Scott W. Sloan, Andrew J. Abbo and Daichao Sheng
Effective explicit algorithms for integrating complex elastoplastic constitutive models, such as those belonging to the Cam clay family, are described. These automatically divide…
Abstract
Effective explicit algorithms for integrating complex elastoplastic constitutive models, such as those belonging to the Cam clay family, are described. These automatically divide the applied strain increment into subincrements using an estimate of the local error and attempt to control the global integration error in the stresses. For a given scheme, the number of substeps used is a function of the error tolerance specified, the magnitude of the imposed strain increment, and the non‐linearity of the constitutive relations. The algorithms build on the work of Sloan in 1987 but include a number of important enhancements. The steps required to implement the integration schemes are described in detail and results are presented for a rigid footing resting on a layer of Tresca, Mohr‐Coulomb, modified Cam clay and generalised Cam clay soil. Explicit methods with automatic substepping and error control are shown to be reliable and efficient for these models. Moreover, for a given load path, they are able to control the global integration error in the stresses to lie near a specified tolerance. The methods described can be used for exceedingly complex constitutive laws, including those with a non‐linear elastic response inside the yield surface. This is because most of the code required to program them is independent of the precise form of the stress‐strain relations. In contrast, most of the implicit methods, such as the backward Euler return scheme, are difficult to implement for all but the simplest soil models.
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“WE come now to another aspect of the question, and it must be admitted that the resource and ingenuity of the opposition have left nothing unnoticed. This is the common and…
Abstract
“WE come now to another aspect of the question, and it must be admitted that the resource and ingenuity of the opposition have left nothing unnoticed. This is the common and constantly repeated assertion that novels are so cheap that every working man in the country can buy all he needs for less than the annual library rate. This statement was first made some years ago when publishers commenced to issue cheap reprints of non‐copyright novels at 1s. and 6d. each. Previous to this the halfpenny evening paper had been relied upon as affording sufficient literary entertainment for the working man, but when it was found to work out at 13s. per annum, as against a library rate of 1od. or 1s. 4d., the cheap newspaper argument was dropped like a hot cinder. We doubt if the cheap paper‐covered novel is any better. Suppose a workman pays £20 per annum for his house, and is rated at £16, he will pay 1s. 4d. as library rate, or not much more than 1¼d. per month for an unlimited choice of books, newspapers and magazines. But suppose he has to depend on cheap literature. The lowest price at which he can purchase a complete novel of high quality by any author of repute is 3d., but more likely 4½d. or 6d. However, we will take 3d. as an average rate, and assume that our man has leisure to read one book every fortnight. Well, at the end of one year he will have paid 6s. 6d. for a small library by a restricted number of authors, and it will cost him an additional 4s. or 5s. if he contemplates binding his tattered array of books for future preservation. Besides this, he will be practically shut off from all the current literature on topics of the day, as his 3d. a fortnight will hardly enable him to get copyright books by the best living authors. With a Public Library at his command he can get all these, and still afford to buy an occasional poet or essayist, or novel, or technical book, well bound and printed on good paper, such as his friend who would protect him against an iniquitous library rate would not blush to see on his own shelves. It seems hard that the working men of the country should be condemned to the mental entertainment afforded by an accumulation of pamphlets. Literature clothed in such a dress as gaudy paper covers is not very inspiring or elevating, and even the most contented mind would revolt against the possession of mere reading matter in its cheapest and least durable form. The amount of variety and interest existing among cheap reprints of novels is not enough, even if the form of such books were better. It is well known to readers of wide scope that something more than mere pastime can be had out of novels. Take, for example, the splendid array of historical novels which have been written during the present century. No one can read a few of these books without consciously or unconsciously acquiring historical and political knowledge of much value. The amount of pains taken by the authors in the preparation of historical novels is enormous, and their researches extend not only to the political movements of the period, but to the geography, social state, costume, language and contemporary biography of the time. Thus it is utterly impossible for even a careless reader to escape noticing facts when presented in an environment which fixes them in the memory. For example, the average school history gives a digest of the Peninsular War, but in such brief and matter of fact terms as to scarcely leave any impression. On the other hand, certain novels by Lever and Grant, slipshod and inaccurate as they may be in many respects, give the dates and sequence of events and battles in the Peninsula in such a picturesque and detailed manner, that a better general idea is given of the history of the period than could possibly be acquired without hard study of a heavy work like Napier's History. It is hardly necessary to do more than name Scott, James, Cooper, Kingsley, Hugo, Lytton, Dumas, Ainsworth, Reade, G. Eliot, Short‐house, Blackmore, Doyle, Crockett and Weyman in support of this claim. Again, no stranger can gain an inkling of the many‐sided characteristics of the Scot, without reading the works of Scott, Ferrier, Galt, Moir, Macdonald, Black, Oliphant, Stevenson, Barrie, Crockett, Annie Swan and Ian Maclaren. And how many works by these authors can be had for 3d. each? The only way in which a stay‐at‐home Briton can hope to acquire a knowledge of the people and scenery of India is by reading the works of Kipling, Mrs. Steel, Cunningham, Meadows Taylor, and others. Probably a more vivid and memory‐haunting picture of Indian life and Indian scenery can be obtained by reading these authors than by reading laboriously through Hunter's huge gazetteer. In short, novels are to the teaching of general knowledge what illustrations are to books, or diagrams to engineers, they show things as they are and give information about all things which are beyond the reach of ordinary experience or means. It is just the same with juvenile literature, which is usually classed with fiction, and gives to that much‐maligned class a very large percentage of its turnover. The adventure stories of Ballantyne, Fenn, Mayne Reid, Henty, Kingston, Verne and others of the same class are positive mines of topographical and scientific information. Such works represent more than paste and scissors industry in connection with gazetteers, books of travel and historical works; they represent actual observation on the part of the authors. A better idea of Northern Canada can be derived from some of Ballantyne's works than from formal topographical works; while the same may be said of Mexico and South America as portrayed by Captain Mayne Reid, and the West Indies by Michael Scott. The volume of Personal Reminiscences written by R. M. Ballantyne before he died will give some idea of the labour spent in the preparation of books for the young. The life of the navy at various periods can only be learned from the books of Smollett, Marryat and James Hannay, as that of the modern army is only to be got in the works of Lever, Grant, Kipling, Jephson, “John Strange Winter” and Robert Blatchford.
Yongliang Wang, Jin Huang and Guocheng Wang
This study aims to analyse the deep resource mining that causes high in situ stress, and the disturbance of tunnelling and mining which may induce large stress concentration…
Abstract
Purpose
This study aims to analyse the deep resource mining that causes high in situ stress, and the disturbance of tunnelling and mining which may induce large stress concentration, plastic deformation and rock strata compression deformation. The depth of deep resources, excavation rate and multilayered heterogeneity are critical factors of excavation disturbance in deep rock. However, at present, there are few engineering practices used in deep resource mining, and it is difficult to analyse the high in situ stress and dynamic three-dimensional (3D) excavation process in laboratory experiments. As a result, an understanding of the behaviours and mechanisms of the dynamic evolution of the stress field and plastic zone in deep tunnelling and mining surrounding rock is still lacking.
Design/methodology/approach
This study introduced a 3D engineering-scale finite element model and analysed the scheme involved the elastoplastic constitutive and element deletion techniques, while considering the influence of the deep rock mass of the roadway excavation, coal seam mining-induced stress, plastic zone in the process of mining disturbance of the in situ stress state, excavation rate and layered rock mass properties at the depths of 500 m, 1,500 m and 2,500 m of several typical coal seams, and the tunnelling and excavation rates of 0.5 m/step, 1 m/step and 2 m/step. An engineering-scale numerical model of the layered rock and soil body in an actual mining area were also established.
Findings
The simulation results of the surrounding rock stress field, dynamic evolution and maximum value change of the plastic zone, large deformation and settlement of the layered rock mass are obtained. The numerical results indicate that the process of mining can be accelerated with the increase in the tunnelling and excavation rate, but the vertical concentrated stress induced by the surrounding rock intensifies with the increase in the excavation rate, which becomes a crucial factor affecting the instability of the surrounding rock. The deep rock mass is in the high in situ stress state, and the stress and plastic strain maxima of the surrounding rock induced by the tunnelling and mining processes increase sharply with the excavation depth. In ultra-deep conditions (depth of 2,500 m), the maximum vertical stress is quickly reached by the conventional tunnelling and mining process. Compared with the deep homogeneous rock mass model, the multilayered heterogeneous rock mass produces higher mining-induced stress and plastic strain in each layer during the entire process of tunnelling and mining, and each layer presents a squeeze and dislocation deformation.
Originality/value
The results of this study can provide a valuable reference for the dynamic evolution of stress and plastic deformation in roadway tunnelling and coal seam mining to investigate the mechanisms of in situ stress at typical depths, excavation rates, stress concentrations, plastic deformations and compression behaviours of multilayered heterogeneity.