ANALYSIS OF A DILATOME-TER TEST IN OVER-CONSOLIDATED SEDIMENTS, BASIN OF THE DUERO RIVER, SPAIN Keywords Dueñas, geotechnical parameters, hardening soil model, soft rocks and clays deformation Abstract A dilatometer test is a useful method for in-situ geotechnical surveys. It can be compared with the results obtained using a mathematical model. The mathematical model of concentric rings shown in this article is governed by the constitutive equation of the "Hardening Soil Model". A large number of tests made on the Dueñas Geological Facies, with a consistency ranging from firm clays to soft rocks, are compared to the model results. In this way, the "Hardening Soil Model"parameters are adjusted to the Dueñas Facies materials. 1 INTRODUCTION The pressuremeter test is very useful for determining the geotechnical feature parameters of original soils and for reducing the most common changes in the mechanical characteristics caused by sampling. It also allows us to test the original soil in its natural state of effective and pore-water pressure [1,2] Another advantage of this test is that a greater volume of material is tested in situ than would be tested in the laboratory, thus being closer to the real loading state encountered afterwards in engineering works. A pressuremeter test is an in-situ stress-strain test performed on the wall of a borehole using a cylindrical probe that is expanded radially. To obtain viable test results, any disturbance to the borehole wall must be minimized. The equipment used is called a PBP (pre-bored pres-suremeter), because it is best suited to the type of substrate studied (over-consolidated clays and soft rocks) and the standard applied is the ASTM D 4719-87 [3]. Table 1 shows the applicability of different types of pressuremeters [4]. In lightly over-consolidated clays, in a lot of consolidated ones as well as in a wide range of soft rocks, the volume F. Escolano Sánchez University Polytechnic of Madrid, Civil Engineering Department Alfonso XII, 3 y 5 - 28014 Madrid, Spain E-mail: felix.escolano@upm.es M. Bueno Aguado Euroconsult SA 28700. S.S. Reyes. Madrid, Spain Table 1. Applicability. SUBSTRATE PROBE PBP PROBE SBP PROBE PIP Soft Clays AAA Hard Clays AAA Sparse Sands B1 A A Dense Sands B1 B C Gravels CNN Soft rocks A B N Hard rocks ANN A = High; B = Medium; C = Low; N = None (1) Using fluted sleeve (Clarke 1996). Acta Geotechnica Slovenica, 2015/1 17. F. E. Sánchez & M. B. Aguado: Analysis of a dilatometer test in over-consolidated sediments, basin of the Duero river, Spain of soil examined by the pressuremeter test reaches states of tension that exceed the elastic levels. The interpretation and study of the strain and deformation states, produced in these cases, requires the use of soil constitutive models that allow this simulation. The current wide variety of computing programs includes soil advanced constitutive equations that simulate plastic states. Although these models should be implemented according to some initial parameters, these are usually far from those obtained in geotechnical tests. In the case of the over-consolidated clays and soft rocks, the constitutive model known as the "Hardening Soil Model" reliably reproduces the different stages of strain and deformation observed in field and laboratory tests. This effect on the constitutive model has been studied [1-2]. Thanks to the interpretation of the pressuremeter test using this constitutive model, a sound comprehension of the soil tensional processes, as well as a suitable adjustment of the tested model parameters, are achieved. During the geotechnical studies carried out for the highspeed train line between Valladolid and Burgos, several dilatometer tests were carried out in Dueñas Geological Facies. The geotechnical knowledge of Dueñas and the dilatometer test have been thoroughly studied with the support of the constitutive equation. A specific programme has been developed to define the pressuremeter tests that are also appropriate for other geotechnical units and used in the mentioned unit. This article explains the most relevant features of the method and compares its results with those obtained in the tests' campaign. Finally, this study brings forward the geotechnical parameters of Dueñas Facies according to the "Hardening Soil Model" constitutive equation. 2. GEOGRAPHICAL AND GEOLOGICAL FRAME OF THE SURVEY AREA The survey area is located in the Arlanzon river valley, between the Burgos and Palencia provinces, in the Iberian Peninsula NW quadrant. From the geological point of view, it is located inside the sedimentary basin of the Duero river, which spreads along approximately 50,000 km2 (Figure 1). Figure 1. Geological and geographical location of the study area and the thickness of the sediments. 38. Acta Geotechnica Slovenica, 2015/1 F. E. Sánchez & M. B. Aguado: Analysis of a dilatometer test in over-consolidated sediments, basin of the Duero river, Spain The sedimentary basin of the Duero river is an intra-plate depression that began to form at the end of the Cretaceous Period due to the Alpine movement of old basement fractures, produced during the Hercynian orogeny [5]. The sediments that filled this depression are organized according to a centripetal model in such a way that the terrigenous materials are disposed along the external edge of the basin and the chemical facies (carbonate) can only be found in the centre. It should be pointed out that there is a noticeable asymmetry of the basin so that the chemical central facies are displaced towards the oriental edge. The thickness of the sediments that filled the depression is uneven, reaching a thickness of over 2500 m in some areas [5]. The thickest areas are located on a WSW-ESE oriented surface that impacts the cities of León, Palencia, Aranda de Duero and Soria (Figure 1). This pattern shows the behavior of the bedrock fractures during the basin sedimentation following the hors-graben general model. The colmatation of this basin was not constantly and continuously carried out, it was achieved by "impulses" of maximum subsidence combined with periods of calm and even others of no sedimentation. It was a continental sedimentation corresponding with a perimetral system of coalescent alluvial fans, which drain into a central saline endorheic lacustral basin. The climatic conditions were typical of an arid or semi-arid climate with a variable seasonal rainfall. These general climatic conditions were almost constant during the whole Neogene Period. In the Quaternary geological period the basin fill is eroded, becoming in that way an exorheric basin and the fluvial net fits in. This process arranges along the time and is showed in the sedimentation of many terrace levels. 2.1. Stratigraphy of the survey area All the exposed materials of the area are sedimentary and they can be gathered into four major soil groups: - "Dueñas" formation. This is the most representative. It comprises an alternation of thin layers of clays, marlstones, marly limestones and gypsumy marlstones. This lithologic group has a colour that goes from light-green to whitish, its aspect is massive and its thickness is uniform. - "Tierra de Campos" formation. This is a lithologic group composed by clays, whose colour goes from pink to reddish, mixed with sandstones, gravels and conglomerates, whose colour goes from yellowish to reddish. - "Cuestas" formation. This comprises an alternation of limestones, marly clays and marlstones. Its general coloration is whitish or cream and it forms a uniform level of soil, whose thickness goes from 45 to 50 m, approximately. - "Páramo" limestone formation. This is composed of a group of thick limestone layers whose grain is fine, its structure massive and its colour from whitish to cream. Its widest thickness is from 5 to 10 m approximately. As was mentioned above, the importance and representativeness of the "Dueñas" formation, from a geological point of view, is the subject of this article. 3 DUEÑAS FACIES GEOTECHNICAL FEATURES Dueñas Facies is part of the tertiary sediments in the Duero depression. The basin sediments have been eroded by the fluvial net and have formed wide valleys. In the hillsides and fields of these valleys, there are horizons of clays, marlstones and limestones corresponding to the units called "Cuestas Facies", "Tierra de Campos and Dueñas Facies". The Dueñas Facies, chronologically older than the previous ones, comprises an alternation of 0.20-0.60 m, layers of clays, marlstones, marly limestones and gypsumy marlstones. Its colour goes from light-green to whitish and its general aspect is massive and uniform. The diffraction analyses with oriented aggregates carried out on samples from both layers give the mineralogical composition, as stated below in Table 2. Table 2. Mineralogical composition of Dueñas Facies. MINERALS Unity Quartz Dolomite Micas + kaolinites Calcite Gypsum Motmorillonite TD/y <7% 30 s 50% 10 a 30% <5% 30 a 55% <10% TD/m <10% 20 a 50% 20 a 55% 10 a 15% <0.5% <10% 38. Acta Geotechnica Slovenica, 2015/1 F. E. Sánchez & M. B. Aguado: Analysis of a dilatometer test in over-consolidated sediments, basin of the Duero river, Spain The superior layer, named TD/m, comprises clays and dolomites in similar levels. The inferior layer, named TD/y, has a gypsum mineral in almost a 50% proportion. This mineralogical composition reflects in its plastic features. The values obtained in the tested samples are shown in the plasticity chart below, Figure 2. In the case of gypsum marlstones (TD/y), as well as in the clays (TD/m), the samples have a wide level of liquid limits with values from 20 to 90. In both cases the points are mainly on line A. In addition, at the same liquid limit the clayey unit (TD/m) usually has a lower plasticity rate. In a natural state, the density and humidity in both units are placed in rates of different values. The results from the different tests are depicted in Figure 3. A higher density and a lower humidity are observed in the samples of gypsumy marlstones unit (TD/y). The quali- ties of the resistance and the deformation in both units are also different from those obtained in the dilatometer tests. These results will be discussed afterwards. 4 HARDENING SOIL MODEL The constitutive equation called the "Hardening Soil Model (HS-model)" has been developed [6]. It is a model formulated inside the framework of elastoplastic theory, which explains the behaviour of a simulated soil by pseudo-elastic models, and among them the hyperbolic model stands out as being the best known. In this section only the most relevant features that allowed an explanation of the pressuremeter test are mentioned. As in any elastoplastic model, the HS-model comprises: AO 00 Liquid Limit Figure 2. Graph of plasticity. 0 5 10 15 20 25 30 35 40 50 55 SO BS 70 Natural humldily ¡W¡ Figure 3. Dueñas Facies natural density and humidity. 38. Acta Geotechnica Slovenica, 2015/1 F. E. Sánchez & M. B. Aguado: Analysis of a dilatometer test in over-consolidated sediments, basin of the Duero river, Spain - A defined failure criterion for effective pressures. - An elastic behaviour for strain states under the failure level. - A plastic power function that determines the direction of plastic deformations. - A hardening law that modifies the failure criterion according to the previously achieved strain states and deformation tests. A typical feature of an HS model is that the hardening law is defined by the plastic deformation through the previous shear. The HS model's failure criterion is depicted in the equation: f = qJEso q/(qa - q) - 2q/Eur - Yp (1) where: q: stress deviator (q = 01-03) qa: failure deviator asymptote obtained by the equation: qa = qf/Rf (2) qf: failure deviator for an average effective pressure p, from: qf = 6 sin(0)/(3 - sin(0)) (p + c cotan(0)) (3) where: - c and 0 are the Morh Coulomb's failure criterion parameters. - The E50 and Eur load module and download module obtained by the expressions: E50 = E50ref (o3 + c cotan(0))/(oref + c cotan(0)))m (4) Eur = Eurref (o3 + c cotan(0))/(oref + c cotan(0)))m (5) where: - E50ref and Eurref are the reference modules for the confining pressure 0ref. - m is the influence exponent of the confining pressure in the deformation module. - Yp is the value of plastic shearing deformation obtained by the expression: Yp =£ip - £2p - £3p (6) The elastic behaviour below the failure level is an elastic equation with a deformation module Eur and a Poisson's coefficient v. Finally, the plastic deformations are defined by the plastic potential function "g" with the expression: gi3 = O - ffa)/2 - ((ffi + o3)/2) sin(f) (7) gi2 = (oi - 02)/2 - ((oi + 02)/2) sin(f) (8) where: f is the dilatancy angle. The second surface simulates the plastic deformation direction when two main strains match up (compression and traction biaxial states). To sum up, there are seven essential geotechnical parameters to define the constitutive equation: c: the effective cohesion 0: the effective friction angle E50ref: the load module for a reference pressure Eurref: the reload module for a reference pressure Rf : the failure relation m: the influence exponent of the confining pressure in deformation module v: the Poisson's coefficient f: the dilatancy angle. 5 THE INTERPRETATION MODEL OF THE PRESSUREMETER TEST The interpretations of the pressuremeter tests were performed according to a concentric-rings model [7]. Figure 4 shows a schematic representation of the used model. It is an axisymmetric model made of forty concentric cylindrical rings of variable thickness. This thickness grows with its radius so that the narrowest ring is close to the bore hole. The external radius of the model is approximately 10 metres. The internal one is the borehole radius, which is usually 5 cm in size. Initially, the internal radius of each ring is determined by the expression: ri = ri-1 + i2/2000 (9) 38. Acta Geotechnica Slovenica, 2015/1 F. E. Sánchez & M. B. Aguado: Analysis of a dilatometer test in over-consolidated sediments, basin of the Duero river, Spain where: ri is the internal radius of the "i" ring in the meter. An outline condition of no radial deformation is established on the external edge of the 40th ring of the model. On the internal edge of the first ring a "u" displacement takes place. In order to use the small deformation hypothesis, the magnitude of the "u" displacement is limited, so the variation in the radial deformation in any ring must be under 0.5% For small deformations, each ring responds to the displacement according to an elastic and linear behavior. The used parameters are the unload deformation module Eur and the Poisson's ratio v of the element when the displacement takes place. As a result, a "u" displacement is obtained in each ring in its internal outline. According to the displacement of each ring, the average deformation ring is determined by the expressions: £ri = (Ui+1 - u,)/(ri+1 - ri) (10) £-ti = (u + u+i)/(ri + r+i) (11) where: eri and eti are the radial and circumferential deformations, respectively. The vertical deformation is obtained by considering the total vertical pressure constant. Taking these deformations as a starting point and using a numerical integration procedure, the effective strains compatible with the constitutive equation are determined. After each deformation increment, the ring model is updated with the new radii dimensions. In the case of the undrained test, the deformation module is a transformation of the previous one, obtained by the condition of a constant shear modulus G. Gu = G Eu/(1 + Vu) = Eur/(1 + v) (12) The adopted undrained Poisson's module is 0.495. The generated pore-water pressure in each element is a function of the volumetric deformation (ev) and the water-compression module. It is supposed to have a superior magnitude than the soil magnitude. The generated pore-water pressure in each interval and ring (vi) is determined using the expression [8]. v{ = 300 Eur (Vu -v) / {3 (1 + v) (1 - 2 * v)} £v (13) With these effective pressures and the pore-water pressure, the total pressures are determined as: a = a'+ v (14) The total radial pressure of the first ring corresponds to the one applied inside the borehole. Additionally, the traction states are limited so that no negative effective stress could appear. No negative values are allowed for the interstitial pressure either. The model requires the definition of an initial state pressure, which must be similar to the corresponding geostatic one. The initial pore-water pressure will be a function of the phreatic level measured in the borehole. 6 MODEL CHARACTERISTIC RESULTS The application of successive displacements inside the first ring of the model implies a relation between the internal pressure and the deformation of the borehole wall with a relatively hyperbolic shape [9]. Figure 5a shows the evolution of the total pressure on the borehole wall. The total radial pressure has two stages. The first one with mainly elastic deformation is characterized by large increments of pressure for small deformations. The second one, in which the plastic deformation is increasingly more relevant and, the deformation grows quickly in increments of pressure similar to those found in the first phase. The radial pressure extends constantly versus the deformation, so that the shape of the curve is an inclined asymptote. The circumferential pressure also has two stages, although in this case the pressure has lower values than the initial one. On the other hand, the total vertical pressure remains constant and close to the initial value. Figure 5b depicts the same representation as the previous one with the three effective pressures close to the interstitial pressure. There is also an elastic initial stage followed by a plastic one for the radial and circular pressures. However, in the latter, the circumferential pressure reached a horizontal asymptotic value. This value reflects the total plastication of the internal rings. The HS model is a constitutive equation whose function of breakage and plastication criterion can be represented in the plan p-q: p = a + a2 + a3)/3 (15) q = a1 - a3 (16) 38. Acta Geotechnica Slovenica, 2015/1 F. E. Sánchez & M. B. Aguado: Analysis of a dilatometer test in over-consolidated sediments, basin of the Duero river, Spain a) —Radial pressure —Circu la r pressu re —-Vertical pressure / / / / ( 0,043 0.05t 0053 Inner radiusoffrie cavity (im) b) I.ODO 500 co flOO £ m 700 g o 600 h o xi 500 cd £ c o 400 œp 5 ud 8 300 i 200 100 0 ^—•Radial pressure ^Circular pressure tertical cress ure Inters titial pre ssure / / 0,047 0.C65 3.057 0049 0.051 O.CH Inner radius of 1he cavity (m) Figure 5. Pressures on the borehole drilling. Total pressures (a) and effective and interstitial pressures (b). As the function that defines the breakage criterion depends on the previous shear plastic deformation, its representation is a group of curves, the superior limit of which is the qa value. Figure 6 shows the p and q evolution in the test, together with the qa limit. Ü- 2SD —qa —1 ? / 3.0-19 (1,(151 II .053 Inner radius of the cavity (ml Figure 6. Test p-q graph. 38. Acta Geotechnica Slovenica, 2015/1 F. E. Sánchez & M. B. Aguado: Analysis of a dilatometer test in over-consolidated sediments, basin of the Duero river, Spain The graph shows how the strain deviator q grows until it becomes asymptotic with the line defined by qa . The plastic deformations take place along the whole loading process. It must be made clear that the dilatometer test is basically a test of p=constant. This model allows a study of the evolution of pressures inside the soil. Figure 7 shows this evolution. It is clear that the volume of soil affected by the test does not expand by more than 2.0 m around the borehole. The strain variations between 2.0 m and 10 m of the model are almost null. The circumferential effective pressure decreases quickly close to the borehole wall. As it moves away from the borehole wall, the circumferential pressure decreases slowly, until it reaches an asymptotic value corresponding to its initial value. A similar behaviour is observed in the circular and vertical pressure. In the same way, the farther we are from the borehole, the lower the pore-water pressure becomes as it reaches its initial value. 7 COMPARISON BETWEEN THE TEST RESULTS AND THE MODEL_ The results of the model have been compared with in-situ tests in the Dueñas unit. Among the thirty-five pressuremeter tests carried out, three have been distinguished. In the first group gypsumy marlstones (TD/y) are tested, in the second one there are clays from hard to very hard from Dueñas clayey layers (TD/m) and, finally, in the third group there are clays of high consistency, also from Dueñas clayey layers (TD/m). The graphs in Figure 8a and 8b below show the four main tests from those carried out with gypsumy marlstones (TD/y). This material is classified as soft rock. This graph depicts the adjustment with the rings model. Three of the tests were adapted to the radial total pressures curve and the fourth one is adjusted to the radial effective pressures curve, both in the same calculation. The parameters used in this calculation are presented in the chart below (Table 3). Table 3. Parameters used in this calculation are gathered in the chart below to a depth of 20 m. HS-Model Parameters for gypsumy marlstones in Dueñas unit Effective cohesion 0.5 Mpa Internal friction angle 45° Dilatancy angle 3° Loading reference module E50ref 400 MPa Downloading reference module Eurref 600 MPa m 0.8 Rf 0.7 Initial state equal to 20 m deep. (*) reference pressure 100 KPa The test results are analogous to those of the proposed model. Nevertheless, two different behaviours are observed. In the three tests of Figure 10 the radial pressure grows to an inclined asymptotic straight line. This behaviour should belong to a model where the pore-water pressure does not disappear, but it is added to the effective pressure to support the pressure on borehole walls. The adjustment of these experimental curves takes place with the total pressure of the model. 1.0 inner rddijt of the csv-lV |m> Figure 7. Evolution of pressures inside the soil. 38. Acta Geotechnica Slovenica, 2015/1 F. E. Sánchez & M. B. Aguado: Analysis of a dilatometer test in over-consolidated sediments, basin of the Duero river, Spain B.IIIG ■-■ 7.000 0. Ï1 = 5.ODD S .000 f ° 4.ODD O c 3.000 D ñ 5) 2.000