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Mobilization analysis of the dolmen of Dombate (Northwest Spain)
Engineering Geology 100 (2008) 59–68
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Engineering Geology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e n g g e o
Mobilization analysis of the dolmen of Dombate (Northwest Spain) Vicente Navarro a,⁎, Luis E. Romera b, Ángel Yustres a, Miguel Candel a a b
Geoenvironmental Group, School of Civil Engineering, University of Castilla-La Mancha, Avda Camilo José Cela s/n, 13071, Ciudad Real, Spain School of Civil Engineering, University of A Coruña, Campus de Elviña, 15071, A Coruña, Spain
A R T I C L E
I N F O
Article history: Received 4 July 2007 Received in revised form 15 February 2008 Accepted 5 March 2008 Available online 12 March 2008 Keywords: Stability Mobilization Megalithic structure Dolmen Northwest Spain
A B S T R A C T This paper presents an analysis of the mobilization of the dolmen of Dombate, a megalithic monument situated in the Northwest of Spain. The study is founded on simple static principles, with the application of basic concepts of soil mechanics (soil reactions were computed by the reaction modulus method) and rock mechanics (a simple secant approach was adopted to model the contact between orthostats). In addition, a simplified geometric model for dolmens was adopted. On the basis of these concepts, a numerical solver able to provide quick estimations of the system's mobilization was developed. Using this tool, a number of sensitivity analyses were conducted to estimate the mobilization that could be caused by a conservation project currently under consideration. It was found that mobilization might be excessive, and therefore, a safer procedure is proposed. In short, this paper puts forth a new rational approach for archaeological practices which may help to estimate the possible consequences of excavations and rehabilitations on megalithic structures. © 2008 Elsevier B.V. All rights reserved.
1. Introduction The dolmen of Dombate, located in Cabana county (Galicia, NW of Spain; see Fig. 1a), is a large scale passage monument, bigger in size that those commonly found in Galicia (Bello et al., 1999). The chamber consists of seven rectangular orthostatic slabs in a sub-rectangular shape measuring approximately 3.6 m by 2.7 m (Fig. 1b) and 3 m in height. The passage is 4 m long and consists of 3 orthostats on either side. The tumulus that is placed over the dolmen is made of clayed soil, probably obtained after sieving, and is covered by coarse gravel to prevent erosion. While at the present time the tumulus is not fully covered by the gravel, it was probably initially protected by a complete layer (Bello et al., 1999). In its final configuration, as Bello (1993) reports, the tumulus reached the height of the passage and only the upper part of the chamber orthostats was visible (Fig. 2g). The history of the construction of the monument is quite complex. According to Bello (1993), first a smaller dolmen was constructed with a simple, open chamber of considerable length (Fig. 2a and b). Then the actual dolmen was added to this monument. After digging the foundation trenches (Fig. 2c), the keystone was positioned (Fig. 2d). Then, the rest of the chamber and passage orthostats were laid out (Fig. 2e and f). Finally, the covers were put into place. There is no apparent evidence of how this
⁎ Corresponding author. Tel.: +34 926 295 300x3264; fax: +34 926 295 391. E-mail addresses: [email protected] (V. Navarro), [email protected] (L.E. Romera), [email protected] (Á. Yustres), [email protected] (M. Candel). 0013-7952/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.enggeo.2008.03.002
operation was carried out or if it was done before or after the tumulus was placed. All the data were gathered over the course of three study periods (summers 1987–88–89) when partial excavations were carried out to reveal the present state of the dolmen, as shown in Fig. 3, and its initial state in Fig. 1c. The sedimented fill which accumulated in the chamber during the lifetime of the dolmen had been completed excavated and reached the natural ground surface. Among the significant finds, it should be stress the importance of the paintings that decorate the chamber slabs and those of the entrance passage. These paintings date to around 5000– 4500 B.C. (Bello et al., 1996). In order to avoid possible stability problems caused by excavation in the dolmen, an oak roof truss was put in as shown in Fig. 3d. The effectiveness of this method cannot be verified since no monitoring tool was used. In any case, the potential mobilization was not observed at first glance. A conservation project of the entire site is currently under consideration. This project is studying the possibility of executing a series of architectural works in the area surrounding the dolmen to achieve favourable environmental conditions for the conservation of the paintings. The project would also allow limited access to the public contingent upon the application of security measures (Bello et al., 1999). The substitution of the oak truss for a permanent element has been proposed under this project. At this point in time, it is of utmost importance to estimate the possible mobilization that may occur during the process of truss substitution before this operation is carried out. The estimation of this mobilization is the immediate goal of this paper, although a more general objective has also been targeted, i.e. the development of a
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Fig. 1. (a) Location of the dolmen. (b) Plan view of the dolmen without the cover, and numbering system of the orthostats. (c) Artistic representation of the dolmen before the investigation (Provincial Government of La Coruña web site).
feasible methodology to estimate the sensitivity of megalithic structures to the actions currently being carried out in archaeological practices. 2. Complexity of the system Generally speaking when archaeologists set out to work on a megalithic structure, particularly a dolmen, reliable estimates of the consequences of their works on the stability of the structure are scarce. As a result, the assessment of potential mobilization is sometimes based only on intuition. While these procedures may seem arbitrary, owing to the system's complexity, there really is no other choice. Basically, a dolmen is a structure formed by rigid slabs(the orthostats), which are set in the ground almost vertically with lateral supports in between. The structure is usually covered by a capstone or cover (Fig. 1c). The analysis of a dolmen's behaviour is a complete problem of structures, continuum mechanics, soil and rock mechanics. Hence, in the area where the orthostats contact the soil foundation, there are both a classical lateral earth pressure problem, and a settlement problem. On the other hand, at contact between the orthostats and between the orthostats and the cover, there are contact surfaces which can be solved using the existing formulations in rock mechanics to analyze the behaviour of joints. So, the simulation of a dolmen's behaviour is an extremely complex problem whose resolution requires a great deal of information, which is very difficult to obtain. Moreover, even if simple mechanical models are used, an aspect as basic as the geometry of the orthostats will still be unknown. Unknown factors including not only the shape of the buried parts of the orthostats, but also the shape of their visible parts, will be difficult to input exactly into calculations. As a result, it is reasonable to assume an idealization of the dolmen to evaluate the mobilization induced by excavation and other works that may have altered its original condition. Given the flat shape of the orthostats and the cover, the purpose of this work is to schematize the geometry through a “slabs model” (see Figs. 4 and 5). The middle plane of each orthostat is ideally represented by an irregular hexagon. The thickness variation is assumed to be linear between the base and the central area, and between the central area and the top surface (thickness H1, H2 and H3 in Fig. 4). The position of each slab with respect to a global reference system is determined by defining the reference coordinates of points P1 and P2 (see Fig. 4) (6 unknowns), the local coordinates of P1L (Fig. 4) in the slab plane (2 unknowns), and the values of e1 and e2 (2 unknowns). Moreover, to define the slab geometry it is necessary to provide the dip direction and angle (2 unknowns), the values of H1, H2 and H3 (3 unknowns), and, finally, the
coordinates of points 1, 3, 9,10, and 6 with reference to point 8 in the slab plane (10 unknowns). There are a total number of 25 geometrical unknowns per slab. In order to determine the unknowns in the seven orthostats and in the cover of the dolmen's chamber, a high precision topographical study was carried out, measuring 50 points per stone. Also, the embedded depth of the orthostats in the ground was estimated by means of a geoelectric investigation based on the application of sounding and electric tomography techniques. By combining these data with the information gathered in previous excavations (Bello et al., 1999), the digital model shown in Fig. 5a was created, which then allowed us to identify the slabs model presented in Fig. 5b. Also obtained from the digital model, was an estimated foundation width and the equivalent widths of the lateral contacts between the orthostats and the ground (B1, B2 and B3 in Fig. 6a). These widths were used in the slabs model to calculate the foundation reaction (t1) and the thrust exerted by the ground on the lateral surfaces of the orthostats (thrusts t2, t3, t4 and t5 in Fig. 6b). All these forces were assumed to be contained in the middle plane. On the other hand, the thrusts generated by the movement of the slabs against the foundation ground (tI and tE1) and against the tumulus on the external face of each orthostat (tE2), were assumed to be normal to the slabs. Both the base reaction and all the thrusts are conditioned by the water table position (ZWT, Fig. 6a), which is situated near the ground surface in winter (level 0), and at a depth of 3.30 m in summer (Carrera, in Bello et al., 1999). Despite its limitations (among others, lack of soil continuity, and dependence of the soil model on the problem analyzed; Poulos and Davis, 1980; see also, Potts, 1993), the Winkler method has been widely employed in foundation practice because it provides a relatively simple means of analysis and enables factors such as nonlinearity, variation of soil stiffness with depth, and layering of the soil profile to be taken into account readily, if only approximately (Poulos and Davis, 1980). Therefore, both reaction and lateral earth pressure were computed by the Winkler method. As mentioned in the preceding paragraph, shear stresses were ignored, which is common practice in these kinds of approaches (Potts,1993). The subgrade reaction modulus was assumed to be equal to 40 times the ultimate bearing pressure (Bowles, 1988), which was computed by Hansen's bearing capacity method (see also Bowles, 1988, for example). Lateral earth pressure was computed using the load–movement relationship depicted in Fig. 7. Active, ua, and passive, up, pressures were computed using the Müller-Breslau
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Fig. 2. Constructive process of the monument: (a) and (b) construction of the small dolmen; (c) excavation of the foundation trenches; (d), (e) and (f) placement of the orthostats; (g) construction of the tumulus and placement of the covers. From Bello (1993).
formulation (Müller-Breslau, 1906; in Clayton et al., 1993), while earth pressure at rest, uo, was calculated using the Jacky's equation (Jacky, 1944). On the basis of this formulation, the ground was characterized by bulk density, ρn, internal friction angle, φ, cohesion, c, and displacements, δa and δp (Fig. 7). In keeping with the current practice in Spain, the friction between the ground and the orthostats, δ, was assumed to be 2/3 of φ (ROM, 1994). The slabs model not only provides an “orientation” of the ground reactions (Fig. 6b), but it also suggests the direction of the contact forces between the orthostats. During the construction process of the chamber, the new orthostats were set so that they leaned against the existing ones (see Fig. 2d and e), generating basically orthogonal contact forces to the middle planes of the new orthostats. This led to the adaptation of a contact model between the orthostats based fundamentally on a normal force, fN, which is a function of the separation between the orthostats, u. It is common practice to estimate the growth of fN while u decreases by means of hyperbolic models (see for instance, Bandis et al., 1983; or Barton et al., 1985), or
logarithmic models (Rutqvist and Tsang, 2003). For both model types, the main parameters are the maximum contact amplitude, uM, and the curvature or velocity at which the contact force increases as the distance between contact surfaces changes. In this work, while value uM of the asperity amplitude was estimated from the roughness profiles published by Barton and Choubey (1977) to define the joint roughness coefficient (JRC) of the contacts (Fig. 8), there was not enough information to determine the curvature parameter. As a result, a simple secant model characterized by the normal contact stiffness kN was adopted. Unlike the case of the contact areas between the orthostats, the shear forces were not ignored in the bearing areas of the cover. Although these forces would be small in magnitude, they always have a considerable eccentricity. For this reason, these shear forces may play an important role in stabilizing the structure. In order to calculate these forces, the bilinear formulation shown in Fig. 9 was used. The ultimate shear force, fTU, was calculated by applying a simple frictional model in which the basic friction angle ϕb was used as a friction angle
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Fig. 3. Present state of the dolmen: (a) Aerial view. (b) View from the passage. (c) View from the orthostat 4. (d) Oak truss. Provincial Government of La Coruña web site.
(see Barton, 1973). Therefore, a conservative hypothesis was assumed whereby it was disregarded an increase in resistance against shear due to the contact roughness.
minimum value of ϕb for rock joints without fill (Barton et al., 1974). Finally, if the peak shear displacement vPEAK is assumed to be equal to the maximum contact amplitude uM, then the characteristic orthostat
3. Estimation of the model parameters Although the previously described model assumes a major simplification of the system, a good number of parameters still need to be defined. Fortunately, some of these parameters were obtained with fairly good precision. For instance, the bulk density of the orthostats, ρO, was determined to be 2.54 g/cm3, according to the calculations made by the Edaphology and Agricultural Chemistry Department at the University of Santiago (Silva et al., 1996). This research group obtained a uniaxial compressive strength value of 83.5 MPa for the parallel planes, and 57.7 MPa for the normal planes to the exfoliation of the orthogneiss forming the orthostats. While the latter two parameters are not used directly in the model, they are of interest because they indicate that the orthostat material has a relatively low strength. The orthostats were also estimated to have a JRC value of 10, identified visually by the roughness profiles of Barton and Choubey (1977). According to this value and what is shown in Fig. 8, the asperity amplitude of the contact was deduced to be about 5.2 mm, with a resulting uM value of around 10.4 mm. If it was assumed that, after this movement, the normal compression in the contact areas is somewhat lower than the uniaxial compressive strength in the most resistant direction of the rock, then the contacts' normal stiffness will be a little over 7 GPa/m. This is a very conservative estimation (see for instance Itasca, 2002) So, it will lead to overdimensioned estimations of the mobilization of the dolmen. The estimations are magnified to an even greater extent, since, owing to the lack of data, it was decided to use a basic friction angle of 25° — the
Fig. 4. Idealized geometry of an orthostat : “slab model”.
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Fig. 5. (a) Digital model of the dolmen chamber: Front view from the passage. (b) Idealization of the dolmen using the slabs model.
parameters included in Table 1 are obtained. The contact areas between the orthostats, and between the orthostats and the cover, are also included in Table 1. The boring holes (Carrera, 1999) and the excavations carried out (Bello et al., 1999) played a key role in determining the ground parameters. Thanks to these investigations, it was possible to establish that the sandy soil with a considerable fraction of fines (soil SC in the Unified Soil Classification System, USCS) of the foundation is the weathering product of the schists and paragneisses of the Laxe formation. Its average gravimetric water content is 30%. Therefore, assuming a solid particle density of 2.7 g/cm3 and a degree of saturation close to 1, the following values were obtained: a porosity of nearly 0.45, a dry density of approximately 1.49 g/cm3 and a bulk density of around 1.94 g/cm3 (Table 2). On the basis of SPT testing (average number of blows NSPT = 20), and taking into account past experience with similar material from the same area, the resistant behaviour of the foundation ground is correctly described by an internal friction angle of 30° and a cohesion of 18 kPa. On the other hand, after sieving a number of samples, the tumulus material was identified to be a fine grained soil, categorized as CL-ML in the USCS (liquid limit of 20 and a plasticity index of 6). The average gravimetric water content was estimated to be 32% on the basis of the
samples analyzed. As a result, if the solid particle density is considered to be 2.7 g/cm3 and the average degree of saturation is equal to 98%, a porosity of 0.4, a dry density of 1.44 g/cm3, and a bulk density of 1.89 g/cm3 were deduced (Table 2). The degree of saturation was estimated using suction data from tensiometer measurements carried out by Carrera (in Bello et al., 1999), and assuming a water retention curve consistent with its textural characteristics. Only 5 direct shear consolidated-drained tests were successfully performed, and quite disperse results were obtained. Conservative values were adopted for an internal friction angle of 20° and a cohesion of 10 kPa. The estimation of the active and passive displacements, δa and δp in Fig. 7, is always a complex task. Without going into a detailed explanation of the problem, since a discussion of this type would be beyond the scope of this paper, it is obvious that the simplification inherent to the use of Winkler models is especially “conspicuous” since it is necessary to adopt a “magic” parameter that defines both the yield condition, and the stiffness of the “soil-spring”. Although this depends, without a doubt, on soil type, it is not a constitutive question, rather it is a problem of identifying parameters to improve the Winkler model. In the case of the dolmen of Dombate, the δa and δp values proposed in Table 2 represent a compromise. Firstly, these values are low enough to be able to simulate
Fig. 6. (a) Foundation width, B1, and lateral contacts, B2 and B3, between the orthostats and the ground used in the slabs model. (b) Thrust generated by the ground reaction against the slab movements.
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V. Navarro et al. / Engineering Geology 100 (2008) 59–68 Table 1 Properties of the orthostats
Fig. 7. Simplified load–movement relationship adopted to compute lateral earth pressure against orthostats.
Fig. 8. Frequency diagram of the asperity amplitude associated with JRC of 10 obtained from the digitalization of the roughness profile proposed by Barton and Choubey (1977).
the dolmen construction (see Table 3) without predicting a collapse. Secondly, they are high enough to predict over-dimensioned mobilizations. Thus, with the values of Table 2, at a depth of 1 m, the soil foundation will have an active reaction modulus of 1196 kN/m3 while the passive modulus will be equal to 7869 kN/m3. These values are very low, considering the fact that a reaction modulus is commonly assumed to be between 5000 and 16 000 kN/m3 for loose sand (Bowles, 1988). 4. Simulation of the mobilization of the dolmen and sensitivity analysis After defining the conceptual model and estimating its parameters, a calculation module capable of reproducing the dolmen's behaviour
Parameter
Value
Rock bulk density, ρo Uniaxial compressive strength (parallel to foliation) Uniaxial compressive strength (perpendicular to foliation) Joint roughness coefficient, JRC (°) Basic friction angle, ϕb (°) Maximum amplitude of the contact, uM Peak shear displacement, vPEAK Contact normal stiffness, kn
2.54 g/cm3 83.5 MPa 57.7 MPa 10 25 10.4 mm 10.4 mm 7 GPa/m
Contact areas between orthostats Orthostats 1 and 2 Orthostats 2 and 3 Orthostats 3 and 4 Orthostats 4 and 5 Orthostats 5 and 6 Orthostats 6 and 7
0.065 m2 0.06 m2 0.08 m2 0.02 m2 0.08 m2 0.05 m2
Contact areas between orthostats and cover (bearing areas) Orthostat 1 Orthostat 4 Orthostat 6
0.03 m2 0.03 m2 0.03 m2
was developed. Given the uncertainty of the parameters, the objective of the module (called “DeMo”) was not to predict the system's movements, but to estimate the magnitude of these movements, that is, to quantify the mobilization of the dolmen. DeMo was programmed in Fortran. The slabs were assumed to be rigid bodies, with six degrees of freedom each. The construction process was simulated (see Table 3) by solving the nonlinear equilrium problem associated with each step. A Newton–Raphson procedure was implemented. It is interesting to note that, when computing earth pressures, ea, eo and ep were assumed to vary not only with soil type (natural soil or tumulus material), but also with depth. The truss was simulated by means of its stiffness matrix, assumed to be constant from the truss construction. However, foundation reactions, lateral earth pressures and contact forces between orthostats were updated in all the iterations of each construction step. The Jacobian matrix, computed by means of a numerical approximation based on a central difference scheme, was also updated in each iteration. It is also worth mentioning that an approximation of the effective stress based on the formulation of Bishop (1959) was introduced, where coefficient χ was considered to be equal to the relative degree of saturation Sr. The model predictions cannot be validated since no data are available on the movements produced during the previous excavations. However, the solver can be verified to guarantee that it is able to reproduce the behaviour of the slabs system satisfactorily. For this reason, a finite element model (Fig. 5a) was developed using a finite element commercial program (Cosmos/m v.2.8, 2003). The convergence of the model was difficult to achieve due to the contact areas. So, a shell model with variable thickness was adopted, in which the ground and the contacts are simulated using nonlinear spring and superficial contact elements (Crisfield, 1997). Also assumed were elastic orthostats with the common elasticity modules of granite. It was proven that, while the results from the finite element method and the slabs model were not identical, they Table 2 Summary of the mechanical properties of the foundation and the tumulus
Fig. 9. Bilinear estimation of the shear force.
Parameter
Soil 1 (foundation)
Soil 2 (tumulus)
Bulk density, ρn g/cm3 Internal friction angle, φ (°) Cohesion, c (kPa) Active displacement, δa (cm) Passive displacement, δp (cm)
1.94 30 18 1.8 1.8
1.89 20 10 1.8 1.8
V. Navarro et al. / Engineering Geology 100 (2008) 59–68 Table 3 Steps considered in the simulation of the dolmen's mobilization Step #
Action
1 2 3 4 5 6 7 8 9 10
Build orthostat 4 (keystone) Build orthostats 3 and 5 Build orthostats 2 and 6 Build orthostats 1 and 7 Tumulus bank up Cover Fill sedimentation into the chamber Chamber excavation Partial excavation of the soil foundation of orthostat 4 Oak truss removal
Table 4 Maximum mobilization caused by the removal of the oak truss without installing a new truss Orthostat #
FEM model
DeMo
1 2 3 4 5 6 7
0.0075 0.0117 0.0199 0.0287 0.0116 0.0071 0.0027
0.0054 0.0060 0.0161 0.0227 0.0089 0.0042 0.0023
were on the same order (see Table 4), and showed the same mobilization tendencies. At this point, it is fitting to review the need for DeMo once a finite element model has been developed. Nevertheless, it should be remembered that the uncertainty associated with the parameters makes it very important to conduct a number of sensitivity analyses to estimate the reliability of the results. It is therefore essential to be able to rely on a quick calculation tool. With DeMo the simulation of the dolmen's historical construction and the replacement of the oak truss can be computed in less than 1 min using a personal computer with an AMD ATHLON 64 3500 2.2 GHz processor With the finite element model, the
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simulation of the excavation and the replacement of the truss alone take approximately 10 min using the same computer. Thus, DeMo offers clear advantages. Of all the cases analyzed and with all the combinations of parameters considered, it was orthostat 4 (Fig. 1b) that registered the greatest mobilization, understood as the maximum displacement experienced at any point on the orthostat (this mobilization always takes place in the contact zone of the cover). On the other hand, after the partial excavation of orthostat 4 (see Table 3), it was orthostat 7 that registered the least mobilization (see Table 4). Hence, in order to simplify the presentation, the figures display only the mobilizations of these two orthostats (the values associated with orthostat 4 are plotted in bold face, whereas the values associated with orthostat 7 are depicted in light face). First of all, the sensitivity of the model to the contact parameters was analyzed. As shown in Tables 5 and 6, the movement recorded was not modified by any of the following: a sudden drop in the potential of the basic friction angle ϕb (a value of 12° was used as the characteristic of the mica found in the orthogneiss forming the orthostats); the variation in peak displacements vPEAK, or a significant variation in the maximum contact aperture uM. In all cases the differences in the mobilization are always less than 5% throughout the constructive process (steps 1 to 7 in Table 3), as well as during and the estimation and prediction of the mobilization generated by the excavations and the possible removal of the oak truss (steps 8 to 10, Table 3). The differences are even smaller when the sensitivity to the variation of the contact areas is analyzed. Even if a 50% reduction is assumed for either contact 4 alone (the greatest stress concentration takes place between orthostats 4 and 5) or for all of the contacts between orthostats, the mobilization estimation is only modified by 1%. The same thing happens with the cover bearing areas, if an area of 600 cm2 is adopted instead of a very pessimistic value of 300 cm2. Even an increase of one order of magnitude in the normal stiffness (from a very conservative value of 7 GPa/m to 70 GPa/m) does not affect mobilization. Consequently it can be assumed that the estimation of mobilization has a low sensitivity to the contact parameters, and the conservative values of Table 1 define a valid set of contact parameters. This fact does not imply that the contacts do not play a role in the dolmen's behavior. Varying these parameters modifies the normal and shear displacements. However, even when the
Table 5 Variation of the mobilization (m) of orthostat 4 when contact parameters are changed Step #
ϕb = 12°
vPEAK = 5 mm
vPEAK = 2 cm
uM = 6.4 mm
Acontact = 6e− 2 m2
50% AMAX
kn = 70 GPa/m
1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 −2.3 × 10− 3 −2.31 × 10− 3 0 −3.97 × 10− 4 −1.03 × 10− 3
0 0 0 0 0 1.13 × 10− 3 1.13 × 10− 3 0 2.57 × 10− 4 −3.67 × 10− 5
0 0 0 0 0 −1.96 × 10− 3 −1.96 × 10− 3 0 −3.49 × 10− 4 −6.10 × 10− 4
0 3.84 × 10− 9 1.51 × 10− 8 6.97 × 10− 9 1.50 × 10− 3 1.21 × 10− 3 1.21 × 10− 3 0 2.17 × 10− 4 − 8.34 × 10− 5
0 0 0 0 0 2.75 × 10− 6 2.75 × 10− 6 0 2.53 × 10− 7 3.91 × 10− 7
0 3.74 × 10− 6 8.04 × 10− 6 6.95 × 10− 6 1.65 × 10− 3 1.47 × 10− 4 1.47 × 10− 4 0 8.46 × 10− 6 2.13 × 10− 5
0 − 3.37 × 10− 6 − 7.25 × 10− 6 − 6.26 × 10− 6 3.41 × 10− 4 − 1.90 × 10− 5 − 1.90 × 10− 5 0 − 9.24 × 10− 7 − 3.19 × 10− 4
Table 6 Variation of the mobilization (m) of orthostat 7 when contact parameters are changed Step #
ϕb = 12°
vPEAK = 5 mm
vPEAK = 2 cm
uM = 6.4 mm
Acontact = 6e−2 m2
50% AMAX
kn = 70 GPa/m
1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 4.01 × 10− 5 4.01 × 10− 5 0 2.86 × 10− 5 3.03 × 10− 4
0 0 0 0 0 − 2.59 × 10− 5 − 2.59 × 10− 5 0 − 2.57 × 10− 4 − 6.90 × 10− 4
0 0 0 0 0 3.48 × 10− 5 3.48 × 10− 5 0 5.13 × 10− 5 2.93 × 10− 4
0 0 0 −3.58 × 10− 8 1.51 × 10− 4 −2.80 × 10− 5 −2.80 × 10− 5 0 −1.83 × 10− 4 −7.09 × 10− 4
0 0 0 0 0 −5.65 × 10− 8 −5.65 × 10− 8 0 −2.50 × 10− 8 −9.41 × 10− 8
0 0 0 −4.73 × 10− 6 −7.30 × 10− 5 −4.46 × 10− 6 −4.46 × 10− 6 0 2.06 × 10− 6 −4.42 × 10− 6
0 0 0 4.26 × 10− 6 −4.19 × 10− 6 1.67 × 10− 6 1.67 × 10− 6 0 2.40 × 10− 6 −5.11 × 10− 5
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Fig. 10. Increase in mobilization estimation when shear force between the orthostats and the cover was not considered.
parameters in Table 1 are used, the stiffness of the contacts is considerably greater than that of the ground. Therefore, the modifications of the contact parameters barely change the contact forces, and the working scheme of the dolmen is practically the same in all cases. Conversely, as was intuitively stated, the work scheme becomes clearly modified if the shear forces between the cover and the supports are not considered. In this case, it was obtained a mobilization estimation roughly 40% higher (see Fig. 10), given that the cover brace effect is ignored. When the oak truss is removed, orthostat 4 tends to move toward the interior side of the dolmen as a result of the excavation carried out in its foundation. Then the friction with the cover becomes active, and shear forces start to work on the other bearing areas of the cover (orthostats 1 and 6) to support orthostat 4. This is evident because orthostat 7 registers the lowest mobilization if it is ignored by the shear force (see Fig. 10). Mobilization is also very sensitive to the active and passive displacement values, δa and δp. As shown in Fig. 11, the movements are considerably lower (31% between steps 1 and 7, and 34% between steps 8 and 10) considering a yield value (passive or active) of 1.2 cm (the reference value is 1.8 cm). On the other hand, a yield value of 2.4 cm increases the mobilization value by 30%. In any case, the mobilizations illustrated in Fig. 11 are probably too high. This is so not only because of the reaction moduli, which are probably lower than the real values, but
also because it was assumed that the water table is always at 0 level (level of the natural soil and the chamber floor). In reality, as mentioned earlier, the water table varies seasonally between 0 and −3.3 m level (Carrera, in Bello et al., 1999). In order to analyze the effect of this seasonal fluctuation on the moisture condition of the soil foundation, a simulation was performed using the Seep/W program (Geo-Slope, 2002). A ground permeability of 0.8 × 10− 6 m/s was assumed, on the basis of the results of the slug tests done by Carrera (in Bello et al., 1999). In addition, a Van Genuchten (1980)–Mualem (1976) flow model was adopted. The model parameters were selected according to the textural data. Seasonal fluctuations in the water table were found to be quickly followed by suction distribution, which means that the hydrostatic water pressure distribution was consistent. As a result, when the water table is about 3.3 m below the surface, the suction is approximately 30 kPa, a value similar to the total overburden stress at 1.5 m depth, where the foundation of orthostat 4 is located. Otherwise, suction variations are comparable to the maximum total stress initially existing in the ground. Consequently, water table fluctuation may play an important role in the behaviour of the system. To prove this, the mobilization of the dolmen was estimated assuming a constant water table level of −3.3 m and using the parameters in Tables 1 and 2. As shown in Fig. 12, the mobilizations generated in this manner were 40% lower than the ones produced with the water table at level 0. Therefore,
Fig. 11. Sensitivity of the system's mobilization to the displacement associated with soil yielding (δa, active, and δp, passive, assumed to be the same).
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Fig. 12. Dismantlement of the oak truss: Comparison between the mobilizations generated by the operation at water table level 0 (winter) and −3.3 m (summer).
this demonstrates that it is advisable to remove the oak truss during the summer season. Even if the conservative values of foundation stiffness indicated in Table 2 are used and a saturated foundation is assumed, the estimation of the mobilization after the removal of the existing truss is always less than 3 cm (see Figs. 10–12). Therefore it would seem advisable to remove the oak truss without applying any complementary measures. However before recommending any action, an important question should be considered. In the above calculations it was assumed that the partial excavation of the foundation of orthostat 4 in 1988 (step 9 of Table 3) caused a 30% decrease in the passive thrust efficiency of orthostat 4 (this means a 30% reduction in earth pressure, tE in Fig. 7b). This estimation took into account the area excavated to the rear of orthostat 4 (see Fig. 3c). However, the excavation was done on “two levels”, and the reduction of the passive thrust is somewhat difficult to estimate. If a 40% reduction is assumed, with the given parameters, the mobilization will be 40% greater, while a reduction of 50% will result in a mobilization that is 82% higher (Fig. 13). If the reduction is assumed to be 60%, the dolmen would collapse upon the removal of the oak truss. This may be somewhat of an overestimation since very conservative parameters have been adopted. In any case, it certainly does indicate that the mobilization may be excessive during the dismantlement process. Using the reference parameters, an analysis was carried out on the use of a temporary truss, having a stiffness of approximately 50% less, and a permanent truss, with the same stiffness as that of the oak truss. In
step10 (following the numbering used in Table 3), the existing truss is removed and the temporary one is set, while in step 11, the temporary one is removed and the permanent one is set. The mobilizations predicted during the entire process are shown in Fig. 14. In this figure, the lines 9–10 of Fig. 4 are represented by the first line of each orthostat (from the interior side of the chamber toward the exterior side), lines 4– 5 are represent by the second line, the lines 2–7 the third, and lines 1–8 the fourth. The lines in bold face define the position before the excavation works, while the lines in light face represent the final positions after placing and removing the temporary truss and installing the permanent one. It should be emphasized that the process will not only reduce total mobilization by almost 50%, but it will also cut the mobilization associated with the repositioning process to practically zero (see in Fig. 15). It is important to mention that, as a result of the small mobilizations taken into account, both the secant approach used to simulate the contact between orthostats and the Winkler method become more reliable. Therefore, since conservative parameters were used throughout
Fig. 13. Increase in mobilization recorded upon the excavation of the exterior surface of orthostat 4.
Fig. 15. Comparison between the mobilizations recorded upon the removal of the existing truss “1c” without using a complementary truss, and “3c” with a temporary truss.
Fig. 14. Top view of the mobilization of the dolmen chamber upon completion of the rehabilitation work. Displacements have been amplified 20 times to make graphs easier to read.
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the analysis, the utilization of a temporary truss is considered to be a safe procedure. In fact, the projected trusses would be unnecessary. Nevertheless these security measures, taking the dolmen into consideration, are easy to implement. 5. Conclusions A new approach to evaluate the mobilization of a dolmen has been presented here. The methodology is based on the fundamental concepts of rock and soils mechanics. Hence, contact between orthostats was simulated by a simple secant approximation, and both the reaction of the foundation and lateral earth pressures were computed by means of the Winkler method. While these models make it possible to introduce the principal factors governing the mechanical behaviour of dolmens, they do, however, entail the use of a number of simplifications that may be excessive. Nevertheless, in view of the importance of dolmens as part of our heritage, only low-impact mobilizations should be considered. Hence the simplifications would not necessarily be critical, and the solver developed (DeMo) would provide a valid estimation of the mobilization. After its verification, DeMo was used to analyze the sensitivity of the dolmen of Dombate (Northwest Spain) to actions associated with a conservation project. The importance of the shear forces generated between the cover and the rest of the orthostats was confirmed. Also demonstrated was the important role played by the water table. Lastly, it was possible to determine the consequences that past excavations might have on the conservation project currently under consideration. These analyses have helped to establish a rational procedure for the action and the implementation of complementary security measures. The approach of this study may be applied to other similar monuments. Hence the methodology proposed here may be used as a new assessment method in archaeological practices. Acknowledgements The authors are grateful to the Provincial Government of La Coruña for providing the research contract to carry out this study. We would also like to thank this organization for their support with the graphics by allowing us to use pictures from their web site. This research was also financed in part by a Research Grant awarded to Mr. Yustres and to Mr. Candel by the Education and Research Department of the Castilla-La Mancha Regional Government and the European Social Fund within the framework of the Integrated Operative Programme for Castilla-La Mancha 2000–2006, approved by Commission Decision C(2001) 525/1.
References Bandis, S., Lumsden, A.C., Barton, N.R., 1983. Fundamentals of rock joint deformation. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 20 (6), 249–268. Barton, N., 1973. Review of a new shear-strength criterion for rock joints. Engineering Geology 7 (4), 287–332. Barton, N., Choubey, V., 1977. The shear strength of rock joints in theory and practice. Rock Mechanics 10 (1–2), 1–54. Barton, N., Lien, R., Lunde, J., 1974. Engineering classification of rock masses for the design of tunnel support. Rock Mechanics 6 (106), 189–239. Barton, N., Bandis, S., Bakhtar, K., 1985. Strength, deformation and conductivity coupling of rock joints. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 22 (3), 121–140. Bello, J., 1993. El monumento de Dombate en el marco del megalitismo del noroeste peninsular (Volumes XIII–XIV). Portugalia Nova Série, La Coruña, Spain. Bello, J., Carrera, F., Cebrián, F., 1996. Studies for the conservation of the paintings from the “Dolmen of Dombate”. Revista Electrónica Galega de Arqueoloxía. from http:// www.geocities.com/RainForest/1185/investig.htm. Bello, J., Carrera, F., Cebrián, F., 1999. Plan Director de las actuaciones sobre el monumento megalítico de Dombate y su entorno. Provincial Government of La Coruña, La Coruña, Spain. from http://www.dicoruna.es. Bishop, A., 1959. The principle of effective stress. Teknisk Uklebad 106 (39), 859–863. Bowles, J.E., 1988. Foundation Analysis and Design, 4th ed. McGraw-Hill, New York. 408 pp. Carrera, J., 1999. Estudio de la hidrogeología local, in Plan Director de las actuaciones sobre el monumento megalítico de Dombate y su entorno. Provincial Government of La Coruña, La Coruña, Spain. from http://www.dicoruna.es. Clayton, C.R.I., Milititsky, J., Woods, R.I., 1993. Earth Pressure and Earth-retaining Structures, 2nd ed. Blackie Academic, London. Cosmos/m, 2003. Finite element analysis system. User's Guide, Basic Modules, Command Reference and Advanced Modules (Version 2.8). Los Angeles, USA. Crisfield, M.A., 1997. Non-linear finite element analysis of solids and structures. Advanced Topics, vol. 2. Wiley, Chichester. 411 pp. Geo-Slope, 2002. Seep/W for finite element seepage analysis. User's Guide (Version 5). Geo-Slope International, Canada. Itasca, 2002. Interfaces in FLAC 3D: Theory and Background. Itasca Consulting Group, Minneapolis, USA. Jacky, J., 1944. The coefficient of earth pressure at rest. Journal of the Society of Hungarian Architects and Engineers 78 (22), 355–358. Mualem, Y., 1976. A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resources Research 12, 513–522. Müller-Breslau, H., 1906. Erddruck auf stutzmauert. Alfred Kroner, Stuttgard. Potts, D.M., 1993. The analysis of earth retaining structures. In: Clayton, C.R.I. (Ed.), Retaining Structures. Thomas Telford, London, pp. 167–186. Poulos, H.G., Davis, E.H., 1980. Pile foundation analysis and design. John Wiley and Sons, Singapore. Rutqvist, J., Tsang, C.-F., 2003. Analysis of thermal–hydrologic–mechanical behavior near an emplacement drift at Yucca Mountain. Journal of Contaminant Hydrology 62–63, 637–652. ROM, 1994. Recomendaciones geotécnicas para el proyecto de obras marítimas y portuarias: ROM 0.5-94. Ministerio de Fomento, Madrid. 446 pp. Silva, B., Rivas, T., Prieto, B., Delgado, J., 1996. A comparison of the mechanisms of plaque formation and sand disaggregation in granitic historic buildings. Degradation and Conservation of Granitic Rocks in Monuments, Protection and Conservation of the European Cultural Heritage, Report no. 5. European Commission, Brussels. Van Genuchten, M.T., 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal 44, 892–898.
Contents lists available at ScienceDirect
Engineering Geology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e n g g e o
Mobilization analysis of the dolmen of Dombate (Northwest Spain) Vicente Navarro a,⁎, Luis E. Romera b, Ángel Yustres a, Miguel Candel a a b
Geoenvironmental Group, School of Civil Engineering, University of Castilla-La Mancha, Avda Camilo José Cela s/n, 13071, Ciudad Real, Spain School of Civil Engineering, University of A Coruña, Campus de Elviña, 15071, A Coruña, Spain
A R T I C L E
I N F O
Article history: Received 4 July 2007 Received in revised form 15 February 2008 Accepted 5 March 2008 Available online 12 March 2008 Keywords: Stability Mobilization Megalithic structure Dolmen Northwest Spain
A B S T R A C T This paper presents an analysis of the mobilization of the dolmen of Dombate, a megalithic monument situated in the Northwest of Spain. The study is founded on simple static principles, with the application of basic concepts of soil mechanics (soil reactions were computed by the reaction modulus method) and rock mechanics (a simple secant approach was adopted to model the contact between orthostats). In addition, a simplified geometric model for dolmens was adopted. On the basis of these concepts, a numerical solver able to provide quick estimations of the system's mobilization was developed. Using this tool, a number of sensitivity analyses were conducted to estimate the mobilization that could be caused by a conservation project currently under consideration. It was found that mobilization might be excessive, and therefore, a safer procedure is proposed. In short, this paper puts forth a new rational approach for archaeological practices which may help to estimate the possible consequences of excavations and rehabilitations on megalithic structures. © 2008 Elsevier B.V. All rights reserved.
1. Introduction The dolmen of Dombate, located in Cabana county (Galicia, NW of Spain; see Fig. 1a), is a large scale passage monument, bigger in size that those commonly found in Galicia (Bello et al., 1999). The chamber consists of seven rectangular orthostatic slabs in a sub-rectangular shape measuring approximately 3.6 m by 2.7 m (Fig. 1b) and 3 m in height. The passage is 4 m long and consists of 3 orthostats on either side. The tumulus that is placed over the dolmen is made of clayed soil, probably obtained after sieving, and is covered by coarse gravel to prevent erosion. While at the present time the tumulus is not fully covered by the gravel, it was probably initially protected by a complete layer (Bello et al., 1999). In its final configuration, as Bello (1993) reports, the tumulus reached the height of the passage and only the upper part of the chamber orthostats was visible (Fig. 2g). The history of the construction of the monument is quite complex. According to Bello (1993), first a smaller dolmen was constructed with a simple, open chamber of considerable length (Fig. 2a and b). Then the actual dolmen was added to this monument. After digging the foundation trenches (Fig. 2c), the keystone was positioned (Fig. 2d). Then, the rest of the chamber and passage orthostats were laid out (Fig. 2e and f). Finally, the covers were put into place. There is no apparent evidence of how this
⁎ Corresponding author. Tel.: +34 926 295 300x3264; fax: +34 926 295 391. E-mail addresses: [email protected] (V. Navarro), [email protected] (L.E. Romera), [email protected] (Á. Yustres), [email protected] (M. Candel). 0013-7952/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.enggeo.2008.03.002
operation was carried out or if it was done before or after the tumulus was placed. All the data were gathered over the course of three study periods (summers 1987–88–89) when partial excavations were carried out to reveal the present state of the dolmen, as shown in Fig. 3, and its initial state in Fig. 1c. The sedimented fill which accumulated in the chamber during the lifetime of the dolmen had been completed excavated and reached the natural ground surface. Among the significant finds, it should be stress the importance of the paintings that decorate the chamber slabs and those of the entrance passage. These paintings date to around 5000– 4500 B.C. (Bello et al., 1996). In order to avoid possible stability problems caused by excavation in the dolmen, an oak roof truss was put in as shown in Fig. 3d. The effectiveness of this method cannot be verified since no monitoring tool was used. In any case, the potential mobilization was not observed at first glance. A conservation project of the entire site is currently under consideration. This project is studying the possibility of executing a series of architectural works in the area surrounding the dolmen to achieve favourable environmental conditions for the conservation of the paintings. The project would also allow limited access to the public contingent upon the application of security measures (Bello et al., 1999). The substitution of the oak truss for a permanent element has been proposed under this project. At this point in time, it is of utmost importance to estimate the possible mobilization that may occur during the process of truss substitution before this operation is carried out. The estimation of this mobilization is the immediate goal of this paper, although a more general objective has also been targeted, i.e. the development of a
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Fig. 1. (a) Location of the dolmen. (b) Plan view of the dolmen without the cover, and numbering system of the orthostats. (c) Artistic representation of the dolmen before the investigation (Provincial Government of La Coruña web site).
feasible methodology to estimate the sensitivity of megalithic structures to the actions currently being carried out in archaeological practices. 2. Complexity of the system Generally speaking when archaeologists set out to work on a megalithic structure, particularly a dolmen, reliable estimates of the consequences of their works on the stability of the structure are scarce. As a result, the assessment of potential mobilization is sometimes based only on intuition. While these procedures may seem arbitrary, owing to the system's complexity, there really is no other choice. Basically, a dolmen is a structure formed by rigid slabs(the orthostats), which are set in the ground almost vertically with lateral supports in between. The structure is usually covered by a capstone or cover (Fig. 1c). The analysis of a dolmen's behaviour is a complete problem of structures, continuum mechanics, soil and rock mechanics. Hence, in the area where the orthostats contact the soil foundation, there are both a classical lateral earth pressure problem, and a settlement problem. On the other hand, at contact between the orthostats and between the orthostats and the cover, there are contact surfaces which can be solved using the existing formulations in rock mechanics to analyze the behaviour of joints. So, the simulation of a dolmen's behaviour is an extremely complex problem whose resolution requires a great deal of information, which is very difficult to obtain. Moreover, even if simple mechanical models are used, an aspect as basic as the geometry of the orthostats will still be unknown. Unknown factors including not only the shape of the buried parts of the orthostats, but also the shape of their visible parts, will be difficult to input exactly into calculations. As a result, it is reasonable to assume an idealization of the dolmen to evaluate the mobilization induced by excavation and other works that may have altered its original condition. Given the flat shape of the orthostats and the cover, the purpose of this work is to schematize the geometry through a “slabs model” (see Figs. 4 and 5). The middle plane of each orthostat is ideally represented by an irregular hexagon. The thickness variation is assumed to be linear between the base and the central area, and between the central area and the top surface (thickness H1, H2 and H3 in Fig. 4). The position of each slab with respect to a global reference system is determined by defining the reference coordinates of points P1 and P2 (see Fig. 4) (6 unknowns), the local coordinates of P1L (Fig. 4) in the slab plane (2 unknowns), and the values of e1 and e2 (2 unknowns). Moreover, to define the slab geometry it is necessary to provide the dip direction and angle (2 unknowns), the values of H1, H2 and H3 (3 unknowns), and, finally, the
coordinates of points 1, 3, 9,10, and 6 with reference to point 8 in the slab plane (10 unknowns). There are a total number of 25 geometrical unknowns per slab. In order to determine the unknowns in the seven orthostats and in the cover of the dolmen's chamber, a high precision topographical study was carried out, measuring 50 points per stone. Also, the embedded depth of the orthostats in the ground was estimated by means of a geoelectric investigation based on the application of sounding and electric tomography techniques. By combining these data with the information gathered in previous excavations (Bello et al., 1999), the digital model shown in Fig. 5a was created, which then allowed us to identify the slabs model presented in Fig. 5b. Also obtained from the digital model, was an estimated foundation width and the equivalent widths of the lateral contacts between the orthostats and the ground (B1, B2 and B3 in Fig. 6a). These widths were used in the slabs model to calculate the foundation reaction (t1) and the thrust exerted by the ground on the lateral surfaces of the orthostats (thrusts t2, t3, t4 and t5 in Fig. 6b). All these forces were assumed to be contained in the middle plane. On the other hand, the thrusts generated by the movement of the slabs against the foundation ground (tI and tE1) and against the tumulus on the external face of each orthostat (tE2), were assumed to be normal to the slabs. Both the base reaction and all the thrusts are conditioned by the water table position (ZWT, Fig. 6a), which is situated near the ground surface in winter (level 0), and at a depth of 3.30 m in summer (Carrera, in Bello et al., 1999). Despite its limitations (among others, lack of soil continuity, and dependence of the soil model on the problem analyzed; Poulos and Davis, 1980; see also, Potts, 1993), the Winkler method has been widely employed in foundation practice because it provides a relatively simple means of analysis and enables factors such as nonlinearity, variation of soil stiffness with depth, and layering of the soil profile to be taken into account readily, if only approximately (Poulos and Davis, 1980). Therefore, both reaction and lateral earth pressure were computed by the Winkler method. As mentioned in the preceding paragraph, shear stresses were ignored, which is common practice in these kinds of approaches (Potts,1993). The subgrade reaction modulus was assumed to be equal to 40 times the ultimate bearing pressure (Bowles, 1988), which was computed by Hansen's bearing capacity method (see also Bowles, 1988, for example). Lateral earth pressure was computed using the load–movement relationship depicted in Fig. 7. Active, ua, and passive, up, pressures were computed using the Müller-Breslau
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Fig. 2. Constructive process of the monument: (a) and (b) construction of the small dolmen; (c) excavation of the foundation trenches; (d), (e) and (f) placement of the orthostats; (g) construction of the tumulus and placement of the covers. From Bello (1993).
formulation (Müller-Breslau, 1906; in Clayton et al., 1993), while earth pressure at rest, uo, was calculated using the Jacky's equation (Jacky, 1944). On the basis of this formulation, the ground was characterized by bulk density, ρn, internal friction angle, φ, cohesion, c, and displacements, δa and δp (Fig. 7). In keeping with the current practice in Spain, the friction between the ground and the orthostats, δ, was assumed to be 2/3 of φ (ROM, 1994). The slabs model not only provides an “orientation” of the ground reactions (Fig. 6b), but it also suggests the direction of the contact forces between the orthostats. During the construction process of the chamber, the new orthostats were set so that they leaned against the existing ones (see Fig. 2d and e), generating basically orthogonal contact forces to the middle planes of the new orthostats. This led to the adaptation of a contact model between the orthostats based fundamentally on a normal force, fN, which is a function of the separation between the orthostats, u. It is common practice to estimate the growth of fN while u decreases by means of hyperbolic models (see for instance, Bandis et al., 1983; or Barton et al., 1985), or
logarithmic models (Rutqvist and Tsang, 2003). For both model types, the main parameters are the maximum contact amplitude, uM, and the curvature or velocity at which the contact force increases as the distance between contact surfaces changes. In this work, while value uM of the asperity amplitude was estimated from the roughness profiles published by Barton and Choubey (1977) to define the joint roughness coefficient (JRC) of the contacts (Fig. 8), there was not enough information to determine the curvature parameter. As a result, a simple secant model characterized by the normal contact stiffness kN was adopted. Unlike the case of the contact areas between the orthostats, the shear forces were not ignored in the bearing areas of the cover. Although these forces would be small in magnitude, they always have a considerable eccentricity. For this reason, these shear forces may play an important role in stabilizing the structure. In order to calculate these forces, the bilinear formulation shown in Fig. 9 was used. The ultimate shear force, fTU, was calculated by applying a simple frictional model in which the basic friction angle ϕb was used as a friction angle
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Fig. 3. Present state of the dolmen: (a) Aerial view. (b) View from the passage. (c) View from the orthostat 4. (d) Oak truss. Provincial Government of La Coruña web site.
(see Barton, 1973). Therefore, a conservative hypothesis was assumed whereby it was disregarded an increase in resistance against shear due to the contact roughness.
minimum value of ϕb for rock joints without fill (Barton et al., 1974). Finally, if the peak shear displacement vPEAK is assumed to be equal to the maximum contact amplitude uM, then the characteristic orthostat
3. Estimation of the model parameters Although the previously described model assumes a major simplification of the system, a good number of parameters still need to be defined. Fortunately, some of these parameters were obtained with fairly good precision. For instance, the bulk density of the orthostats, ρO, was determined to be 2.54 g/cm3, according to the calculations made by the Edaphology and Agricultural Chemistry Department at the University of Santiago (Silva et al., 1996). This research group obtained a uniaxial compressive strength value of 83.5 MPa for the parallel planes, and 57.7 MPa for the normal planes to the exfoliation of the orthogneiss forming the orthostats. While the latter two parameters are not used directly in the model, they are of interest because they indicate that the orthostat material has a relatively low strength. The orthostats were also estimated to have a JRC value of 10, identified visually by the roughness profiles of Barton and Choubey (1977). According to this value and what is shown in Fig. 8, the asperity amplitude of the contact was deduced to be about 5.2 mm, with a resulting uM value of around 10.4 mm. If it was assumed that, after this movement, the normal compression in the contact areas is somewhat lower than the uniaxial compressive strength in the most resistant direction of the rock, then the contacts' normal stiffness will be a little over 7 GPa/m. This is a very conservative estimation (see for instance Itasca, 2002) So, it will lead to overdimensioned estimations of the mobilization of the dolmen. The estimations are magnified to an even greater extent, since, owing to the lack of data, it was decided to use a basic friction angle of 25° — the
Fig. 4. Idealized geometry of an orthostat : “slab model”.
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Fig. 5. (a) Digital model of the dolmen chamber: Front view from the passage. (b) Idealization of the dolmen using the slabs model.
parameters included in Table 1 are obtained. The contact areas between the orthostats, and between the orthostats and the cover, are also included in Table 1. The boring holes (Carrera, 1999) and the excavations carried out (Bello et al., 1999) played a key role in determining the ground parameters. Thanks to these investigations, it was possible to establish that the sandy soil with a considerable fraction of fines (soil SC in the Unified Soil Classification System, USCS) of the foundation is the weathering product of the schists and paragneisses of the Laxe formation. Its average gravimetric water content is 30%. Therefore, assuming a solid particle density of 2.7 g/cm3 and a degree of saturation close to 1, the following values were obtained: a porosity of nearly 0.45, a dry density of approximately 1.49 g/cm3 and a bulk density of around 1.94 g/cm3 (Table 2). On the basis of SPT testing (average number of blows NSPT = 20), and taking into account past experience with similar material from the same area, the resistant behaviour of the foundation ground is correctly described by an internal friction angle of 30° and a cohesion of 18 kPa. On the other hand, after sieving a number of samples, the tumulus material was identified to be a fine grained soil, categorized as CL-ML in the USCS (liquid limit of 20 and a plasticity index of 6). The average gravimetric water content was estimated to be 32% on the basis of the
samples analyzed. As a result, if the solid particle density is considered to be 2.7 g/cm3 and the average degree of saturation is equal to 98%, a porosity of 0.4, a dry density of 1.44 g/cm3, and a bulk density of 1.89 g/cm3 were deduced (Table 2). The degree of saturation was estimated using suction data from tensiometer measurements carried out by Carrera (in Bello et al., 1999), and assuming a water retention curve consistent with its textural characteristics. Only 5 direct shear consolidated-drained tests were successfully performed, and quite disperse results were obtained. Conservative values were adopted for an internal friction angle of 20° and a cohesion of 10 kPa. The estimation of the active and passive displacements, δa and δp in Fig. 7, is always a complex task. Without going into a detailed explanation of the problem, since a discussion of this type would be beyond the scope of this paper, it is obvious that the simplification inherent to the use of Winkler models is especially “conspicuous” since it is necessary to adopt a “magic” parameter that defines both the yield condition, and the stiffness of the “soil-spring”. Although this depends, without a doubt, on soil type, it is not a constitutive question, rather it is a problem of identifying parameters to improve the Winkler model. In the case of the dolmen of Dombate, the δa and δp values proposed in Table 2 represent a compromise. Firstly, these values are low enough to be able to simulate
Fig. 6. (a) Foundation width, B1, and lateral contacts, B2 and B3, between the orthostats and the ground used in the slabs model. (b) Thrust generated by the ground reaction against the slab movements.
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V. Navarro et al. / Engineering Geology 100 (2008) 59–68 Table 1 Properties of the orthostats
Fig. 7. Simplified load–movement relationship adopted to compute lateral earth pressure against orthostats.
Fig. 8. Frequency diagram of the asperity amplitude associated with JRC of 10 obtained from the digitalization of the roughness profile proposed by Barton and Choubey (1977).
the dolmen construction (see Table 3) without predicting a collapse. Secondly, they are high enough to predict over-dimensioned mobilizations. Thus, with the values of Table 2, at a depth of 1 m, the soil foundation will have an active reaction modulus of 1196 kN/m3 while the passive modulus will be equal to 7869 kN/m3. These values are very low, considering the fact that a reaction modulus is commonly assumed to be between 5000 and 16 000 kN/m3 for loose sand (Bowles, 1988). 4. Simulation of the mobilization of the dolmen and sensitivity analysis After defining the conceptual model and estimating its parameters, a calculation module capable of reproducing the dolmen's behaviour
Parameter
Value
Rock bulk density, ρo Uniaxial compressive strength (parallel to foliation) Uniaxial compressive strength (perpendicular to foliation) Joint roughness coefficient, JRC (°) Basic friction angle, ϕb (°) Maximum amplitude of the contact, uM Peak shear displacement, vPEAK Contact normal stiffness, kn
2.54 g/cm3 83.5 MPa 57.7 MPa 10 25 10.4 mm 10.4 mm 7 GPa/m
Contact areas between orthostats Orthostats 1 and 2 Orthostats 2 and 3 Orthostats 3 and 4 Orthostats 4 and 5 Orthostats 5 and 6 Orthostats 6 and 7
0.065 m2 0.06 m2 0.08 m2 0.02 m2 0.08 m2 0.05 m2
Contact areas between orthostats and cover (bearing areas) Orthostat 1 Orthostat 4 Orthostat 6
0.03 m2 0.03 m2 0.03 m2
was developed. Given the uncertainty of the parameters, the objective of the module (called “DeMo”) was not to predict the system's movements, but to estimate the magnitude of these movements, that is, to quantify the mobilization of the dolmen. DeMo was programmed in Fortran. The slabs were assumed to be rigid bodies, with six degrees of freedom each. The construction process was simulated (see Table 3) by solving the nonlinear equilrium problem associated with each step. A Newton–Raphson procedure was implemented. It is interesting to note that, when computing earth pressures, ea, eo and ep were assumed to vary not only with soil type (natural soil or tumulus material), but also with depth. The truss was simulated by means of its stiffness matrix, assumed to be constant from the truss construction. However, foundation reactions, lateral earth pressures and contact forces between orthostats were updated in all the iterations of each construction step. The Jacobian matrix, computed by means of a numerical approximation based on a central difference scheme, was also updated in each iteration. It is also worth mentioning that an approximation of the effective stress based on the formulation of Bishop (1959) was introduced, where coefficient χ was considered to be equal to the relative degree of saturation Sr. The model predictions cannot be validated since no data are available on the movements produced during the previous excavations. However, the solver can be verified to guarantee that it is able to reproduce the behaviour of the slabs system satisfactorily. For this reason, a finite element model (Fig. 5a) was developed using a finite element commercial program (Cosmos/m v.2.8, 2003). The convergence of the model was difficult to achieve due to the contact areas. So, a shell model with variable thickness was adopted, in which the ground and the contacts are simulated using nonlinear spring and superficial contact elements (Crisfield, 1997). Also assumed were elastic orthostats with the common elasticity modules of granite. It was proven that, while the results from the finite element method and the slabs model were not identical, they Table 2 Summary of the mechanical properties of the foundation and the tumulus
Fig. 9. Bilinear estimation of the shear force.
Parameter
Soil 1 (foundation)
Soil 2 (tumulus)
Bulk density, ρn g/cm3 Internal friction angle, φ (°) Cohesion, c (kPa) Active displacement, δa (cm) Passive displacement, δp (cm)
1.94 30 18 1.8 1.8
1.89 20 10 1.8 1.8
V. Navarro et al. / Engineering Geology 100 (2008) 59–68 Table 3 Steps considered in the simulation of the dolmen's mobilization Step #
Action
1 2 3 4 5 6 7 8 9 10
Build orthostat 4 (keystone) Build orthostats 3 and 5 Build orthostats 2 and 6 Build orthostats 1 and 7 Tumulus bank up Cover Fill sedimentation into the chamber Chamber excavation Partial excavation of the soil foundation of orthostat 4 Oak truss removal
Table 4 Maximum mobilization caused by the removal of the oak truss without installing a new truss Orthostat #
FEM model
DeMo
1 2 3 4 5 6 7
0.0075 0.0117 0.0199 0.0287 0.0116 0.0071 0.0027
0.0054 0.0060 0.0161 0.0227 0.0089 0.0042 0.0023
were on the same order (see Table 4), and showed the same mobilization tendencies. At this point, it is fitting to review the need for DeMo once a finite element model has been developed. Nevertheless, it should be remembered that the uncertainty associated with the parameters makes it very important to conduct a number of sensitivity analyses to estimate the reliability of the results. It is therefore essential to be able to rely on a quick calculation tool. With DeMo the simulation of the dolmen's historical construction and the replacement of the oak truss can be computed in less than 1 min using a personal computer with an AMD ATHLON 64 3500 2.2 GHz processor With the finite element model, the
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simulation of the excavation and the replacement of the truss alone take approximately 10 min using the same computer. Thus, DeMo offers clear advantages. Of all the cases analyzed and with all the combinations of parameters considered, it was orthostat 4 (Fig. 1b) that registered the greatest mobilization, understood as the maximum displacement experienced at any point on the orthostat (this mobilization always takes place in the contact zone of the cover). On the other hand, after the partial excavation of orthostat 4 (see Table 3), it was orthostat 7 that registered the least mobilization (see Table 4). Hence, in order to simplify the presentation, the figures display only the mobilizations of these two orthostats (the values associated with orthostat 4 are plotted in bold face, whereas the values associated with orthostat 7 are depicted in light face). First of all, the sensitivity of the model to the contact parameters was analyzed. As shown in Tables 5 and 6, the movement recorded was not modified by any of the following: a sudden drop in the potential of the basic friction angle ϕb (a value of 12° was used as the characteristic of the mica found in the orthogneiss forming the orthostats); the variation in peak displacements vPEAK, or a significant variation in the maximum contact aperture uM. In all cases the differences in the mobilization are always less than 5% throughout the constructive process (steps 1 to 7 in Table 3), as well as during and the estimation and prediction of the mobilization generated by the excavations and the possible removal of the oak truss (steps 8 to 10, Table 3). The differences are even smaller when the sensitivity to the variation of the contact areas is analyzed. Even if a 50% reduction is assumed for either contact 4 alone (the greatest stress concentration takes place between orthostats 4 and 5) or for all of the contacts between orthostats, the mobilization estimation is only modified by 1%. The same thing happens with the cover bearing areas, if an area of 600 cm2 is adopted instead of a very pessimistic value of 300 cm2. Even an increase of one order of magnitude in the normal stiffness (from a very conservative value of 7 GPa/m to 70 GPa/m) does not affect mobilization. Consequently it can be assumed that the estimation of mobilization has a low sensitivity to the contact parameters, and the conservative values of Table 1 define a valid set of contact parameters. This fact does not imply that the contacts do not play a role in the dolmen's behavior. Varying these parameters modifies the normal and shear displacements. However, even when the
Table 5 Variation of the mobilization (m) of orthostat 4 when contact parameters are changed Step #
ϕb = 12°
vPEAK = 5 mm
vPEAK = 2 cm
uM = 6.4 mm
Acontact = 6e− 2 m2
50% AMAX
kn = 70 GPa/m
1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 −2.3 × 10− 3 −2.31 × 10− 3 0 −3.97 × 10− 4 −1.03 × 10− 3
0 0 0 0 0 1.13 × 10− 3 1.13 × 10− 3 0 2.57 × 10− 4 −3.67 × 10− 5
0 0 0 0 0 −1.96 × 10− 3 −1.96 × 10− 3 0 −3.49 × 10− 4 −6.10 × 10− 4
0 3.84 × 10− 9 1.51 × 10− 8 6.97 × 10− 9 1.50 × 10− 3 1.21 × 10− 3 1.21 × 10− 3 0 2.17 × 10− 4 − 8.34 × 10− 5
0 0 0 0 0 2.75 × 10− 6 2.75 × 10− 6 0 2.53 × 10− 7 3.91 × 10− 7
0 3.74 × 10− 6 8.04 × 10− 6 6.95 × 10− 6 1.65 × 10− 3 1.47 × 10− 4 1.47 × 10− 4 0 8.46 × 10− 6 2.13 × 10− 5
0 − 3.37 × 10− 6 − 7.25 × 10− 6 − 6.26 × 10− 6 3.41 × 10− 4 − 1.90 × 10− 5 − 1.90 × 10− 5 0 − 9.24 × 10− 7 − 3.19 × 10− 4
Table 6 Variation of the mobilization (m) of orthostat 7 when contact parameters are changed Step #
ϕb = 12°
vPEAK = 5 mm
vPEAK = 2 cm
uM = 6.4 mm
Acontact = 6e−2 m2
50% AMAX
kn = 70 GPa/m
1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 4.01 × 10− 5 4.01 × 10− 5 0 2.86 × 10− 5 3.03 × 10− 4
0 0 0 0 0 − 2.59 × 10− 5 − 2.59 × 10− 5 0 − 2.57 × 10− 4 − 6.90 × 10− 4
0 0 0 0 0 3.48 × 10− 5 3.48 × 10− 5 0 5.13 × 10− 5 2.93 × 10− 4
0 0 0 −3.58 × 10− 8 1.51 × 10− 4 −2.80 × 10− 5 −2.80 × 10− 5 0 −1.83 × 10− 4 −7.09 × 10− 4
0 0 0 0 0 −5.65 × 10− 8 −5.65 × 10− 8 0 −2.50 × 10− 8 −9.41 × 10− 8
0 0 0 −4.73 × 10− 6 −7.30 × 10− 5 −4.46 × 10− 6 −4.46 × 10− 6 0 2.06 × 10− 6 −4.42 × 10− 6
0 0 0 4.26 × 10− 6 −4.19 × 10− 6 1.67 × 10− 6 1.67 × 10− 6 0 2.40 × 10− 6 −5.11 × 10− 5
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V. Navarro et al. / Engineering Geology 100 (2008) 59–68
Fig. 10. Increase in mobilization estimation when shear force between the orthostats and the cover was not considered.
parameters in Table 1 are used, the stiffness of the contacts is considerably greater than that of the ground. Therefore, the modifications of the contact parameters barely change the contact forces, and the working scheme of the dolmen is practically the same in all cases. Conversely, as was intuitively stated, the work scheme becomes clearly modified if the shear forces between the cover and the supports are not considered. In this case, it was obtained a mobilization estimation roughly 40% higher (see Fig. 10), given that the cover brace effect is ignored. When the oak truss is removed, orthostat 4 tends to move toward the interior side of the dolmen as a result of the excavation carried out in its foundation. Then the friction with the cover becomes active, and shear forces start to work on the other bearing areas of the cover (orthostats 1 and 6) to support orthostat 4. This is evident because orthostat 7 registers the lowest mobilization if it is ignored by the shear force (see Fig. 10). Mobilization is also very sensitive to the active and passive displacement values, δa and δp. As shown in Fig. 11, the movements are considerably lower (31% between steps 1 and 7, and 34% between steps 8 and 10) considering a yield value (passive or active) of 1.2 cm (the reference value is 1.8 cm). On the other hand, a yield value of 2.4 cm increases the mobilization value by 30%. In any case, the mobilizations illustrated in Fig. 11 are probably too high. This is so not only because of the reaction moduli, which are probably lower than the real values, but
also because it was assumed that the water table is always at 0 level (level of the natural soil and the chamber floor). In reality, as mentioned earlier, the water table varies seasonally between 0 and −3.3 m level (Carrera, in Bello et al., 1999). In order to analyze the effect of this seasonal fluctuation on the moisture condition of the soil foundation, a simulation was performed using the Seep/W program (Geo-Slope, 2002). A ground permeability of 0.8 × 10− 6 m/s was assumed, on the basis of the results of the slug tests done by Carrera (in Bello et al., 1999). In addition, a Van Genuchten (1980)–Mualem (1976) flow model was adopted. The model parameters were selected according to the textural data. Seasonal fluctuations in the water table were found to be quickly followed by suction distribution, which means that the hydrostatic water pressure distribution was consistent. As a result, when the water table is about 3.3 m below the surface, the suction is approximately 30 kPa, a value similar to the total overburden stress at 1.5 m depth, where the foundation of orthostat 4 is located. Otherwise, suction variations are comparable to the maximum total stress initially existing in the ground. Consequently, water table fluctuation may play an important role in the behaviour of the system. To prove this, the mobilization of the dolmen was estimated assuming a constant water table level of −3.3 m and using the parameters in Tables 1 and 2. As shown in Fig. 12, the mobilizations generated in this manner were 40% lower than the ones produced with the water table at level 0. Therefore,
Fig. 11. Sensitivity of the system's mobilization to the displacement associated with soil yielding (δa, active, and δp, passive, assumed to be the same).
V. Navarro et al. / Engineering Geology 100 (2008) 59–68
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Fig. 12. Dismantlement of the oak truss: Comparison between the mobilizations generated by the operation at water table level 0 (winter) and −3.3 m (summer).
this demonstrates that it is advisable to remove the oak truss during the summer season. Even if the conservative values of foundation stiffness indicated in Table 2 are used and a saturated foundation is assumed, the estimation of the mobilization after the removal of the existing truss is always less than 3 cm (see Figs. 10–12). Therefore it would seem advisable to remove the oak truss without applying any complementary measures. However before recommending any action, an important question should be considered. In the above calculations it was assumed that the partial excavation of the foundation of orthostat 4 in 1988 (step 9 of Table 3) caused a 30% decrease in the passive thrust efficiency of orthostat 4 (this means a 30% reduction in earth pressure, tE in Fig. 7b). This estimation took into account the area excavated to the rear of orthostat 4 (see Fig. 3c). However, the excavation was done on “two levels”, and the reduction of the passive thrust is somewhat difficult to estimate. If a 40% reduction is assumed, with the given parameters, the mobilization will be 40% greater, while a reduction of 50% will result in a mobilization that is 82% higher (Fig. 13). If the reduction is assumed to be 60%, the dolmen would collapse upon the removal of the oak truss. This may be somewhat of an overestimation since very conservative parameters have been adopted. In any case, it certainly does indicate that the mobilization may be excessive during the dismantlement process. Using the reference parameters, an analysis was carried out on the use of a temporary truss, having a stiffness of approximately 50% less, and a permanent truss, with the same stiffness as that of the oak truss. In
step10 (following the numbering used in Table 3), the existing truss is removed and the temporary one is set, while in step 11, the temporary one is removed and the permanent one is set. The mobilizations predicted during the entire process are shown in Fig. 14. In this figure, the lines 9–10 of Fig. 4 are represented by the first line of each orthostat (from the interior side of the chamber toward the exterior side), lines 4– 5 are represent by the second line, the lines 2–7 the third, and lines 1–8 the fourth. The lines in bold face define the position before the excavation works, while the lines in light face represent the final positions after placing and removing the temporary truss and installing the permanent one. It should be emphasized that the process will not only reduce total mobilization by almost 50%, but it will also cut the mobilization associated with the repositioning process to practically zero (see in Fig. 15). It is important to mention that, as a result of the small mobilizations taken into account, both the secant approach used to simulate the contact between orthostats and the Winkler method become more reliable. Therefore, since conservative parameters were used throughout
Fig. 13. Increase in mobilization recorded upon the excavation of the exterior surface of orthostat 4.
Fig. 15. Comparison between the mobilizations recorded upon the removal of the existing truss “1c” without using a complementary truss, and “3c” with a temporary truss.
Fig. 14. Top view of the mobilization of the dolmen chamber upon completion of the rehabilitation work. Displacements have been amplified 20 times to make graphs easier to read.
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the analysis, the utilization of a temporary truss is considered to be a safe procedure. In fact, the projected trusses would be unnecessary. Nevertheless these security measures, taking the dolmen into consideration, are easy to implement. 5. Conclusions A new approach to evaluate the mobilization of a dolmen has been presented here. The methodology is based on the fundamental concepts of rock and soils mechanics. Hence, contact between orthostats was simulated by a simple secant approximation, and both the reaction of the foundation and lateral earth pressures were computed by means of the Winkler method. While these models make it possible to introduce the principal factors governing the mechanical behaviour of dolmens, they do, however, entail the use of a number of simplifications that may be excessive. Nevertheless, in view of the importance of dolmens as part of our heritage, only low-impact mobilizations should be considered. Hence the simplifications would not necessarily be critical, and the solver developed (DeMo) would provide a valid estimation of the mobilization. After its verification, DeMo was used to analyze the sensitivity of the dolmen of Dombate (Northwest Spain) to actions associated with a conservation project. The importance of the shear forces generated between the cover and the rest of the orthostats was confirmed. Also demonstrated was the important role played by the water table. Lastly, it was possible to determine the consequences that past excavations might have on the conservation project currently under consideration. These analyses have helped to establish a rational procedure for the action and the implementation of complementary security measures. The approach of this study may be applied to other similar monuments. Hence the methodology proposed here may be used as a new assessment method in archaeological practices. Acknowledgements The authors are grateful to the Provincial Government of La Coruña for providing the research contract to carry out this study. We would also like to thank this organization for their support with the graphics by allowing us to use pictures from their web site. This research was also financed in part by a Research Grant awarded to Mr. Yustres and to Mr. Candel by the Education and Research Department of the Castilla-La Mancha Regional Government and the European Social Fund within the framework of the Integrated Operative Programme for Castilla-La Mancha 2000–2006, approved by Commission Decision C(2001) 525/1.
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