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Background: The paper represents the first comprehensive experimental and numerical study for engineering failure analysis and appropriate design for the permanent mechanical support system for the tomb of the Sons of Ramesses II (KV5). It is, in fact, one of the largest rock cut tombs ever found in Egypt. During the late 18th Dynasty and throughout the19th, the tombs are usually located further down the Valley some distance from the rock walls. The builders often quarried through talus slopes, such as in the case of the tomb of Sons of Ramses II. It is clear that the tomb of sons of Ramsses II is much more susceptible to surcharge geostatic loading from the overburden rock strata, rock bursting, and structural damage of support pillars and walls induced to the water and past/recent flash floods impacts caused by heavy rain in the Valley. Since some of this tomb also makes contact with the underlying shale layers, that have the potential for swelling and shrinkage under changing moisture conditions. Expansive damages to these underground structures have been widely noticed in the Valley of the Kings. This tomb tends to be the worst preserved tomb in the Valley of the Kings. The Esna shale in the valley is particularly weak and unstable. It not only posed problems to the ancient quarryman, but to the modern conservator as well. When the shale comes into contact with moisture, it expands and can literally tear a hill side apart. Results: The main adjectives of the geoenvironmental and geotechnical analyses carried out in the present study are to investigate the static stability, safety margins and engineering failure of the tomb of Sons of Ramsses II (KV5) under their present conditions, against unfavorable environmental (i.e. extensive weathering due to water and flash floods impact in the past and present), utter lack of preservation, geostatic overloading of structural rock support pillars, geotechnical and extreme seismic conditions. Also to design an appropriate geotechnical support system, according to the engineering rock mass classification, in particularly the rock mass rating RMR and quality rock tunneling index Q-system. (Continued on next page) Correspondence: email@example.com Conservation Department, Faculty of Archaeology, Cairo University, Giza, Egypt Aristotle University of Thessaloniki, Thessaloniki, Greece © The Author(s). 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Hemeda Geoenvironmental Disasters (2018) 5:12 Page 2 of 24 (Continued from previous page) Conclusions: The engineering analysis had been carried out through the following four steps: 1-Evaluation of the surrounding rocks (marl limestone) by experimental investigation and the Roclab program to obtain Hoek Brown Classification criterion, Mohr- Coulomb fit and the rock mass parameters in particular the global strength and deformation modulus. 2- Qualitative and quantitative estimations of relevant factors affecting the stability of the tomb in particularly the overburden or geostatic and dynamic loading. 3- 2D and 3D integrated geotechnical modeling of the tomb environment for stress, displacement analyses and determination of volumetric strains and plastic points using advanced codes and programs like Examine 2D and PLAXIS 3D. The numerical analysis results indicated that the safety factor of the rock pillar structural supports is 1.37 and the overstress state is 1.28 MPa. 4-Remedial and retrofitting policies and techniques, static monitoring and control systems which are necessary for the strengthening and stability enhancement of the tomb, where the rock mass classification indicated the rock mass where the KV5 is excavated is poor rock, with RMR 39 and Q value 1.87. Based on the underground engineering stable equilibrium theory and rock mass classification, three support structure techniques are provided and detailed illustrated with the case of KV5 in this study. Keywords: Geotechnical problems, Rock character, Support structure, Tomb of the sons of Ramses II, Valley of the kings Background this focused on the research center testing and the esti- Amongst the many monument types which exist all over mation of fragile crack limits (Deere and Varde 1990). the world, underground sites such as caves, tombs, The Geotechnical instability problems and degradation crypts and catacombs can be singled out as a category phenomena of rock cut tombs in the Valley of the Kings which has its own particular set of “adversaries”. These (KV) is likely to be dominated by gravity fall and sliding locations are to a certain extent “protected” by the earth on structural features, also other factors such as exces- or rock surrounding them; this is especially so when sively high rock stress, creep effect, poor geotechnical these sites remain sealed, or has only one small or par- properties of rock structures, weathering and /or swell- tially blocked opening to the exterior. However, when an ing rock and flash floods caused by heavy rains in the interred site is discovered and uncovered, its microcli- Valley, vibrations and dynamic loading as well as utter mate is disturbed and fluctuations in internal conditions lack of preservation become important and can be evalu- commence. These variations become accentuated if the ated by means of a classification of rock quality. The protective covering is removed either during excavation Esna shale in the valley is particularly weak and unstable. or later to create a new wider access to the site. This in- It not only posed problems to the ancient quarryman, stability eventually leads to deterioration of the site and but to the modern conservator as well. When the shale in particularly any decorations or paintings it may con- comes into contact with moisture, it expands and can tain. Further deterioration is caused by other unrelated literally tear a hill side apart. sources such as water seepage and occasionally also The tomb was robbed in antiquity. Since then, it has flooding like the tomb KV5 which under investigation, been hit by at least eleven flash floods caused by heavy salt damage and the accumulation of dust, debris and rains in the Valley. These have completely filled the other contaminants. The problems are common to all tomb with debris and seriously damaged its comprehen- painted underground and semi-buried sites in the valley sively decorated walls. From about 1960 to 1990, tour of kings at Luxor, Egypt. buses parked above the tomb; their vibrations caused It is important to say that in geological engineering, serious damage to parts of the tomb near the roadway, including in underground rock engineering and rock as did a leaking sewer line installed over the entrance mechanics, lots of the hazards sources arise from geo- when the Valley of the Kings rest house was built. technical uncertainty or error. The sources of uncer- In October and November of 1994, two flood events tainty can be classified as: (1) inalienable spatial and occurred in the Valley of Kings, sending a warning to all fleeting fluctuation; (2) estimation and observing blun- heritage managers. In both cases, a local desert rain- ders; (3) demonstrating vulnerability; (4) load and storm occurred in the vicinity of the Valley of Kings. stresses vulnerability (Brown 2012). In geotechnical en- Storm-water runoff and sediment entered the tomb of gineering it is perceived that stone disfigurement is im- Sons of Ramsses II and other many o tombs and caused perative in deciding the advancement of characteristic erosion of gully floors. structures and structural highlights. Numerous investi- Current farming procedures have additionally added to gations and field work has been done to comprehend the topographical traits of the Nile Valley bowl. Today, the fragile break procedures and systems. Quite a bit of ground water levels have ascended here, and debilitate Hemeda Geoenvironmental Disasters (2018) 5:12 Page 3 of 24 Fig. 1 Aerial photograph indicates the east (main) Valley of the Kings (KV) at Luxor Egypt. Modified after Google earth map. The tomb of Sons of Ramsses II (KV5) is located at the middle of the Valley of the Kings, East Valley, Thebes West Bank at Thebes. The Theban Mapping Project’s excavations have shown that KV 5 contains not just the six rooms first seen by Burton in 1825, but over 150 corridors and chambers dug deep into the hillside low lying shaft tombs and the morgue sanctuaries on the discovered by Theban Mapping Project in 1995 (Clayton edge of the development, and in addition the outstand- 1995, Weeks 1992, 1994 and 1995), as showninFig. 2. ing Luxor and Karnak sanctuaries on the east bank. There is an adjustment in the tomb’s essential pivot The tomb of Sons of Ramsses II (KV5) is located at the after chamber 3; a few chambers lie underneath different middle of the Valley of the Kings, East Valley, Thebes West chambers; two hallways reach out toward the northwest Bank at Thebes (Reeves and Wilkinson 1966). The Theban underneath the passageway and the street before the Mapping Project’sexcavations have shownthatKV5con- tomb. Pillared chamber 3 has more columns (sixteen) tains not just the six rooms first seen by Burton in 1825, than some other chamber in the Valley of the Kings. The but over 150 corridors and chambers dug deep into the measured dimensions of the KV5 are maximum height hillside, as shown in Fig. 1. of 2.85 m, width of 0.61~ 15.43 m, total length of KV 5 itself is the largest rock cut tomb in the Valley of 443.2 m; total area of 1266.47 m and total volume of the Kings; pillared chamber 3 is the largest chamber of any 2154.82 m . Pillars Conditions are excavated, decoration tomb in the Valley of the Kings. Chambers 1 to 6 had been damaged, damaged structurally (Weeks 1998, 2000 and discovered in 1825 by James Burton, all other had been 2006), as shown in Fig. 3. Fig. 2 Location of the tomb of Sons of Ramsses II (KV5) at the east (main) Valley of the Kings (KV), Luxor Egypt. KV 5 itself is the largest rock cut tomb in the Valley of the Kings; pillared chamber 3 is the largest chamber of any tomb in the Valley of the Kings. Chambers 1 to 6 had been discovered in 1825 by James Burton, all other had been discovered by Theban Mapping Project in 1995 (Clayton 1995) Hemeda Geoenvironmental Disasters (2018) 5:12 Page 4 of 24 Fig. 3 The present layout and plan of the tomb of Sons of Ramsses II (KV5). The Measurements of the KV5 are: Maximum height: 2.85 m. 2 3 Minimum width: 0.61 m. Maximum width: 15.43 m. Total length: 443.2 m. Total area: 1266.47 m . Total volume: 2154.82 m . Pillars Conditions are excavated, cutting finished, decorated, decoration damaged, damaged structurally Methods and experimental and analyze a three-dimensional (3D) finite element The rock mass petrography and mechanical strength model (FEM) of the pillared chamber 3 with its structur- where the tomb of sons of Ramses II is excavated has been ally damaged sixteen rock pillars and the large northern analyzed by experimental investigations, which include hall which are excavated in this poor and extensively XRD, XRF and DTA-TGA analysis and thin section exam- weathered marl limestone deposit (member 1), using the ination under polarized light microscope. A comprehen- PLAXIS 3D code. sive program for petro physical and mechanical testing The Rock Mass Classification calculations are utilized include the uniaxial compression test and ultra-sonic wave for the general assessment of the rock mass where the velocity through the materials (PUNDT) has been estab- KV5 is excavated. The results of the rock mas rating lished. The RocLab program has been utilized to calculate (RMR) and Q-system values were utilized to design an the Hoek-Brown Classification and criterion also to appropriate support system. calculate the Mohr-Coulomb fits and rock strength parameters in particularly the deformation modulus The geology of Gebel El-Gurnah, Luxor (RocLab 1.0. 2018). Underground structures safety ana- Gebel El-Gurnah is located some 4 km to the west of lysis is performed using the finite element (FE) method. the River Nile, opposite to Luxor. The main exposed The research presents a comprehensive study for the rock rock units in Gebel El-Gurnah are the Esna Shale and cut tombs safety analysis. The safety analysis includes not Thebes limestone formations. The tombs of the kings only a failure analysis but the effect of weathering, in were excavated in the Thebes formations at northern particular the materials wear on the differential settlement side of Gebel El-Gurnah and the tombs of the queens have been investigated. The commercial FE package Exam- were excavated at the southern side (Litherland 2013, ine 2D is used for conducting stress, as well as settlement Dunn 2014, Wüst and McLane 2000). analysis. Examine 2D is a finite element program developed The main exposed rocks in Gebel El-Gurnah are the for numerical analysis of geotechnical and underground Esna Shale (late Paleocene- Early Eocene) and the con- and subterranean structures (Examine 2D 2018). formatably overlying Thebes formation (Early Eocene). The deformation of these rock cut tombs has been computed as realistically as possible, utilizing an advanced Esna Shale nonlinear elasto-plastic material model needs to be utilized The lower 25 m of this formation is less calcareous, usu- in PLAXIS 3D which is capable of utilizing such advanced ally is green dark grey, and sometimes nearly block. The material models (PLAXIS 3D Software 2018). 3D Plastic upper shale is whitish grey and greenish, more compact model is used for deformation and consolidation analysis in and carries more gypsum vienlets. The iron oxides vary this research. The consolidation analysis is performed using in color. Brownish red and yellow hematitic and limon- PLAXIS 3D. Also in this research, we attempt to construct itic concretions are present; the ferruginous concretions Hemeda Geoenvironmental Disasters (2018) 5:12 Page 5 of 24 are characteristic feature foe the whole formation. The stress conditions lead to rockbursting (the sudden re- gypsum vienlets run mostly parallel to the bedding lease of stored strain energy) bursts manifest themselves planes (Wüst and McLane 2000), as shown in Fig. 4a. through sudden. Thebes formation Results of the experimental investigation The Thebes formation exposed in the valley of kings Geotechnical properties of intact rock specimens and could be subdivided into three members (from base to discontinuities top) Hamadat, Beida and Al-Geer members however, the Twenty-three cylindrical rock specimens have been pre- Thebes formation conformably overlying the Esna Shale. pared from the surrounding rock and the supporting pil- The lower member Hamadat is white, chalky indurated lars to delineate the physical and mechanical properties. limestone with flint concretions, the middle member Specific gravity, unit weight, water absorption, porosity Beida is made up indurated, thick bedded, nodular lime- and degree of saturation are the physical aspects deter- stone with flint bands extending parallel to the bedding mined. While, the mechanical characterization included planes, the uppermost member Al-Geer consists mainly the determination of the uniaxial compressive strength, of white limestone, (Aubry et al. 2008 and Siliotti 1997), elastic static modulus of elasticity and Brazilian splitting as shown in Figs. 4b and 5. tensile strength, as well as the Non-Destructive Ultrasonic There are many faults in the SW corner of the Valley of Pulse Testing to the wave velocity through the brick speci- the Kings; it is very composite in its nature. Number of mens, the dynamic Young’s modulus and shear modulus. faults are cutting the Eocene limestone Formations. Typic- All the soil/rock testing referring to the ASTM. ally, those issue dividers bring differentiated throughout Thin-sections prepared on the limestone samples where sliding, and veins about crystalline calcite have developed the KV5 is excavated, refers that the limestone is in the interceding spaces. The calcite may be stringy Fur- fine-grained calcite, embedded in amicriticmatrixrichin thermore structures overstepping bundles, which provide amorphous silica, fossils like Foraminifera and large grains for the course What’s more sense from claiming slip. of quartz. Ordinary faults, demonstrating level development for The XRD analysis indicated that the major contents of An NE-SW direction, are abundant. However, one sub- Esna shale are quartz (SiO ) and Montmorillonite (Na 2 0.2 stantial fault, on the Nw side of the valley, may be dom- Ca Al Si O (OH) .(H O) , the minor contents in- 0.1 2 4 10 2 2 10 inantly strike-slip (and left-lateral), while others need aid clude the Kaolinite and Illite with Calcite traces. The bulk oblique-slip (left-normal, alternately right-normal). Des- unit weight of the Esna shale is 1.79 to 1.86 g/cm ,and pite those five faults that required been measured are the uniaxial compressive strength is 4.22 to 4.43 kg/cm . not enough will a chance to be statistically significant, Petro-physical properties: Physical measurements re- they are commonly perfect as shown in Figs. 6 and 7. ferred that the unit weight (γ) of marl limestone of KV5 Figures 8 and 9 present the state of preservation of the is between 20 and 21 kN/m , water absorptions (Wa) KV5 and the geological and geotechnical induced rock- were between 10 and 12% and the apparent porosity (n) mass stability problems. Where the brittle rock, high ranged from 14 to 19%. ab Fig. 4 a Esna Shale and b Marl Limestone (Member 1), Gebel El-Gurnah. The main exposed rocks in Gebel El-Gurnah are the Esna Shale (late Paleocene- Early Eocene) and the conformatably overlying Thebes formation (Early Eocene) Hemeda Geoenvironmental Disasters (2018) 5:12 Page 6 of 24 Fig. 5 Geological setting of the Valley of the Kings, Luxor, Egypt. (Geological Egyptian Authority). The Thebes formation exposed in the valley of kings could be subdivided into three members (from base to top) Hamadat, Beida and Al-Geer members however, the Thebes formation conformably overlying the Esna Shale. The lower member Hamadat is white, chalky indurated limestone with flint concretions, the middle member Beida is made up indurated, thick bedded, nodular limestone with flint bands extending parallel to the bedding planes, the uppermost member Al-Geer consists mainly of white limestone Fig. 6 Thebes Formations, Valley of the Kings, Luxor, Egypt. Gebel El-Gurnah is located some 4 km to the west of the River Nile, opposite to Luxor. The main exposed rock units in Gebel El-Gurnah are the Esna Shale and Thebes limestone formations. The tombs of the kings were excavated in the Thebes formations at northern side of Gebel El-Gurnah and the tombs of the queens were excavated at the southern side Hemeda Geoenvironmental Disasters (2018) 5:12 Page 7 of 24 Fig. 7 Rock structures such as joints, bedding’s characters of the Valley of the Kings (KV) Shear Wave Velocities (Vs): Shear wave velocities of The static Young’s modulus (E) = 10 GPa, Poisson limestone samples were measured by PUNDT (ASTM Ratio (ν) = 0.28–0.30, Fig. 10 shows the test set and the 597, ASTM D 2845–83). They varied from 0.7 to results are summarized in Tables 1, 2, 3 and 4. 1.0 km/s (with an average of 1 km/s for an orientation perpendicular on the bedding plane. Uniaxial Compression Test: The compressive strength Analysis of rock mass strength using RocLab program (σ ) for the sidewalls is between 6 and 7 MPa, while the RocLab is a software program for determining rock mass (σ ) for the supporting rock pillars is 1 MPa because of strength parameters, based on the latest version of the the impact of the past and recent flash floods. generalized Hoek-Brown failure criterion. Fig. 8 Extensive structural damage in KV5. Engineering failure of the structural pillars, sidewalls and Ceiling of the Corridors and Chambers in the KV5 (http://www.thebanmappingproject.com/). Permission was granted by Weeks, K.R. © Theban Mapping Project 2006 to reuse this figure Hemeda Geoenvironmental Disasters (2018) 5:12 Page 8 of 24 Fig. 9 Brittle rock, high stress conditions. Rockbursting (the sudden release of stored strain energy) bursts manifest themselves through sudden. (After TMP) Hoek-Brown Classification: Intact uniaxial compres- Results of the numerical analysis and sive strength of intact rock (σ ) =7 Mpa, GSI geo- geotechnical modeling ci logical structure index = 50, intact modulus (mi) = 10, 2D static analysis disturbance factor (D) = 0, intact rock deformation In the initial 2D static analysis, the Sons of Ramses II modulus Ei = 3500 Mpa, modulus ratio (MR) = 500. tomb is modeled by assuming non-linear soil / rock The generalized Hoek-Brown Criterion failure cri- plastic model and the Mohr-Coulomb failure criterion, terion: mb =1.677, s = 0.0039. a = 0.506, where (s) and (Hemeda and Pitlakis 2010), the 2D examine code is (a) are constants of the rock mass, calculated from used for present study. The following parameters are 2 2 the geological strength index (GSI) and disturbance used: φ =30°, c = 500 kN/m , E = 10.100E + 06 KN/m , factor (D). ν = 0.3, Vs = 800 m/sec for the rock material. Mohr-Coulomb Fit: Cohesion c = 0.349 Mpa, Friction The results from the preliminary static analysis angle φ = 30°. which are illustrated in Figs. 13, 14, 15, 16, 17, 18, 19 Rock mass parameters: Tensile strength of intact and 20 indicate that the maximum total displace- rock σ = − 0.016 Mpa, Uniaxial compressive strength, ments of the rock pillars in the large sixteen pillar − 4 Figs. 11 and 12. chamber 3 were 1.2 × 10 mand the vertical Fig. 10 Esna Shale and marl limestone samples under investigation Hemeda Geoenvironmental Disasters (2018) 5:12 Page 9 of 24 Table 1 The geotechnical properties of the intact rock samples Table 3 Shear parameters of the discontinuities (KV5) Type Peak Friction Residual Friction In-Situ No PI (MPa σc (MPa) Sidewalls σc (MPa) Pillars Vs (km/s) RN Joints 30° 30° JRC (L = 1 m) = 3–4 1 0.4 7.1 0.9 0.7 18 Joints 35° 25° c = 30 kPa Φ = 35° 2 0.5 6.9 0.8 0.5 19 Joints 35° 30° – 3 0.4 7.5 0.95 0.8 20 4 0.3 7.0 0.9 0.9 18 Chamber with its sixteen supporting structural rock 5 0.5 6.9 0.8 0.7 17 pillars. 6 0.3 6.6 0.7 0.6 18 A three-dimensional (3D) numerical model for the pil- lared chamber 3 (the largest chamber in Valley of the 7 0.4 7.0 1.1 0.7 19 Kings (with its sixteen supporting rock pillars) and the large northern hall which are excavated in marl lime- displacements were small (of the order of millimeters stone deposit are constructed. he goal of the 3D exami- − 4 − 5 1.5 X10 m), Horizontal displacement 1.25 × 10 m, nations is to assess the pressure state in the columns − 5 the maximum volumetric strain is 3.5 × 10 m, and considering the 3D geometry. The 3D impacts issue is the spalling criterion is 0.22. While the maximum considered on a fundamental designing methodology in ground vertical displacements on the roof of the large the consequent areas. The different reenactments − 5 western two halls were large 4.5 × 10 mand the depicted thus are directed utilizing the PLAXIS 3D code –6 volumetric strain is 7 × 10 . (PLAXIS 3D). The rock pillars in the sixteen pillars largest hall The results from the 3D static analysis which repre- (pillared chamber 3) are under relatively high com- sented in Figs. 21, 22, 23 and 24 indicate that, the rock pression stresses. The calculated effective peak prin- pillars in chamber 3 are under relatively high compres- cipal compressive stresses on supporting rock pillars sion stresses. The calculated peak effective principal are about 900 kPa. The maximum shear stress is vertical compressive stresses on supporting rock pillars 0.15 MPa, and the maximum shear strain is 1.3 × is 827.58 kN/m , the horizontal effective mean stresses − 5 2 10 . 588.91 kN/m , the total displacement of the pillars − 6 − 6 For the large northern hall, The calculated effective 210.01 × 10 m, the vertical displacement 208.36 × 10 m, − 6 peak principal compressive stresses is about 600 kPa the horizontal displacement 32.94 × 10 m, the vertical in- − 6 but the maximum vertical displacement on the roof is cremental displacement 11.29 × 10 m, and the volumetric − 4 − 3 too large 1.2 × 10 m and the maximum volumetric strain 3.62 × 10 %. − 6 strain is 4.5 × 10 , the results of the mathematical For the large northern chamber, the extreme effective modeling are represented in Figs. 13, 14, 15, 16, 17, mean stresses is 567.73 kN/m , the total displace- − 6 18, 19 and 20. Also the maximum vertical stress on ment 475.95 × 10 m, the vertical displacement − 6 − 3 the roofs and sidewall of Chamber 1 and Chamber 2 475.59 × 10 m, the volumetric strain 12.42 × 10 %, − 3 reached 350 KPa, and the maximum vertical displace- the extreme volumetric strain incremental 1.38 × 10 %, − 5 − 6 ment reached 4.5 × 10 m, see Fig. 15, 16, 17, 18, 19 and the horizontal displacement 53.60 × 10 m, and 20. Figs. 24, 25, 26, 27, 28 and 29. Also the maximum vertical stress on the roofs and sidewall of Chamber 1 3D static analysis Table 4 RMR value for the KV5 is determined as follow The low rock strength where the KV5 is excavated af- Item Value Rating fects seriously the safety of the tomb both under static Uniaxial Compressive 900 KPa 1 and seismic loading conditions. The PLAXIS 3D was Strength used for the 3-D numerical analysis of the central main RQD 50 13 Spacing of Discontinuities <60 mm 5 Table 2 The geotechnical properties of the intact rock samples with depth (KV5) Conditions of Separation 1–5 mm. 10 Discontinuities Continuous joints Depth Weathering Grade UCS (MPa) E (MPa) Ground water Completely dry 15 0-2 m IV 1–5 2000 Adjustment for Joint −5 2-4 m III 5–10 6000 Orientation 4-6 m II-III 10–11 10,000 Total RMR 39 Poor 6-8 m III 12–13 10,000 rock Hemeda Geoenvironmental Disasters (2018) 5:12 Page 10 of 24 Fig. 11 Major and minor principal stress curve of marl limestone (KV5) using the RocLab program and Chamber 2 reached 688 kPa, on the separate wall lowering of the ceiling level of these small burial cham- between them, the 2D model did not calculate it, and bers. Figure 27 represents the displacement progressive the maximum vertical displacement of the ceiling curve for the supporting rock pillars. − 3 reached 0.18 × 10 m. as shown in Figs. 30, 31, 32 and 33. Evaluate the safety factor and stress state in the Figures 25 and 26 represent the analysis results of the structural support pillars large model which represents the complete east-west It is demonstrated that induced stresses of signifi- cross section of the tomb indicated that the stress distri- cant magnitude and ambiguous distribution are to be bution and displacement values on the structural rock expected in the supporting pillars. Multiple openings pillars in the Chamber 3 and Chamber 1 and 2 did not and excavations designed on the basis of the average increase due to the excavation process extended behind stress in the pillar σv given by the tributary area the sixteen pillared Chamber 3 may it is due to the theory, as explained in Eq. 1. Fig. 12 Shear stress-Normal stress curve of Marl limestone (KV5), using the RocLab program Hemeda Geoenvironmental Disasters (2018) 5:12 Page 11 of 24 Fig. 13 Effective vertical stresses distribution through the rock pillars in Chamber 3. Examine 2D. All units of distance and depth in all figures are in meter pillar q , because shape anδ size effects introduce signifi- At u σv− ¼ σv ð1Þ cant modifications from the breaking strength of uncon- AP fined compressive cylinders. The strength in compression for rectangular pillars of Where, square cross section can be estimated from the Eq. 2. – A is the area supported by the pillar 0:5 W h – Α is the area of the pillar σ ¼ 0:875 þ 0:250 ðÞ q ð2Þ p p H hcri – σ is the vertical stress at the level of the roof of the excavation (catacombs) Where, To evaluate the degree of safety of a pillar, we must be compare the above average pillar stress σ with the pillar – σ is the strength of the pillar, ν p strength σ . The latter is not simply the unconfined – W and H are the width and height of the pillar p − compressive strength of the material comprising the respectively, Fig. 14 Spalling Criterion through the rock pillars in Chamber 3. Examine 2D Hemeda Geoenvironmental Disasters (2018) 5:12 Page 12 of 24 Fig. 15 Vertical displacement distribution through the rock pillars in Chamber 3. Examine 2D – q is the UCS strength of the pillar material on we assume h = 0.2 m and h = 1 m for q = 900 Kpa, u crit u cylinders with height (h) equal to twice the diameter we have σ = 1922 kPa. σp and And the Factor of Safety F.S = ¼ = 1.37 which σv− 1400 – h is the minimum height of the cubical specimen crit very low and indicate to the dangerous and unsafe situ- of pillar material such that an increase in the ation and losing of the structural function of these load specimen dimension will produce no further bearing pillars. Hoek and Bray quote Salamon and Mun- reduction in strength. ro s suggestion of acceptable safety factors > 1.6. Such values may be adequate for the excavation stability, For the pillars, see Fig. 21, σ = 700Kpa, A =2 m and ν t (Hemeda et al. 2010). Α =1 m we can derive: σc 900KPa Also overstress state ¼ ¼ ¼ 1:28MPa σv 700kPa σv ¼ x700 ¼ 1400 KPa 1 ð3Þ The strength of the pillar σ can be estimated from The tributary theory is based on average pillar the equation: For the pillar we have W = 1 m, H = 3 m. If stresses and derived stress value is generally close to Fig. 16 Volumetric strain distribution through the rock pillars in Chamber 3. Examine 2D Hemeda Geoenvironmental Disasters (2018) 5:12 Page 13 of 24 Fig. 17 Effective vertical stresses, the ceiling and sidewalls of northern Chamber. Examine 2D the averages predicted by PLAXIS 3D.On other hand, Design of structural supporting systems the overloading of geostatic loading due to the over- The first option, which depend on the RMR burden strata on the supporting rock pillars is obvi- Rock Mass Rating system is based on combination of ous and it induced critical vertical cracks in these six parameters = Intact Rock Strength, RQD, Joint pillars also some sections have an overriding influence Spacing, Joint Conditions, Groundwater and Adjust- on the pillar stability, Eq. 3, particularly in terms of ment factor. long-term creep effects and associated strength loss The first option depends on the BieniawskisRMR or thinning-out of the effective load bearing pillars (Bieniawski 1989) (Rock Mass Rating System) calcula- and section, (Hemeda 2008). In the original study of tion, where the strength of intact rock is 900 kPa Salamon and Munro this occurred between safety fac- (with rate 1), the RQD is 50 (with rate 13), the spa- tors of 1.3 to 1.9 with the mean being 1.6. This value cing of joints less than 60 mm (with rate 5), the con- was recommended for the design of production pillars ditions of discontinuities is Separation 1–5 mm with in South African bord and pillar workings (Salamon Continuous joints (with rate 10) and the ground and Munro 1967). water conditions are completely dry (with rate 15), Fig. 18 Spalling Criterion for the ceiling and sidewalls of northern Chamber. Examine 2D Hemeda Geoenvironmental Disasters (2018) 5:12 Page 14 of 24 Fig. 19 Vertical displacement of the ceiling and sidewalls of northern Chamber. Examine 2D for the adjustment for joint orientation is −5then The Q-system of Barton et al. (Barton et al. 1974, The RMR of the Sons of Ramses II tomb is (39) Barton 1988) expresses the quality of the rock mass in which classified as poor rock with high stresses, as the so-called Q-value. The Q-value is determined as fol- showninTable 4. lows, Eq. 4: According to the RMR value, the design of the support From the Q-system parameters which include the system for the pillars and whole KV5 can include Sys- RQD is 50, Jn with value 4, Jr. with value 3, Ja with value tematic bolts 4–5 m long, spaced 1–1.5 m in Crown and 1, Jw with value 1. walls with wiremesh.100–150 mm in Crown and100mm RQD Jr Jw insides with Light to medium ribs Spaced 1.5 m where Q ¼ : x x ð4Þ required. Jn Ja SRF For a depth below surface of 17 m, the overburden stress 2 3 will be approximately 17m X21kN/ m =396 kpa. The The second option, which depend on the Q-system major principal stress σ1 is 2 ×396 =792 kPa. Given the The 2nd option depends on the Barton’s Q-system or uniaxial compressive strength of the supporting rock pillars the rock tunneling quality index of the rock mass where σc 900 the tomb is excavated. is approximate 900 KPa, this gives a ratio of = = σ1 792 Fig. 20 Volumetric strains of the ceiling and sidewalls of northern Chamber. Examine 2D Hemeda Geoenvironmental Disasters (2018) 5:12 Page 15 of 24 Fig. 21 Effective mean stresses distribution through the rock pillars in Chamber 3. PLAXIS 3D 1.136 < 2.5 which refer to a high stressed poor rock with 5–9 cm. Length of rockbolts with L = 2+ (0.15B/ESR) SRF 20, then Q or rock mass quality value is 1.87 (poor and Maximum span (unsupported) = 2 ESR X Q rock according to the Q-system), as shown in Table 5. (Fig. 28). The strength properties of FRPs collectively For an excavation span (the width of the pillared make up one of the primary reasons for which select them chamber 3) of 15.6 m, the equivalent diameter, De = in the strengthening and seismic retrofitting. A material’s 15.46/1.6 = 9.66, where the ESR or the permanent open- strength is governed by its ability to sustain a load without ing is 1.6 and the width of the pillared chamber 3 is excessive deformation or failure. Also it is recommended 15.46 m. to use the Carbon FRP also nowadays we can use the ad- The value of De of 9.66 and value of Q of 1.87 vanced or Nano CFRP because of its good mechanical places the tomb of sons of Ramses II in category (5) properties in particularly the compressive and tensile which require Fiber Reinforced Shotcrete and bolting strength. Fig. 22 Vertical displacements of the support rock pillars in Chamber 3. PLAXIS 3D Hemeda Geoenvironmental Disasters (2018) 5:12 Page 16 of 24 Fig. 23 Horizontal displacements of the support rock pillars in Chamber 3. PLAXIS 3D The third option so intimately interlocked that vertical walls do not require The third option for the permanent support for this lateral support. In rocks of this type, both spalling and pop- complex kind of underground structures could be de- ping conditions may be encountered. signed as presented in Fig. 34, Where the rock bolts with It is notice that In brittle rock, high stress conditions 4–9 cm and prestressed anchors or micro piles with may lead to rock bursting (the sudden release of stored 100 mm Diameter for the permanent support system for strain energy) bursts manifest themselves through sudden, the rock pillars and sidewalls of the KV5. as shown in Fig. 9. Analysis and interpretation of the numerical and la- Discussion of numerical, laboratory analysis boratory results and the field observations led to the fol- results and the field observations lowing findings:- Therock masswhich thesonsofRamsesIItombis excavated can be classified as moderately to extensively 1. Most of the Royal Tombs in the Valley of the Kings jointed or fractured rock contains joints and hair cracks, were excavated into the marls of the middle and but the blocks between joints are locally grown together or lower part of Member I. Fig. 24 Volumetric strains of the support rock pillars in Chamber 3. PLAXIS 3D Hemeda Geoenvironmental Disasters (2018) 5:12 Page 17 of 24 Fig. 25 Vertical displacement of rock pillars in Chamber 3and others small burial chambers 2. Presence of swelling-type clay minerals (Montmoril- changes in the underlying Esna shale, as shown lonite) in some rocks of the Thebes in Fig. 6. Formation but, more importantly, in the underlying 6. The lowermost unit of the Thebes Formation. rocks of Esna formation. (Clay layers swelling). However, KV5 penetrate into the underlying 3. The index properties show that the shale layers are interbedded shale and marls of the Esna Formation. medium expansive. All of them show severe, irreversible rock structure 4. Anhydrite found in abundant quantities in the Esna deterioration originating from swelling and Shale, may be a factor contributing to swelling of shrinkage. Water and debris from the past and the Esna Shale. recent flash floods had major impacts on wall 5. Rock slope deformations (spreading) of the decoration of the uppermost chambers and on Thebes limestone blocks caused by volume pillars and wall structure in the chambers 1, 2 and Fig. 26 Volumetric strains of rock pillars in Chamber 3and others small burial chambers Hemeda Geoenvironmental Disasters (2018) 5:12 Page 18 of 24 Fig. 27 Displacement progressive curve for the supported rock pillars in KV5 Fig. 28 Proposal support system for the (KV5) according to the Barton’s Q-system Hemeda Geoenvironmental Disasters (2018) 5:12 Page 19 of 24 Fig. 29 Temporarily support system for the KV5, installed recently by the Theban Mapping Project. After TMP. Permission was granted by Weeks, K.R. © Theban Mapping Project 2006 to reuse this figure. 8. Gravity rock falls and sliding of rock features along 3. Historic flooding since the discovery of the tomb has caused major destruction of walls and pillars by inclined discontinuities at the surrounding area. repeated swelling and shrinkage of the shale. 9. Extensive jointing (rock discontinuities) present in Moreover, accelerated humidity changes over the the rock at tomb depth. past 100 years have contributed to increasing 10. The overloading of geostatic loading due to the deterioration of the rock structure. overburden strata on the supporting rock pillars is 7. The removal of shake units preceding the tomb obvious and it induced critical vertical cracks in uncovering brought about copious shake joints, which these pillars also some sections have an overriding can be re-actuated amid quakes or other quick pres- influence on the pillar stability, particularly in terms sure discharges, for example, by swelling of the shale. of long-term creep effects and associated strength At the point when water enters the tombs, it comes loss or thinning-out of the effective load bearing into contact with the shale at the lower chambers, and pillars and section, as shown in Fig. 35. causes swelling, splitting and auxiliary disappointments 11. Rock detachment and falls from the ceiling, as in the floors, dividers, and columns. shown in Fig. 9. Fig. 30 Effective mean stresses in the ceiling and sidewalls of northern Chamber. PLAXIS 3D Hemeda Geoenvironmental Disasters (2018) 5:12 Page 20 of 24 Fig. 31 Plastic Points in the ceiling and sidewalls of northern Chamber. PLAXIS 3D 12. Shape and measures deformation of the tombs or sections and supporting rock pillars to less than some sections of them. 1 MPa. Those secondary fossils content, due 13. Detachment and falls of renders with its wall basically on shells about foraminifers and a paintings. portion mollusks, provide for climb on structural 14. Intensive weathering and erosion of lower parts of heterogeneity, which reflected in the variability of the structural elements in particularly the the mechanical properties What’smoreinthe supporting rock pillars in Chamber 3. The main poor reproducible of the test results (Bukovansky structural deficiency attributed to the impact of et al. 1997). flash floods in the past and few years ago, as 16. Nearness of extensive, vertical, open cracks at the shown in Fig. 8. surface of slopes on the two sides of the valley. 15. Physical, mechanical and chemical changes in the These breaks can be followed both in the valley construction materials. The strength reduction is parcels where the tombs are found. The cracks obvious and the UCS reached in some critical are effortlessly obvious in the greater part of the Fig. 32 Vertical displacement of the ceiling and sidewalls of northern Chamber. PLAXIS 3D Hemeda Geoenvironmental Disasters (2018) 5:12 Page 21 of 24 Fig. 33 Volumetric strains of the ceiling and sidewalls of northern Chamber. PLAXIS 3D region. The beginning of these cracks has never maximum span (unsupported) = 2 ESR X Q ; also been deciphered, albeit a few geologists viewed nowadays we can use the advanced or nano carbon them as issues. tubes because of its advanced physical and mechan- 17. The numerical analysis results indicated that the ical properties in particularly the compressive and safety factor of the structural support rock pillars in shear strength. The third proposal is the installation chamber 3 is very low in order of 1.37 and the of rock bolts with 4–9 cm and prestressed anchors or overstress state is 1.28 MPa. micro piles with 100 mm Diameter for the permanent support system for the rock pillars and sidewalls of Remedial and retrofitting policies and techniques, the KV5. static monitoring and control systems which are ne- cessary for the strengthening and stability enhance- ment of the tomb, where the rock mass classification Conclusions indicated the rock mass where the KV5 is excavated We can state that most of what we can call now geo- is poor rock, with RMR 39 and Q value 1.87. technical problems was faced in the Valley of Kings Systematic bolts with 4–5 m long, spaced 1–1.5 m where most of the large important subterranean deco- in Crown and walls with wiremesh.100–150 mm in rated tombs of the pharaohs like sons of Ramses II Crown and 100 mm insides with Light to medium tomb KV5 are found. This case study illustrates how ribs Spaced 1.5 m where required for strengthening the quantification of various variables permits an un- retrofitting of the KV5. Also it is recommended to derstanding of the problems facing a site and also use Fiber Reinforced Shotcrete and bolting 5–9cm. suggests possible solutions. Length of rock bolts L = 2+ (0.15B/ESR) and In conclusion the detailed engineering analysis of the sons of Ramses II tomb KV5 at Luxor, Egypt proved that these unique monuments present low Table 5 Rock Tunneling quality index, Q-system determined as safety factors of the rock pillars which are structur- follow ally damaged, where the factor of safety F.S is about Parameter Description Value 1.37, (note that the acceptable safety factor for the RQD Rock Quality Designation 50 underground structures is > 1.6 in static state). Also Jn Joint Number 4 the overstress state of the surrounding rocks is be- Jr Joint Roughness 3 yond the elastic regime (limit of domain), and all the rock pillars structural supports are subjected to high Ja Joint Alteration 1 vertical compressive stresses. Many instability prob- Jw Joint Water Reduction Factor 1 lems for static and dynamic loading were recorded SRF Stress Reduction Factor 1.13 and analyzed. Consequently a well-focused strength- Total Q-System 1.87 Poor rock ening and retrofitting program is deemed necessary. Hemeda Geoenvironmental Disasters (2018) 5:12 Page 22 of 24 Fig. 34 Design of rockbolts, prestressed anchors and micropiles for the permanent support system for the rock pillars and sidewalls of the KV5 Hemeda Geoenvironmental Disasters (2018) 5:12 Page 23 of 24 Fig. 35 Present state of the sixteen supporting rock pillars in the Chamber 3. which are structurally damaged. Vertical cracks due to the overloading and strength regression are obvious (http://www.thebanmappingproject.com/). Permission was granted by Weeks, K.R. © Theban Mapping Project 2006 to reuse this figure Abbreviations Publisher’sNote Ja: Joint alteration number; JCS: Joint compressive strength; Jn: Joint set Springer Nature remains neutral with regard to jurisdictional claims in number; Jr.: Joint roughness number; JRC: Joint roughness coefficient; published maps and institutional affiliations. Jw: Joint water reduction factor; Q: Rock mass quality; RMR: Rock mass rating; RQD: Rock mass designation; SRF: Stress reduction factor Received: 9 November 2017 Accepted: 27 May 2018 Symbols Aj: Joint area; At: is the area supported by the pillar; b u: Shear displacement; c: Cohesion between block joints; Ds: Rib spacing; Ei: Modulus of elasticity of References intact rock; hcrit: is the minimum height of the cubical specimen of pillar Aubry, M.-P., W.A. Berggren, C. Dupuis, E. Poorvin, H. Ghaly, D. Ward, C. King, R.O.’.B. material such that an increase in the specimen dimension will produce no Knox, K. Ouda, M. Youssef, and W.F. Galal. 2008. 2015 TIGA: a geoarcheological further reduction in strength; Lcp: Reaction length; M D: Bending moment at project in the theban necropolis. In Proceedings of the X International Congress of yield limit; M p: Bending moment at plastic limit; N p: Normal force at failure; Egyptologists, Rhodes. luxor, Egypt: West Bank. Po: In situ stress; Qcf: Shear force; Qp: Shear force at failure; qu: is the UCS Barton, N.R. 1988. Rock mass classification and tunnel reinforcement selection strength of the pillar material on cylinders with height (h) equal to twice the using the Q-system. In Rock classification system for engineering purposes: diameter; U: The shear displacement at each step of loading; W and H: are ASTM special technical publication 984.1. ASTM International, ed. L. Kirkaldie, the width and height of the pillar respectively,; x τ: Shear stress in resin 59–88. annulus; α: Decay coefficient 1/in which depends on the stiffness of the Barton, N.R., R. Lien, and J. Lunda. 1974. Engineering classification of rock masses system; Αp: is the area of the pillar; β: Angle between the normal to the for the design of tunnel support. Rock mechanics and rock engineering, fracture plane and the horizontal plane; β: Reduction coefficient of dilation Springer. 6 (4): 189–236. angle; ν: Poison ration of rock mass; σ b: Applied stress; σ c: Uniaxial Bieniawski, Z.T. 1989. Engineering rock mass classifications. New York: John Wiley compressive strength of rock; σ n: Normal force; σp: is the strength of the and Sons. pillar,; σν: is the vertical stress at the level of the roof of the excavation (KV5); Brown, E.T. 2012. Risk assessment and management in underground rock ϕ b: basic joint friction angle; ϕ: Friction angle of the fracture engineering—An overview. 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