deformations grow, the permanent deformation approaches the failure envelopes. The failure envelopes for individual types of stone material agree with research results performed by [1]. The analysis of permanent deformations also shows their dependence on the portion of crushed material Dcr in the mixture of crushed and uncrushed stone material. The deformation envelope for uncrushed stone material is situated in the lowest position, regarding the portion of crushed material in the mixture. With an increased portion of crushed material in the mixture of crushed and uncrushed stone material, the deformation envelope is also higher, similarly to the lawfulness of failure envelopes. The relation of failure and deformation envelopes is mathematically established as a function of the portion of crushed grains larger than 2 mm. The comparison of stone material results for different water contents shows that a minimal increase of water content above the optimal one essentially increases deformation.Prispevek podaja rezultate analize trajnih deformacij murskih prodov, na podlagi cikličnih triosnih preizkusov, s katerimi je simulirana prometna obtežba. Namen predstavljene analize je podati napoved razvoja normaliziranih osnih trajnih deformacij ▫$/epsilon_1^{p*}$▫ glede na število obtežnih ciklov N in pripadajoče napetostno stanje med cikličnim obremenjevanjem. V analizi so uporabljeni rezultati cikličnih triosnih preizkusov, izvedenih v sklopu raziskovalnega projekta, ki sta ga izvajala ZAG Ljubljana in Fakulteta za gradbeništvo in geodezijo (FGG) Univerze v Ljubljani [1]. Obravnavanih je pet tipov kamnitega materiala, ki so zmesi drobljenega in nedrobljenega murskega proda. Tipi kamnitega materiala so podani glede na količino drobljenih zrn v produ in vlažnost. Štirje tipi kamnitega materiala so zmesi z različnim deležem Dcr drobljenih zrn nad 2 mm (Dcr = 87.7 %, 58.9 %, 32.6 % in 0 %), njihova vlažnost je okoli w = wopt - 2%. Kamniti material Dcr = 58.9 % pa je analiziran še za vlažnost w = wopt + 0.7 %. Rezultat analize so osne trajne deformacije ▫$/epsilon_1^{p*}$▫, ki so izražene kot funkcije števila obtežnih ciklov N, ter sferne komponente ciklične obtežbe p in distorzijske komponente ciklične obtežbe q. Rezultat lahko izrazimo z deformacijskimi ploskvami v ▫$/epsilon_1^{p*}$▫ - p - q prostoru za poljubno število ciklov N. Odnos med sferno in distorzijsko komponento napetosti pri neki vrednosti osne trajne deformacije ▫$/epsilon_1^{p*}$▫, podaja porušno ovojnico in deformacijske ovojnice v p – q prostoru. Porušne ovojnice so mejna stanja možnega razmerja q/p, deformacijske ovojnice pa podajajo razmerja q/p pri neki izbrani velikosti deformacije. Porušne ovojnice in deformacijske ovojnice so podane za vseh pet tipov kamnitega materiala. Porušne ovojnice za posamezne tipe kamnitega materiala se ujemajo z rezultati raziskave, ki sta jo izvajala ZAG in FGG [1]. Deformacijske ovojnice so pri malih vrednostih osne trajne deformacije ▫$/epsilon_1^{p*}$▫ nizke, z večanjem vrednosti osne trajne deformacije pa se približujejo porušnim ovojnicam. Analiza trajnih deformacij murskih prodov je tudi pokazala, da so le te odvisne od deleža drobljenega materiala Dcr v zmesi drobljenega in nedrobljenega kamnitega materiala. Glede na delež drobljenega materiala so deformacijske ovojnice najnižje pri nedrobljenem kamnitem materialu, z večanjem deleža drobljenega materiala v zmesi pa se deformacijske ovojnice višajo, podobna zakonitost velja tudi za porušne ovojnice. Sovisnost porušnih in deformacijskih ovojnic je matematično ovrednotena kot funkcija deleža drobljenih zrn nad 2 mm Dcr. Primerjava deformacij kamnitega materiala različne vlažnosti kaže, da se že z minimalnim povečanjem vlažnosti nad optimalno deformacije bistveno povečajo