THE GROUND ACCELERATION OF HISTORICAL EARTHQUAKES

There exists in Spain a body of literature on the subject of historic earthquakes which, due to the lack of adequate analysis of the information available, turns out to be practically worthless. This article investigates the Andalusian Earthquake (25/12/1884). Ground liquefaction is analyzed at five sites within the province of Granada and Malaga, as well as in the damage caused to the Restabal Church. The final conclusions show the minimum acceleration value, which causes both the ground liquefaction as well as damage to the building itself. This research's starting point is taken from historic data found in reports carried out by Official Spanish, Italian and French Commissions sent to study the earthquake. Those documents provide us with information about the damage caused both to the buildings themselves, as well as to the effects on the ground. The geotechnical data needed to check ground liquefaction was obtained by penetration tests. The mechanical characteristics and resistance of the materials of the building, essential for the analysis of their seismic resistance, were taken from samples carried out in the laboratory on the same materials or from already existing data from similar materials.

On the other hand, the Spanish Commission refers to the damage caused to churches and the principal buildings of the area, special mention being made of the Restabal Church.
In the first part of this research, the liquefaction potential is analyzed at the following sites: (1), (2), (3), (4), and (6), in order to obtain the minimum value where liquefaction is caused by ground acceleration.
Once the site was chosen and the necessary dynamic penetration test carried out, the ground liquefaction potential was assessed Department of Civil Engineering, University of Granada, Granada, Spain.
by comparing the value of S.P.T. on each layer of the test sample (Figure 3), which was derived in turn from the dynamic penetration diagrams measured in situ, according to Vanelli arid Benassi [20] and Zhou [24], with the Neri, value obtained by the norm established by the Chinese State Capital Construction Commission [16].
Once the liquefaction on a ground layer had been checked, the cyclic stress ratio, 7/a' , and the peak acceleration, A, which would cause its liquefaction, were both calculated according to Seed's simplified procedure [ 15] .
Once the acceleration causing liquefaction in all ground layers of the survey was known, the maximum value of all was assessed, corresponding to the deepest layer.This value, amin, is a limiting value, from which liquefaction in the ground column was found to occur.In other words, the ground acceleration caused by the earthquake on the site was equal or higher to this value amin• The damage caused by the earthquake was serious, nearly a thou~nd houses had to be rebuilt and around fourteen thousand restored.The extent of the damage was due, not only to the high magnitude of the earthquake, but also to the low quality of building materials used in their construction.
The seismic response found within the bell tower of Restabal Church allows us to evaluate its seismic resistance, by relating the stresses obtained by the Finite Element Method, F.E.M., in the elastic field to the resistance of the materials in the damaged areas of the bell tower.If we compare the predicted damage ----estimated (no data) ------------   f:CD•' .' 7] Silty Sand R'""9 Sand & Gravel l (r.f~:.~:1

FIGURE 3 Penetration diagram of Rio Marchan (data obtained with DL030 Sunda Penetrometer)
By the above two procedures we can thus estimate the value of the peak acceleration above which ground acceleration in a historic earthquake in a given place, is situated.

GROUND LIQUEFACTION
In order to check the liquefaction potential, the following equation was used.
, It relates both the depth of the sand layer, d,, in metres, and the depth of the water table, cl,, in metres, with the critical S. P. T. Ncr;,, essential for liquefaction.Critical N values depend on earthquake intensity, I, being N = 16 for I = IX, N = 10 for I = VIII and N = 6 for I = VII.
The earthquake magnitude of 6.6 and the intensity at any of the given sites have been given by Munoz and Udias [12].
S.P.T. values, the density of the ground layers and the depth in the water table were calculated using penetration samples taken from five of the sites mentioned above.The results of the test are summarized in Table 1.For example, Figure 3 shows the penetration diagram in Rio Marchan.Comparing the S.P.T. average value in each layer with N0,;,, we can infer that the second layer is potentially liquefiable for an earthquake of intensity VIII or IX, as the fourth is for an earthquake with intensity IX.

Liquefaction acceleration
The cyclic stress ratio leading to the liquefaction in a ground layer can be calculated from Figure 4 (15] and the corresponding peak acceleration A in the following equation [15]: The maximum value in all accelerations obtained for a survey, amin• corresponding to the deepest layer, is a limiting value for the ground acceleration from which liquefaction in the whole ground column originates.
In other words, the ground acceleration caused by the earthquake had necessarily to be, at least, amin, for ground liquefaction to take place.In four of the five studied sites, ground liquefaction was confirmed and the following results obtained: Santa Cruz del Comercio, am;0 =0.21g.

SEISMIC RESISTANCE OF RESTABAL CHURCH
The walls of Restabal Church were built with brick masonry, being a resistant material, and limestone and dolomite gravel masonry, as stuffing material, both agglomerated J,y 1 : 3 •lime mortar.
Figure 6 shows the prominent cracks taken from the most fissured wall in the church's bell tower.

Mechanical behaviour of the masonry
Those tests carried out on unreinforced masonry walls, subjected to a combination of vertical and horizontal in-plane forces, reveal shear failure which is characte~ized with diagonal cracks in the wall, caused by the principal tensile stresses in the wall • exceeding the tensile strength of masonry, f,.For an elastic, homogeneous and isotropic material, the average shear stress in the horizontal cross-section of the wall when this failure [19] occurs is: Where, a 0 , is the average compressive stress in the horizontal cross-section of the wall due to the vertical load.Factor b determining the distribution of shear stress in the horizontal • cross-sectional area of the wall, takes the value 1.0 in the case of a squat wall (height to width ratio equal to 1.0) and the value 1.5 for slender walls (height to width ratio greater than 1.5) The behaviour of masonry walls when they are loaded out-ofplane, corresponds to the linear relation stress-deformation and to Navier's hypothesis, according to Yokel and Dickers [23] and Benedetti et al. [2].
Considering the mechanical behaviour of masonry, the linearelastic analysis is preferred instead of nonlinear dynamics; more specifically the M.E.F. was adopted in this research.

Mechanical characteristics and strengths in masonry walls of Restabal Church
Three masonry panels were built with solid bricks that dated from the time of the earthquake, and a 1:3 lime mortar, reproducing the way the building was constructed.The three panels were cured for 28 days at 25° C and at a humidity of 50%.The results of the tests carried out with solid bricks, mortar and masonry panels are summarized in Tables 2 and 3.
The remaining mechanical characteristics and resistance of the brick and stone masonry were obtained out from existing data for similar materials.The value of 0.25 MPa (1 Mpa = 10 kg/cm 2 l, was adopted for tensile strength and shear strength of brick masonry, according to those values recommended by Commission of the European Communities [5] for mortar and similar brickwork and the value of 0.20 for the Poisson coefficient was estimated from the works on such material of Page [ 13] and Atkinson et al. [I] .
For the stone masonry, the following values from Tomazevic et al. [18] were adopted: modulus of elasticity, 1000 MPa, tensile strength, 0.15 MPa, and compressive strength, 0.90 MPa.The shear strength was estimated at 0.10 MPa, close to values found in Benedetti and Benzoni [2] and Benedetti et al. [3].The Poisson coefficient was estimated at 0.30 from the works on such material [14].The density, 1600 kg/m 3 , was evaluated from specimens built for this purpose.

Seismic Resistance
The computer program, SAP80 [21], with 3D shell type elements was adopted for this research.The nodes defining the foundations were considered to be embedded.Figures 7 and 8 show the mesh of finite elements corresponding to the church and the bell tower.It can be seen that those elements belonging to the rectory during the earthquake period, now recently demolished, are shown as discontinuous lines.The seismic input adopted was the response spectrum for rock as shown by Seed [15], since the building is cemented on this material, with a damping of 5 % which is a normal value for masonry and was taken from works on similar materials by Ghobarah et al. [9] among other authors.
In each of the possible arrival directions for seismic waves, the tensions obtained in the mesh elements are proportional to the value of the peak acceleration used.Therefore, given a certain arrival direction of the S waves, the peak acceleration cracking the material in the bell tower walls is proportional to the peak acceleration used: The proportionality ratio, r, is the quotient between the cracking strength of the material and the stress obtained in the dynamic calculation, equation 1.

cracking stress r------c-c----::-=----,----;--;
stress predicted by the model From the calculations carried out, shear, compression and torsion stress in the bell tower walls were found to be negligible.This was true for any direction of the ~ismic waves contained within the tangents drawn from the building to the isoseismal line of maximum intensity (Figure 9).As a result of this, flexural tensile was adopted in order to obtain the acceleration causing cracking in equation 1.
The final result obtained was a peak acceleration in the range 0.10g -0.13g, to cause cracking of the lower wall (Figure 7, view 1), in the Restabal Church bell tower (Figure 10).

Ground Acceleration
Figure 5 shows the data for the minimum peak acceleration, being the cause of liquefaction in each one of the studied sites, and the minimum value in the peak acceleration that fissured the Restabal Church bell tower.
The different curves for acceleration versus epicentral distance were adjusted to the above five values by means of the non-.linear regression method (Figure 11).The adjustment was carried out with the help of the computer program Mathematica This curve does not represent a relation for the attenuation of acceleration with distance to the epicentre, due to the iimited data used ih its detennination.It• could be considered as a limiting curve, above which the acceleration values of those sites studied are most likely to be found.In the same figure, two curves have been drawn to show the peak acceleration's attenuation with distance for an earthquake of magnitude 6.6.Curve 2 represents Campbell's curve [4].and curve 3 represents the Fukushima and Tanaka curve [8]; they indicate a possible upper limit to the peak acceleration.

SUMMARY
Fieldwork and tec}miques used in this research have allowed us to develop a method for the calculation of a lower limit for the peak acceleration in the case of historic earthquakes, in sites where, either ground liquefaction or moderate cracking of the buildings effected by the earthquake took place.

FIGURE 4 FIGURE 5
FIGURE 4 Chart for evaluation of liquefaction potential forsands for different magnitude earthquakes[Seed and Idriss, 1982]

FIGURE 7
FIGURE 7 Mesh of finite elements for Restabal church.

FIGURE 8
FIGURE 8 Mesh of finite elements for Restabal church belltower.

3FIGURE 9
FIGURE 9 Range of possible arrival directions for seismic waves S in Restabal.

FIGURE
FIGURE IO Peak acceleration causing the cracking versusincidence angle S waves in the most cracked wall (Figure7, wall 1), in the Restabal church bell tower.
Sites where liquefaction presumably occurred with that caused by the earthquake, i.e. , by relating the stresses obtained by the F.E.M. with the material resistance of the DYNAMIC PENETRATION RESISTANCE (DL030) Sunda Penetrometer N ... (IMM IX) N ... (IMM VIII) Sand IC:<I Sandy Slit

TABLE 1
Characteristics of soil/profiles H = depth of layer of soil (rn) W. T. = depth of water table (rn) p = density of soil (kg/rn 3 )