# Convegence of gallery workings in underground salt mines

## Abstract

The convergence measured in the Polish salt mines was used to identify the relationship between the room closure and geological and mining conditions, for the identification of the phenomenon of the closure of a single room or the group of rooms, for the estimation of the pillar loads, to identify the geomechanical properties of rock mass and to identify the influence of the depth on the closure. However, in the light of the analysis and interpretations shown in the articles and studies it is difficult to consider that the convergence meet this role.
The research is devoted to the study of the convergence model which is designed for the description of the phenomenon of the convergence of workings in underground salt mines. The physical basis of the model is the constitutive relation for a viscous-elastic medium with the Norton-Bailey power creep law developed in the USA and Western Europe in connection with the building of underground hydrocarbon storages and radioactive waste repositories. In this research, on the basis of numerical calculations using the finite element method, a series of model properties determining the functional relations between convergence and the shape and depth of workings, both the elastic and viscous features of the rock mass, including creep compliance, have been revealed. The relationship between convergence and rock mass heterogeneity, the impact of temperature and filling a working with liquids of various density, as well as the impact of adjacent workings – with the use of 2D and 3D modelling – have also been presented.
The research contains a wide review of used methods and instruments for surveying of convergence in salt mines, the assessment of the accuracy and frequency of convergence surveys. The elaborated model has been used for the interpretation of survey results, including Sieroszowice salt mine. A recommended manner of establishing survey station, calculation method, and the revealing of the viscous characteristics of salt rock mass with the use of long-term surveys which can be used for engineering work, as well as to forecast the convergence of workings and rock mass movement have been presented. The guidelines for further convergence measurements and the interpretation of results obtained basing on the convergence model, have been formulated.
The current state of knowledge about the behaviour of rock mass, known and used geomechanical models, numerical methods, relationship between the basic geometric and geomechanical quantities may provide a basis for the back analysis. This applies to the selection of the rheological parameters of the constitutive law, in particular by comparing the results of the calculation to the observed time dependence of the convergence. In this sense the measurements of the convergence may provide important element of the recognition of the behaviour of the rock mass, and only indirectly estimate its safety.
In view of the future use of salt mines as tourist sites, underground storages or waste repositories, it was shown that the use of geomechanical modelling provides the correct interpretation of the results of observation. The determination of the closure of workings, groups of workings, mine fields, and whole mine, and linking it with subsidence should use the convergence model. This model does currently not reflect the full complexity of the rock mass properties, in particular its non-homogeneity, it should be further improved.

... where Q is the activation energy, R is the gas constant, T is temperature in Kelvin, and A is the material constant. The dependence of strain on the values of n and m in the Norton-Bailey power creep law is discussed in (Maj, 2012); in our calculations, the following assumptions were made: n = 2 and m = 1. For those constants, equation (2) has the form of ε • ij = 3 / 2 Bσ ef σ ij . ...

This paper is devoted to the analysis of the stress development process in the homogeneous and non-homogeneous rock mass. The rock-mass model consists of an elastic-viscous medium containing a layer (Fig. 1) that displays distinct geomechanical strain properties. When examining the process of stress equilizing in time, the Norton-Bailey power creep law was applied in the numerical analysis. The relationship between effective stresses and time, the modulus of elasticity, Poisson’s coefficient, and creep compliance were obtained. It was demonstrated that the relationship between effective stress and time or creep compliance, for the assumed conditions in a homogeneous rock-mass, was approximated by hyperbolic functions (10 and 16). The process parameter included a certain value of creep compliance or of time at which there occurred a half-way equilizing of primary stresses. An analogous function binds effective stresses with creep compliance. Our model studies indicated a number of relationships between bulk and shear strain with time and creep compliance in the homogeneous and non-homogeneous rock mass, presented in Figs. 2-14, expressed by the functions of those specific parameters.
The relationships obtained in this work resulted from our model assumptions. However, they demonstrated the influence of the geomechanical strain properties of rocks on the process of shaping the primary stress state in the rock mass and the tendency to reduce the principal stress differences in time. Our research results suggested the necessity to simulate the primary stress state as an initial condition of the geomechanical numerical analysis concerning the rock-mass behaviour showing rheological properties.

A short presentation of the time dependent constitutive equation for rocks is presented. One is starting from the experiments to show how the constitutive equation if formulated. After that one is presenting the results of application of the constitutive equation for many rocks, concrete and particulate materials.

Although columns built almost 5,000 years ago still stand in Egypt, the first theoretical calculation of the load-carrying capacity of columns was published by Euler only 209 years ago. The classical theory established in this publication is still the foundation of all stability analyses and is likely to remain so in the future. It was derived for perfectly elastic columns and for specific end conditions. These end conditions are not realised in the ordinary column test nor do they correspond exactly to the conditions prevailing in an aeroplane wing when it is subjected to a gust or to the shock of landing. They are not the same as the end conditions of a column in a building when it collapses during a tornado or an earthquake.

Relations between form structure of multi-level, room and pillar salt mine and ground surface displacement distribution were found on the base of numerical model researches. It was noticed that the displacement distribution depends on structure slenderness which influences rock mass conditions of equilibrium and volumetric strains. For a mininig field represented by 2D + t model relations between though surface in vertical cross-section and aerial convergence of all chambers were defined. The 2D + t viscous-elastic model of the rock mass were applied in FEM model researches.

Mechanical properties of salt are important to the geologist because they determine the remarkable behavior of salt in large quantities. The ability of salt to flow or creep slowly under sufficient differential pressure is of particular importance in explaining the formation and shape of salt structures. The time-dependent strain or " c r e e p " of salt and other nonmetallic bodies is not well understood, but available data show that, under suitable conditions of pressure, temperature, and environment, salt and other nonmetallic bodies show a behavior similar to that of metals. Some of the available data concerning creep of salt as obtained in the laboratory and in situ are reviewed. From these data it is possible to derive for the given conditions of stress, temperature, and environment an equivalent viscosity for the salt. In this manner a rough idea can be obtained concerning the equivalent viscosity of salt. Unfortunately, the values obtained show a wide variation, which amounts to many orders of magnitude.

Introduction. Estimating in-situ stresses. Methods of in-situ stress measurement. Hydraulic methods. Relief methods. Jacking methods. Strain recovery methods. Borehole breakout methods. Case studies and comparison between different methods. Monitoring of stress change. The state of stress in the earth's crust: from local measurements to the world stress map. Using stresses in rock engineering, geology and geophysics. Appendices.

In 1978, brine leakage occurred in a mining panel at IMC Kalium operation in Colonsay, Saskatchewan. Stringent controls were immediately imposed to control the inflow; with further investigative and remediation work in 1981–1982 and in 1984–1985. The work involved investigative diamond drilling, grouting, instrumentation and backfilling. The instrumentation program was designed to gather information on the grout/backfill system as a mechanism of brine flow control and to monitor the long term stability of the inflow area. The result of this extensive work was the successful control of the inflow. As important, the instrumentation program gave valuable information which permitted a sound and rational engineering decision for complete abandonment of the area. This paper describes the instrumentation planning and design process, the rationale for selecting the rock mechanical instrumentation, the reasons for their placement, the data communication system, the data recorded and interpretation.

After a historical introduction on the importance of the subject, the following topics are treated: geology of evaporite deposits (oceanic origin, mineralogy and petrology, texture and stratification, changes to texture and stratification after consolidation, structural geology, review of salt mining methods), physical properties and mechanical behavior of evaporites (creep mechanism, creep limits, strain hardening, tensile and shearing strengths, permeability, plasticity, stresses), deformations in response to stress relief by excavation (stress relief around isolated and two parallel openings, stress gradients in stress-relief creep zones, elastic deformations around single openings in salt, discharge of fluids from isolated reservoirs), and creep deformations in partially extracted salt deposits (stress-relief creep and pillar reloading in room-and-pillar potash mines, stress-relief creep and pillar reloading - long-pillar mines, creep deformations in panel-and-pillar mining, creep deformations caused by irregular extraction patterns. 245 references, 95 figures, 14 tables. (RWR)

Numerous constitutive models have been proposed for the low temperature creep of salt. This work was the first to develop such a model within the framework of a deformation-mechanism map. Use of this framework permits unfolding of the rather complicated low temperature steady-state creep behavior into three simple responses involving separate regimes with individual controlling mechanisms. The constitutive model developed in this report incorporates primary (transient) creep as a two parameter modification to the steady-state creep equations. The constitutive model presented can be applied to deep mines and, more importantly, to design of the petroleum storage and radioactive waste isolation facilities.

The Waste Isolation Pilot Plant (WIPP) is a research and development facility in bedded salt addressing the technical issues associated with the demonstration of disposal of radioactive waste from the defense programs of the USA. The geomechanical program includes laboratory experimentation, constitutive model and computer code development, and in-situ experimentation. Various material models, including creep for salt, and techniques for predicting room response under thermal and mechanical loads have been developed and are being applied to experiment and facility designs. A Benchmark II study has been conducted to compare the capabilities of nine structural codes to predict response of underground configuration under ambient temperature and with a thermal load of 7.5 W/m/sup 2/. Parametric studies are being conducted to evaluate optimum room configurations. A series of in situ experiments is the next step towards validating models and predictive techniques. These experiments will be conducted in a facility in southeastern New Mexico mined at a depth of 659 m.

Research at the Department of Mining Engineering of the University of Newcastle-Upon-Tyne involves aspects of the structural response and stability of gas storage cavities in salt. The investigation is in 2 areas of interest: the strength problem associated with storage cavities at shallow and intermediate depths, and the flow problem at great depth. Results show that, during the rapid withdrawal of gas from a cavity, the thermal stresses induced in the walls by the resulting change of temperature can be of a magnitude sufficient to fracture the salt. Experience suggests that consideration should be given to the possible consequences of high gas withdrawal rates on the integrity of the wall-rocks of an operational cavity. One approach to quantifying the base pressure is to develop a mathematical model which describes adequately the elastic and creep response of the rock and to apply this model in a numerical simulation of the long-term performance of the storage cavity under various operational conditions. A creep testing facility for salt rocks has been developed to meet these requirements. 24 references.

A multimechanism constitutive model of the creep of polycrystalline rock salt has been developed based on steady state creep as modified to incorporate transient creep through workhardening and recovery. Application of the model is in calculation of the closure of underground rooms excavated in a natural, bedded evaporite salt deposit. This requires an integrated technology consisting of not only the proper constitutive model, but also a range of other system elements relating to the site geology, initial and boundary conditions, and numerical methods peculiar to the application. Through finite element calculations, this model, with appropriate laboratory material parameters and a Tresca flow potential, has predicted the closure of a number of large, in situ experimental rooms at the Waste Isolation Pilot Plant (WIPP). In this paper, an overview of the model development, laboratory parameter generation and numerical simulation capability is given, together with a summary of the comparisons of the calculated and measured creep closure results. The comparisons encompass a range of test room configurations that exercise the predictive capability for stratigraphic setting, room geometry, thermal heating, stress field interaction and two and three-dimensional deformation fields. The simulations have proven satisfactory and suggest the general adequacy of the predictive technology.

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