Uniaxial and Triaxial Creep Performance of Calcarenitic and Sandy Oolitic Limestone Formations for Stability Analysis of Roman Rock-Cut Tombs in Alexandria, Egypt

Abstract

The Greek-Roman rock-cut tombs at Alexandria, Egypt, were excavated mainly in the calcarenitic limestone formations and show varying degrees of damage of rock pillars and ceilings. In order to understand the long-term rock mass behaviour in selected tombs and its impact on past failures and current stability, uniaxial and triaxial Creep tests and rock mass quality assessments had been carried out. Creep behavior of rock plays an important role in underground works, especially for archeological structures subjected to large initial stresses. These conditions yield nonreversible deviatoric creep strains that develop during time at constant stress. In order to describe the time-dependent deformation, various approaches have been established based on analytical, empirical, and numerical methods. Our analyses show that the Roman tombs at Alexandria have been cut into poor quality rock masses. Rock failures of ceilings and pillars were frequently facilitated by local, unfavourably oriented persistent discontinuities, such as tension cracks and joints. Other failures were related to the disintegration of calcarenitic and oolitic limestones. Our data suggest that, in Roman age monumental tomb construction, lowstrength rock masses resulted in modifications of the planned tomb design in order to minimise the risk of rock falls and to prevent collapses.

A micromechanics‐based approach to damage propagation criterion in viscoelastic fractured materials regarded as homogenized media

“…Relying upon creep tests provided in Hemeda 105 for limestone and in Gunzburger and Cornet 106 for Argillite, Burger models were formulated for the uniaxial relaxation modulus of each of the intact rocks: 𝐋𝐢𝐦𝐞𝐬𝐭𝐨𝐧𝐞 ∶ 𝐸 𝑒 𝑠,𝑀 = 3.75 GPa ; 𝐸 𝑣 𝑠,𝑀 = 64500 GPa yr ; 𝐸 𝑒 𝑠,𝐾 = 10.2 GPa ; 𝐸 𝑣 𝑠,𝐾 = 6.1 GPa yr 𝐀𝐫𝐠𝐢𝐥𝐥𝐢𝐭𝐞 ∶ 𝐸 𝑒 𝑠,𝑀 = 2.2 GPa ; 𝐸 𝑣 𝑠,𝑀 = 6.58 GPa yr ; 𝐸 𝑒 𝑠,𝐾 = 2.9 GPa ; 𝐸 𝑣 𝑠,𝐾 = 5.5 × 10 −2 GPa yr (86) with the notations of Figure 7A. In addition, constant Poisson ratios 𝜈 = 0.25 and 𝜈 = 0.3 are considered for limestone and argillite, respectively.…”

“…Relying upon creep tests provided in Hemeda 105 for limestone and in Gunzburger and Cornet 106 for Argillite, Burger models were formulated for the uniaxial relaxation modulus of each of the intact rocks: $$$$\begin{equation} \def\eqcellsep{&}\begin{array}{l} {{\bf Limestone}}:E_{s,M}^e = 3.75\,{\rm{GPa}}\,\,\,;\,\,\,\,E_{s,M}^v = 64500\,{\rm{GPa}}\,{\rm{yr}}\,\,;\,\,\,\,E_{s,K}^e = 10.2\,{\rm{GPa}}\,\,\,;\,\,\,\,E_{s,K}^v = 6.1\,{\rm{GPa}}\,{\rm{yr}}\\[5pt] {{\bf Argillite}}:E_{s,M}^e = 2.2\,{\rm{GPa}}\,\,\,;\,\,\,\,E_{s,M}^v = 6.58\,{\rm{GPa}}\,{\rm{yr}}\,\,\,;\,\,\,\,E_{s,K}^e = 2.9\,{\rm{GPa}}\,\,\,;\,\,\,\,E_{s,K}^v = 5.5 \times {10}^{ - 2}\,{\rm{GPa}}\,{\rm{yr}} \end{array} \end{equation}$$$$with the notations of Figure 7A. In addition, constant Poisson ratios …”