Composite Elasticity of Copenhagen Limestone

Katic, Nataša (Geo, Kgs. Lyngby) | Christensen, Helle Foged (Geo, Kgs. Lyngby)



The elastic properties of the Copenhagen Limestone matrix material are spanning over more than two scales of magnitude. The sizes of rock constituents, the bulk density and the degree of induration of matrix material vary. The measured value of the elastic modulus depends on the inherent material properties, the size of the engaged volume and the measuring technique. The work presents a synthetic approach in determination of rock mass modulus by using theory of mixtures, thereby constructing a framework for interpretation of multi-scale investigations. Trend lines for mixtures observed on the results of acoustic tests are used to combine the UCS test results in order to obtain the modulus of the intact rock mass. Rock mass modulus relating to disturbed rock mass is derived by means of Hoek and Brown model (Hoek et al. 2002) and compared to the results of High Pressure Dilatometer Tests.

1 Introduction

Copenhagen Limestone (CL) is a carbonate rock with varying degree of induration, ranging from unlithified sediments to very strongly indurated rock. Determination of the rock mass modulus for CL presents a challenge, not only due to variation of induration, but also due to variable degree of fracturing. Variations occur on a centimetre scale.

A comprehensive ground investigation has been carried out in relation to Cityring project, comprising several hundreds of borings. Available measurements of elastic moduli include broad series of laboratory and field tests, including unconfined compression strength (UCS) and high pressure dilatometer tests (HPDT), as well as corresponding measurements of the sound velocities on laboratory specimens by means of piezo-crystals (PC) and vertical seismic profiling (VSP) in the field. The interpretation of these tests is aided by series of laboratory classification tests and geophysical tests in the field (porosity and density measurements). A comparative analysis of the results has been conducted and presented earlier (see e.g. Katić & Christensen 2014). For the sake of brevity, the evaluations presented herein are made for the average values covering the Cityring site as a whole.

CL is divided into 3 stratigraphic units, Upper, Middle and Lower (UCL; MCL and LCL, respectively), based on the results of geophysical and core logging, showing specific patterns of limestone and flint forming the rock. The zone of interest for the tunnelling and related support structures such as station walls is mainly above LCL; hence, the evaluation focuses on CL above the LCL. Figure 1 shows typical samples from CL.

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