Time variations of the K0 coefficient in overconsolidated clays due to morphological evolution of slopes

    Time variations of the K 0 coefficient in overconsolidated clays due to morphological evolution of slopes Francesca Bozzano, Alberto Bretschneider, Salvatore Martino, Alberto Prestininzi PII: DOI: Reference:

S0013-7952(13)00331-1 doi: 10.1016/j.enggeo.2013.11.013 ENGEO 3708

To appear in:

Engineering Geology

Received date: Revised date: Accepted date:

23 May 2013 25 October 2013 23 November 2013

Please cite this article as: Bozzano, Francesca, Bretschneider, Alberto, Martino, Salvatore, Prestininzi, Alberto, Time variations of the K0 coefficient in overconsolidated clays due to morphological evolution of slopes, Engineering Geology (2013), doi: 10.1016/j.enggeo.2013.11.013

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ACCEPTED MANUSCRIPT Time variations of the K0 coefficient in overconsolidated clays due to morphological evolution of slopes

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Francesca Bozzanoa, Alberto Bretschneiderb, Salvatore Martinoa, Alberto Prestininzia Department of Earth Sciences and CERI Research Centre on Prevention, Prediction and Control of

Geological Risks, Sapienza University of Rome, Piazzale Aldo Moro, 5 – 00185 Rome, Italy IFSTTAR French institute of science and technology for transport, development and networks, Centre de

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b

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Nantes; Route de Bouaye CS4 44344 Bouguenais Cedex, France

phone: +33240845807

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Corresponding author: [email protected]

Abstract

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The incision of a natural or an artificial slope in a clay deposit initiates a morphological evolution and determines variations of the internal state of stress in the deposit. This evolution can be analyzed

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considering the variations over time of the lateral stress at rest coefficient K 0. This paper is focused on the evolution of the K0 in overconsolidated clay deposits submitted to the incision of natural slopes. The

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proposed idea is that, under specific morphological and evolutionary conditions, a value of K0<1 could be considered reliable even for medium-high OC clay deposits. This idea is here discussed with the support of in-situ and laboratory data from: i) pressuremeter tests performed in overconsolidated clay deposits in Central Italy, ii) a scaled physical modeling experiment reproducing a normally consolidated clay deposit. This study suggests that when dealing with clay deposits subjected to a simultaneous vertical and horizontal unloading due to slope incision, the K0 coefficient should be considered a parameter variable as a function of the different stress-strain evolutions experienced by each portion of the deposit. The portions involved in the slope incision had different evolutions and are represented by different K0 values. As a consequence, diverse amounts of decrease distinguish the evolution of the K0 for natural rather than artificial slopes.

Key words: Lateral stress coefficient; overconsolidated clays; pressuremeter tests; physical modeling

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ACCEPTED MANUSCRIPT 1 Introduction The lateral stress coefficient K0 is one of the most critical parameters to be evaluated in geotechnical

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investigations. Its importance is well known in all those engineering applications dealing, for example, with

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retaining walls, artificial cuts, building foundations and definitely with the stability of natural slopes. The assessment of its value has always been a challenge for Engineering Geologists and Geotechnical

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Engineers, because it cannot be directly measured, but only indirectly estimated by field pressuremeter tests, or numerical modeling. Some laboratory evaluations were carried out, measuring the suction pressure and

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anisotropic elastic parameters (Doran et al., 2000; Sivakumar et al., 2001, 2009). One of the main problems for its evaluation is that this coefficient has variable values due to the variations of horizontal and vertical

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stresses occurred in the soil deposit during the geological and tensional evolution.

The lateral stress at rest coefficient K0 is analytically defined as the ratio between the horizontal effective pressure and the vertical effective pressure acting in the soil, under a geostatic condition. Geostatic

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conditions require two points: i) vertically and horizontally oriented principal effective stresses 1 and 3, ii)

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zero lateral strain. The value of K0 is a function of several different parameters, such as the shear strength of the soil, its stress-strain history and weathering history.

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Based on Jaky (1944), for a normally consolidated soil mass which has not been subjected to removal of overburden, nor to activities that have resulted in lateral straining of the soil, K 0 value can be approximated as K0=1-sin ’, where ’ is the friction angle of the soil in terms of effective stress. The K 0 for an overconsolidated clay is higher than the K0 for the corresponding normally consolidated clay. In the common practice its value is calculated starting from the shear strength angle and the over consolidation ratio OCR. Some empirical relationships generally applied to calculate K 0 value for OC clay, are:

K 0 (OC )  K 0 ( NC )  OCR (sin ' ) (Mayne and Kulhawy 1982) with K 0 ( NC )  1  sin  ' (Jaky, 1944)

or

K0 (OC )  K0 ( NC )  OCR a with a  0.5 (Meyerhof 1976) or a  0.46  0.06 (Lancellotta, 1993)

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ACCEPTED MANUSCRIPT It is generally assumed a K0>1 for the most part of the overconsolidated clay deposits. Nevertheless looking at K0 vs. OCR relationships, its value is higher than 1 for clays with OCR ≥2÷3 (Brooker and Ireland, 1965; Chandler and Apted, 1988; Cooper et al., 1998; Sivakumar et al., 2001). The evaluation of the K0(OC)

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coefficient still represents an open problem. Predictions based on laboratory tests and expressed as a

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function of the effective internal friction angle and of the OCR are still debated. Michalowski (2005) revisits the Jaky’s (1944) solution to K0 for normally consolidated clays. More recently, Sivakumar et al. (2009) faced

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the problem of the determination of the K0 for OC clays, considering the influences given by the anisotropy, and proposing a relationship for the determination of the K0(OC).

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The idea proposed in this paper starts from the consideration that during the long lasting incision of a natural slope (which can last also tens of thousands years) in an OC clay deposit, the horizontal stress decrease can

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be higher than the vertical one. Indeed, since OC clay deposits have already experienced huge vertical stress decrease due to deepening responsible for vertical unloading, the incision of a slope determines a

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stress decrease mainly on the horizontal direction. Such mainly horizontal unloading brings to a decrease of the K0 value achieved with the overconsolidation, and different portions can be distinguished inside the clay

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deposit. In the clay portion nearer to the slope, stress indicators rotate from their original position and horizontal strain occur so that the “at rest” condition is lost. On the contrary, in the internal portion of the

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deposit the stress decrease does not produce any distortion of the stress field or any horizontal strain, due to the confinement of the clay. In this portion the “at rest” condition is still preserved (Fig. 1a) even if the value of the coefficient is decreased.

An evaluation of the K0 coefficient for OC clays at a certain distance from the slope is here reported and analyzed. These data are discussed in the light of the results of a scaled physical modeling experiment. The K0(OC) values evaluated for these clays are lower than those expected by the application of the analytical relations to highly overconsolidated clays. Applying theoretical assumptions supported by experimental data from site and laboratory tests, following deductive logic criteria, an interesting discussion about the reliability of K0<1 for natural slopes excavated in high OCR clays comes out.

2 Evolution of the K0 coefficient in overconsolidated clay natural slopes The relationships for the estimation of the K0 were derived in studies on artificial cuts (Brooker and Ireland, 1965; Pruska, 1973; Meyerhof, 1976; Mitachi and Kitago, 1976; Mayne and Kulhawy, 1982; Simpson, 1992;

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ACCEPTED MANUSCRIPT Shohet, 1995). This means that in these studies the K0 is evaluated considering the response of overconsolidated clay to a quick change of its stresses and boundary conditions. Finite element analyses (Vaughan, 1994; Potts et al., 1997) performed on man-made cuts in OC clays showed the influence of the K0

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in the progressive development of a failure surface, displaying its evolution over a period of about 15 years

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after the excavation was made. The same analyses show the influence of the K 0 on the rupture surface: for low K0 values the surface is relatively shallow, an increase of the K 0 until 1.75 induces a deepening of the

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rupture surface. But with values higher than 2, the rupture surface run further into the slope, and the development of a second almost horizontal surface can be observed (Leroueil, 2001). Recent studies on

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vertical cuts in stiff clays pointed out the influence of the lateral stress at rest coefficient on the development and propagation of shear zones from excavation, and the strong relationship between the slope stability and

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the initial K0 value (Kutschke and Vallejo, 2011, 2013).

The above cited relationships to determine the K0, have always been used also for natural slopes.

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Nevertheless the geological and morphological evolution of a natural slope is something different in comparison with artificial cuts and also with what can be reproduced by laboratory experiments. First, the

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main difference is the very long duration of the incision which brings about an extremely slow morphological evolution. Secondly, a slope can evolve in different ways, depending on lithology, weathering, erosion rate,

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sediment transportation mechanisms, load and unload events, and other influencing parameters.

Applying the analytical relations cited above, a value of K0 for a medium-high OC clay should be always higher than 1, meaning that, under overconsolidated conditions, horizontal effective stresses are higher than the vertical ones. This results from analyses on artificial cuts in OC clays, and it is certainly valid for clay deposits where the overconsolidation is due to vertical unloading only, without any further geological or morphological evolution. Nevertheless high K0 values are commonly used for analyses also on natural slopes, without taking into account the fact that this condition is not verified on natural slopes, where morphological incision processes induce a stress release both on the vertical and horizontal directions. Considering the very long time in which the slope is in a not confined condition, the horizontal stress variations, and consequent K0 decrease, can interest ridges with a width of about 800 m (Bozzano et al., 2006; 2008). Indeed it is difficult to believe that the OC condition achieved from a clay deposit after a vertical unloading (erosion) could be preserved in such a ridge subject during tens of thousands of years to a slope incision process, in absence of external stresses (e.g. tectonic fields).

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ACCEPTED MANUSCRIPT Following this concept, it is reasonable that in the external part of a slope, the stress release is responsible for the distortion of the stress field, and causes a decrease of the coefficient from a K0 to a generic K value (Duncan and Dunlop, 1969; Matheson and Thomson, 1973; McTingue and Mei, 1981; Savage et al., 1985).

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On the contrary in the internal parts of the slope (i.e. far from the slope surface), these stress variations

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occur maintaining the soil under geostatic conditions, the K 0 of the deposit can significantly decrease during the time, but preserving the conditions to be an “at rest” coefficient (i.e. geostatic stresses and zero lateral

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strain). Indeed since a soil is a visco-plastic medium, the horizontal stress decrease experienced by a slope during the valley incision stage is not necessarily coupled with relevant horizontal strains. It follows that only

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the horizontal deformation due to unloading and rotation of stress indicators (Fig. 1a) interests only the peripheral and more surficial portion of the soil mass just below the slope. Starting form an equilibrium

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condition, the natural evolution of the external part of the slope brings the K 0 to decrease until a Kf value, corresponding to a slope failure. The internal portion of the slope, on the contrary, remains under geostatic conditions and no failure can occur. The here discussed variations of the K0 are referred only to the OC clay

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of the internal portion of the slope; because for these clays the only possible stress-paths in the p-q plane are included in the area evidenced in Fig. 1b. This portion of the p-q plane is described by all the K-lines with

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an origin in (0,0) and an angle lower than the angle of the K-failure line.

3 Study methodologies

To discuss the K0 evolution in natural slopes in OC clays in the light of the here proposed evolution, in this study are considered data from: i) in-site pressuremeter tests, ii) a scaled physical laboratory modeling experiment.

Menard Pressuremeter tests were realized in two different sites, both located in Central Italy, characterized by a similar lithology, but with different geological evolutions and stress histories. The first test site is the western slope of the Monte Mario hill, in Rome; the second test site is the southern slope of the Lubriano hill, about 100 km north of Rome (Fig. 2). It is well known that pressuremeter tests allow to obtain a quasi-direct assessment of the K0 coefficient, and it is largely recognized that none of the existing techniques allow an exact evaluation of the ’h0. Indeed, on the one hand the Menard Pressuremeter (MPM) needs a pre-boring that produces a tensional release of the soil in the borehole, on the other hand with the Self Boring Pressuremeter (SBP), the self-perforation induces large influences on the tests given by the penetration rate,

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ACCEPTED MANUSCRIPT the drilling mud, the rotation velocity of the boring tool and its reduced distance from the pressuremeter cell (Ghionna et al., 1981; Cestari, 2005; Lancellotta, 2008). Despite these uncertainties, different methods can be applied for the evaluation of the in situ horizontal stress state depending on the applied pressuremeter

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test technique (Marsland and Randolph, 1977). The MPM pressuremeter tests performed in this study were

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localized in the more internal part of the slopes not affected by stress release.

A physical modeling experiment reproducing the rheology of a clay deposit was performed. The model was

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equipped with an internal stress monitoring system to measure horizontal and vertical stresses. The experiment allowed sketching out a hypothesis about the amount of stresses existing in a clay deposit in

4 Field data: tests on natural slopes

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geostatic at rest conditions.

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Due to its relatively recent geological history, and to the recent formation of the Apennine chain, slopes in OC clays are very common in Central and Southern Italy: the Apennines foredeep basin bounds the eastern

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margin of the peninsula, while in the inner and western parts of the chain a large number of back-arc or piggy back basins are disposed; as a consequence overconsolidated clays widely outcrop. Sometimes OC clays

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are very similar under a lithological point of view, nevertheless each basin had a specific geological evolution, and the resulting stress histories of the involved clay deposits are different. Referring to the geological evolution of central Apennines (Italy), a slope could be thought as the result of tens or hundreds of thousand years of geological evolution (i.e. Pleistocene-Holocene). During the last hundreds of thousands of years, the amount of vertical and horizontal stresses certainly changed as a consequence of: marine and continental sedimentation, volcanic events, erosion processes, variations of the tectonic stress field of the chain. The result of these geological and morphological evolutions resulted in several loading and unloading cycles on the clay deposits, causing stress variations both in the horizontal and vertical directions and the overconsolidation of clays which presently outcrop on several slopes of Central and Southern Apennines. The K0 value that can be evaluated today inherits the stress variations due to this complicated geological evolution.

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ACCEPTED MANUSCRIPT 4.1 Monte Mario The first test site is the western slope of the Monte Mario hill, in Rome (Fig. 3), located in the north-western

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part of the city. With a height of about 150 m above sea level, it is the topmost hill of Rome. The Marne

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Vaticane Fm. clays outcrop at the base of the hill. These deposits constitute the bedrock of the whole Roman area and are made up of silty clays interbedded with silty sands with a dip from sub-horizontal to about 20°. The “Marne Vaticane” clays are overlain, with an unconformity, by the “Monte Mario” unit, a prevalently

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sandy deposit composed by: a 15 m thick level of “Limi di Farneto” silts; a 2 m thick level of gray sands with “Artica Islandica”; an over than 50 m thick level of “Sabbie Gialle di Monte Mario” sands with some top

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beachrock layers, up to 50 cm thick, known as “Panchina a brachiopodi”; the upper level is a grey-greenish lagoonal clay deposit, with a maximum thickness of about 2-3 m, known as ‘‘Argille verdi a Cerastoderma

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Lamarckii’’. (Ambrosetti and Bonadonna, 1967; Bonadonna, 1968; Belluomini, 1985; Malatesta and Zarlenga, 1986; Marra, 1993; Bellotti et al., 1994; Marra and Rosa, 1995a,b; Marra et al., 1998; Cosentino et

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al. 2004). The stratigraphic succession indicates a marine regressive evolution from a depth basin environment, to a lagoonal-continental environment. In some areas of the Monte Mario hill, volcanic deposits

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cap the sedimentary succession. The Tiber River valley incision, occurred in different cycles consequent to

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marine eustatic variations, modelled the slope’s profile to its present shape.

In this test site, some pressuremeter tests were carried out for the construction of a tunnel across the Monte Mario hill. Two boreholes were drilled near the hilltop, crossing the Monte Mario sands and reaching the Marne Vaticane clays. Three pressuremeter tests were performed at depths varying from 25 to 48 m below ground level. At these depths the topographical surface of the slope was distant enough to assure that this part of clay was not involved by horizontal deformations during its geological evolution.

Based on the results reported in technical reports (Table 1) the mean lateral stress ratio K 0 value is about 0.63÷0.65, i.e. clearly lower than the ones expected by applying analytical relationships (Mayne and Kulhawy, 1982; Sivakumar et al., 2009) considering an OCR of about 6 for these clays (Bozzano et al., 2006).

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ACCEPTED MANUSCRIPT 4.2 Lubriano The second test site is located in the southern slope of the Lubriano hill (Northern Latium). The Lubriano hill

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is constituted by a flat shaped volcanic plateau, about 40 m thick, overlying an overconsolidated clay

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substratum (Fig. 4a). The marine blue clay constitutes the geological substratum of the whole Tiberina Valley area, a large area among Northern Latium, Umbria and Tuscany. These clays were deposited between the

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Upper Pliocene and the Lower Pleistocene in the Middle Tiber Valley basin, a marine basin about 100 km long in NNW-SSE direction and 30 km large, set in the back arc of the Apennine chain in northern Latium

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(Funiciello et al., 1981; Bigi et al., 1992; Barberi et al., 1994; Girotti and Mancini, 2003). The clays are grey if not weathered, while their colour changes into yellow when in outcrop and weathered; their attitude is subhorizontal, but in this area it is not evident at all. The clay deposit was implicated in the regional uplift of the

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whole Central Apennines area, and involved in subaerial erosion of its upper portion with a consequent overconsolidation.

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The basal clay was then overlaid by a thick tuff deposit composed by different units, from the bottom to the

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top: i) the Lower Bolsena tuffs, a fall deposit including all the fall volcanic products from ~600 ka to ~350 ka; ii) a Lava flow, outcropping in a small area; iii) the Orvieto-Bagnoregio Ignimbrite, a well-known pyroclastic

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flow aged ~336 ka, used as a stratigraphical marker in all the area and composed by a classical red lithoid tuff with black scoriae facies, and black scoriaceous in fine ash matrix facies; iv) the Upper Bolsena Tuffs, including all the fall events subsequent the Ignimbrite pyroclastic flow.

Two boreholes were drilled on the Lubriano tuff plate about 20 m from the cliff. Due to the tuffs attitude, the boreholes were drilled in the adjoining, across all the ignimbrite and stratified tuffs deposits. Only one of the boreholes reached the clay till 10-15 m below the tuff-clay geological contact (Fig. 4b). Aims of the boreholes were: a) stratigraphic log of the tuff plate above the tuff-clay geological contact; b) reconstruction of the tuffclay contact geometry, c) in situ clay sampling, d) characterization of strength and stiffness of the clay by pressuremeter tests. The sampling of undisturbed clay was very important since the clays under the tuff plate can reasonably be considered to be under geostatic conditions, i.e. no significant deviatoric vertical stress occurred duo to the valley incision. At this regard, it is worth noting that in adjacent areas it had been demonstrated that a geological and stress evolution similar to that experienced by these clays and described above, produced a softening of the upper clay portion, due to the vertical unloading-reloading geologic process (Bozzano et al., 2008a). As a consequence, the stiffness contrast between tuffs and clays becomes

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ACCEPTED MANUSCRIPT higher and modifies the engineering-geology model (Bozzano et al., 2008b). Laboratory tests on undisturbed clay allowed the definition of the physical and mechanical properties for the lithologies, and to define an OCR

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value almost equal to 7 (Farina, 2007).

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Two pressuremeter tests have been performed in clays at the depths of 32.5 m and 46 m below ground level. The results (Table 2) allow the evaluation of the in situ horizontal stress value to estimate the lateral stress ratio K0, whose value is 0.63 at 32.5 m and 0.67 at 46 m. The value of the K 0 resulting from this

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evolution was measured under geostatic conditions, i.e. in a portion of the slope not yet involved by deviatoric vertical stresses. Also in this test site, the obtained value is higher than the K0 (NC) value, thus

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indicating the overconsolidated clay status, but it is clearly lower than what was expected or what could be

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predicted applying the analytical relationships for OC clays.

The similar evolutions experienced by the Monte Mario and Lubriano blue clays result in similar mechanical properties. The analysis of the Lubriano clay physical properties (considering the natural unit weight n,

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natural water content w%, porosity and saturation) allowed to reconstruct the geotechnical stratification of the shallowest clay portion, the logs reported in Fig. 5 highlight the presence of a hardened crust layer in the

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upper part. This finding agrees with the point that the geotechnical stratification of a geological contact

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implicating clays which in their history have been subjected to stress loading-unloading cycles, is much more complicated than the simple lithological layering detectable by a classical geological survey (Bozzano et al., 2006, 2008a).

5 Laboratory data: quantitative physical modeling experiment To measure K0 values under controlled geostatic conditions, a scaled physical laboratory model was planned and realized at the Engineering Geology Laboratory of the Department of Earth Sciences – “Sapienza” University of Rome. The physical model reproduced the “tuff on clay” geological setting typical of the Teverina area in northern Latium (Fig. 6a), and in particular the lithology thickness was considered similar to that of the Lubriano ridge. The mechanical properties of real lithologies were scaled according to the scaling ratios described in the following. The target of this experiment was the measure of the stress distribution in the model.

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ACCEPTED MANUSCRIPT A model always represents a simplification and a schematization of a real situation and the planning stage is always tricky. At this aim, a particular attention was paid on the choice of proper artificial materials for the reproduction of real lithologies. In particular in the process under examination, the role played by the

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deformability is fundamental and, as a consequence, this was the most important parameter that was

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considered in the scaling procedure. Some approximations were necessary: the clays overconsolidation status was not reproduced, since it is not possible to correctly simulate it in physical modelling. Moreover, the

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stiffness variation in the highest portion of the clay deposit (Bozzano et al. 2006, 2008a), due to the slope’s evolution, was also neglected since in the scaled model it became an infinitesimal detail. As a consequence,

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this experiment reproduces in a generalized way the viscoelastic behaviour of a normally consolidated clay layer under stress conditions similar to those existing in the Lubriano case study area. The basal clays were

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approximately reproduced with a unique artificial material representative of the whole lithology.

Studying time-dependent processes, the time factor cannot be neglected. It has been fundamental to

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consider the rheological behaviour of real lithologies in the scaling procedure, and to make use of artificial materials with a rheology similar to that of natural lithologies. These materials were created, tested and used

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in physical modelling experiments performed in the Department of Earth Sciences of the Sapienza University of Rome (Maffei, 1998, 2002; Bretschneider, 2010, Bozzano et al., 2013). The artificial material used for the

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rigid plate was a mixture composed of marble powder from the Carrara quarries and 32.5 R Portland cement, respectively 95% and 5% in weight. This material, named C5, has been considered suitable to represent volcanic rocks on the basis of its physical characteristics, mainly for its deformability value well-fitting with the applied scaling ratio (Fig. 6b). To deduce its mechanical characterization, this material underwent several laboratory tests. To reproduce the rheological behaviour of the basal clays, a grease and Carrara marble powder mixture was used (Fig. 6b). The mixture, named G200, is constituted by a part in weight of a particular grease, whose properties are not affected by temperature changes, and two parts of marble powder, with a controlled grain size. This material has been characterized through different laboratory tests realized in past studies (Maffei, 1998, 2002; Bretschneider, 2010). Beside strength and deformability properties, the rheological behaviour of the mixture was investigated by creep tests and rheometer measures. Rheological analyses allowed to define a proper mechanical model and to estimate the viscosity. The Zener’s model was considered for viscosity calculations, even if the Burger’s mechanical model was the most suitable. The reason is that the Burger’s model includes two viscous elements, each with a different viscosity value, and it is not possible to discriminate between them basing on the test measures. The Zener’s mechanical model (also known as Standard Linear Solid) has one only viscous element and can be

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ACCEPTED MANUSCRIPT completely handled. A nonlinear curve fitting of the parameters of viscosity and Young modulus has been performed with the creep test data. The model’s constitutive equation is here expressed as an (t) function, being 0 the constant load in the creep test and E1, E2,  the two Young’s moduli of the Hook parameters

E2



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0

 E1E2t

 0 E1 ( E1  E2 ) E2

e ( E1E2 )

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 t  

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and the viscosity of the Newton parameter respectively.

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Property values for the artificial materials are reported in the Table 3.

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5.1 Scaling and experimental setup

According to the standard similarity conditions, scaled models should be geometrically, kinematically,

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dynamically and rheologically similar to natural examples (Hubbert, 1937; Ramberg, 1981). In the here -3

realized model, the length ratio is L*~10 , the density ratios between tuffs and clays and their respective

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analogue materials is *~1, the gravity ratio is g*=1 since the experiments are performed under the standard gravitational field. The corresponding stress ratio between model and nature is *=*×g*×L*~10 . -3

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Deformability ratios for the brittle and the ductile materials resulted of the same order of magnitude, giving a good representativeness of the scaled effects due to this parameter.

This experiment takes into account the time-dependent viscoelastic behaviour of the ductile substratum, represented in the models by the G200 mixture and in nature by clays. Viscosity is a very difficult parameter to evaluate on clays, different experiments performed in the Seventies’ from eastern Europe scientists, reported in Viyalov (1986), estimated the viscosity value of stiff clays about 10

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Pa·s. The viscosity value for

G200 is correlated to the strain rate; considering the expected experimental strain rates, an estimated value for the G200 viscosity could be ~10 Pa·s. With this assumption the resulting ratio is * ~10 . Starting from 7

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these ratios, being *=*/2 *, a strain rate ratio * of ~10 , and a time ratio t* of ~ 10 can be calculated, so ·

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that 1000 years of the natural slope evolution are simulated in about one month in the model (Table 4).

The model set up is constituted by a 12 cm thick C5 layer superimposed on a 36 cm thick G200 layer. This layering is consistent with the applied length scale ratio and with a geological setting similar to that of Teverina area, corresponding to a ~40 m thick tuff plate on a ~120 m thick clay level. To perform the

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ACCEPTED MANUSCRIPT experiment, a wooden box 2.00×1.40×0.5 m was built; the model’s sides were laterally bounded and supported by iron props to prevent any horizontal deformation (Fig. 7a), thus representing a roller boundary condition on sides and fixed condition on the base. In a totally horizontal confined condition, the materials

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can settle, with a viscous consolidation process, until a geostatic stress condition is reached.

The dimension of the model, unusual for physical modelling, derives from the necessity to put an internal stress monitoring system without inducing any significant perturbation. Ideally, the sensors and their wires

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should be an infinitesimal part of the model.

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The stress monitoring system was composed by 16 load cells – with a diameter of 19 mm, weight of 15 g, range test of 0÷20 kPa and a precision of 0.2 kPa – put in the G200 mixture. The sensors were set on two

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different levels, 21 and 32 cm from the bottom respectively, eight sensors for each level. On each level three stress sensor couples, were installed at 30, 60 and 120 cm from the model’s front side, along the central longitudinal section, which is the less affected by boundary effects. Two further load cells were set at the

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same distances from the front side, but on the lateral zones, to appreciate the boundary effects (Fig. 7b). The load cells, connected to a data logger, recorded stress values each minute. Humidity and temperature of the

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room were constantly monitored; to evaluate the efficacy of the lateral confining system, dynamometric

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measures were taken on the lateral sides.

5.2 Experimental results

Stresses in the model were constantly monitored till the reaching of a stress equilibrium state under a zero lateral strain condition, corresponding to a geostatic tensional condition.

Over a six months period the model was let to consolidate under its own weight, during this period the stress values and the K ratios were constantly monitored (Fig. 8): starting from a quasi-isotropic condition, stresses slowly redistributed until the reaching - with a good approximation - of a K0 condition corresponding to an equilibrium state. After six months, the values of lateral stress at rest coefficient in the model resulted almost constant, with a mean value of 0.65.

In natural conditions, during the deposition of submarine sediments, the horizontal and vertical stresses increase in a K0 ~0.5÷0.6 ratio; all the subsequent geologic events produce an alteration of this initial value.

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ACCEPTED MANUSCRIPT Following a different path in the model, the stress equilibrium condition was reached through the ductile material’s consolidation and settling.

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To strengthen the experimental data, the K0 was also computed by some loading-unloading tests.

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Homogeneous loads were progressively put on the rigid plate top surface, and then removed step by step (Fig. 9). For each step, the resultant increase and decrease of stresses were measured by all the sensors and the K0 values computed as the ratio of the Δσ h/Δσv. Results were then compared, and the mean values

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are reported in the Table 5. Loading-unloading tests showed that a load located in a single point on the model’s surface was recorded by all sensors, because the rigid plate distributes the stresses homogeneously

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all over the model. This result proves that no deviatoric stress was produced, and a geostatic condition can be assumed. The mean K0 value valid for the entire model resulting from five loading-unloading tests is again

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0.6.

6 Discussion

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This study deals with the assessment of the lateral stress at rest coefficient K 0 in clays considering the stress evolution over time due to the genesis of natural slopes. In engineering geological and geotechnical

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applications it is commonly accepted a K0>1 for medium and heavy overconsolidated clays, depending this value from the K0(NC), the OCR and the friction angle. This assumption is based on studies on man-made cuts in OC clays (Brooker and Ireland, 1965; Schmidt, 1966; Pruska, 1973; Meyerhof, 1976; Mitachi and Kitago, 1976; Mayne and Kulhawy, 1982; Potts et al., 1990, 1997; Simpson, 1992; Vaughan, 1994; Shohet, 1995) and does not consider any different morphological evolution like, for instance, the slow incision of a natural slope in the clay deposit. These authors specify that the assumption of a K0>1 is correct for a clay deposit subjected during its history to only vertical unloading (e.g. erosion). Nevertheless very often in geotechnical studies a K0>1 is used even when a clay deposits has experienced in its history complex vertical and horizontal unloading and reloading cycles. For instance, the K0>1 value has always been applied also to natural slopes in OC clays, even if the geological evolution and the stress conditions of natural slopes differ from the ones of artificial cuts. The most important difference concerns the incision velocity of natural slopes, in comparison with man-made cuts, and the time amount of exposure of the so produced slopes.

These differences are a key feature for the evolution of the lateral stress at rest coefficient, because if an artificial cut is performed in an undisturbed and overconsolidated clay deposit, then a K 0>1 is an admissible

13

ACCEPTED MANUSCRIPT value for this parameter since there is a preservation of the stress condition acquired during the overconsolidation stage. But in the case of a natural slope incision, the long-lasting morphological evolution gives natural slopes the possibility for stress rebalancing towards a new steady state. The slow incision,

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indeed, induces a slow decrease of the lateral confining pressure and this unconfined condition of the slope

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is maintained for a long time after the incision. The so resulting time-dependent clay deformations occur under creep conditions and follow a viscoplastic mechanical behaviour. The effects of the stress decrease

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after thousands or tens of thousands of years affect the whole slope, nevertheless the geostatic condition can be still preserved within the more internal portion of the slope since no distortion of the stress field can

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be assumed even with a decrease of the stress values. As a consequence the geostatic condition is preserved, but not the stress ratio acquired during the overconsolidation status; in these circumstances a

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K0<1 can be an admissible value.

To investigate this hypothesis, the K0 on OC clays natural slopes have been evaluated in two test sites by

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pressuremeter tests performed at an adequate distance from the slope face. Under such condition the clays are considered in a not stress-released zone. Data derived from the investigations, lead to the evaluation of

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K0 mean values comprised within the range 0.63-0.67. These data can be referred to the steady state of OC clay slopes after the stress rebalancing due to their long lasting morphological evolution. As expected, these

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values are very far from what can be obtained by applying the relations derived for artificial cuts on clays with an OCR of 6-7 (Brooker and Ireland, 1965; Schmidt, 1966; Pruska, 1973; Meyerhof, 1976; Mitachi and Kitago, 1976; Mayne and Kulhawy, 1982; Potts et al., 1990, 1997; Simpson, 1992; Vaughan, 1994; Shohet, 1995). The scaled physical modelling experiment reproduced a “tuff on clay” geological setting typical of central Italy. Since no overconsolidation can be assigned to the used artificial materials, the experiment reproduced the stress conditions occurring in a normally consolidated clay. Horizontal and vertical stresses were measured during the stress rebalancing stage till a geostatic condition. An average K0 value of 0.6÷0.65 resulted from tests and measures performed in the physical model. These data support the hypothesis that a K0<1 is even possible in medium-high OCR clay deposits affected by low rate release processes due to natural slope incision.

On the opposite, as it results from literature data, the stress release induced by an artificial cut, or by a landslide event, occurs under undrained conditions. The so induced deformational processes, considered in a time amount of tens of years, depend on primary consolidation but not on creep processes. The deformation of the materials occurs following an elasto-plastic behaviour and causes a less important

14

ACCEPTED MANUSCRIPT influence on the stress decrease of the internal slope portion. The consequent variations on the stress state are dependent by the primary consolidation process, but in this short time period do not significantly modify the previously acquired stress ratio. In these situations a K0>1 is a proper evaluation. Nevertheless, the

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evolution of a cut for secondary consolidation under creep conditions, considered during a thousands of

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years time period, would also bring a K0<1. These deductions allow to regard that long duration creep deformational processes in OC clays, following a visco-elasto-plastic behavior, can be responsible for the

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loss of the overconsolidation “stress memory”, but this loss does not interfere with the “structural memory” of the overconsolidation and with the yielding stress acquired during the overconsolidation of the material (i.e.

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the OCR value is maintained).

After the discussion of these considerations, Fig. 10 graphically explains the idea proposed in this study. The

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line and the arrows indicate two possible evolutions for the K0 values, depending if natural or artificial slopes are excavated in an OC clay deposit. For both these cases, an initial overconsolidation stage brings the K 0

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from of 0.5÷0.6 (Jaky, 1944) to a value higher than 1. Subsequently two possible evolutions are depicted. If we consider an artificial cut, which is rapid, then a K0>1 is consistent. On the contrary on a naturally incised

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slope the stress rebalancing consequent to the slow incision and the long-time morphological evolution, can bring to 0.65
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distortion of the stress field. These values are consistent with the results of the numerical modelling reported in Bozzano et al. (2006), where the more surficial portion of the deposit is interested by horizontal stress release with a K of 0.3-0.4, but within the slope the stress ratio took a value of 0.6 and is a K0. The figure also reports the evolution of the K0 in the physical modeling experiment. Starting from a quasi isotropic condition, the ratio decreased until about 0.65 by viscous creep deformations only. Finally, it must be considered that the stress evolution of an artificial cut during a long time period tends to converge with that of a natural slope. It is worth noting that after the incision, the main differences on the K0 evolution between artificial cuts and natural slopes regard the amount of the K 0 decrease and the stress decrease rate. Moreover the evaluation and identification of the portion inside the slope where the K0 assumes a reduced value is not achieved yet. These two points can represent the targets for further developments of this study.

15

ACCEPTED MANUSCRIPT 7 Conclusions This study focuses on the lateral stress at rest coefficient evolution occurring during natural slopes incisions,

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due to the geological and morphological evolution can lead to K 0 <1.

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by discussing the hypothesis that even in the case of high OCR clays, the stress-strain history of the deposit

To this aim, experimental data on the lateral stress at rest coefficient in OC clays resulting from in situ tests,

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and a laboratory physical modelling experiment were analyzed here. The first ones consisted of pressuremeter tests performed at two different sites; the laboratory experiment consisted of a scaled

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physical model equipped with an internal stress monitoring system. Data derived from pressuremeter tests and from the physical model, were compared with data from scientific literature about this topic (Brooker and

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Ireland, 1965; Schmidt, 1966; Pruska, 1973; Meyerhof, 1976; Mitachi and Kitago, 1976; Mayne and Kulhawy, 1982; Potts et al., 1990, 1997; Simpson, 1992; Vaughan, 1994; Shohet, 1995).

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The K0 values of 0.63÷0.67 derived from both site tests are significantly lower than the ones predicted by applying analytical relationships, contrarily to the K0 values for artificial cuts in OC clays that are generally

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equal to or greater than 1 (depending by the K0-OCR relationships). At last the K0 value of 0.65 derived here

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from the scaled physical model can be referred to NC clay.

Those findings suggest that the K0 can assume a wide range of values depending on clay mechanical properties, duration of slope incision processes, duration of slope exposure under lateral unconfined condition (i.e. natural or artificial slopes). In the case of a slope incision during tens of thousands of years, all the deposit is interested in the stress decrease, but only the external part of the deposit is affected by a stress field distortion. This suggests that:

-

the K0 value for clays cannot be considered only a function of the soil properties (such as the friction

angle and the consolidation state, i.e. the OCR), but it also should be considered a function of the incision rate of the slope/cut and of the resulting stress decrease rate;

-

for natural slopes, the K0 could not be properly evaluated by the use of the relationships derived from

man-made cut slopes;

-

K0 values greater than 1 are reliable if the OC clay deposits have been never affected by stress

release effects due to slow slope incision and longtime evolution;

16

ACCEPTED MANUSCRIPT -

K0 values lower than 1 can also be reliable in the case of natural slopes, involved in low rate stress

release with a slow slope incision and a longtime evolution.

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In addition, from the results of this study comes out that in long time processes, the creep is responsible not

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only for the deformation evolution, but also for the stress preservation, since it is responsible of the loss of the overconsolidation “stress memory”, even if the geostatic condition is maintained. Nevertheless, the loss

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of overconsolidation “stress memory” does not influence in any way the overconsolidated structure acquired by the clay in its past history, and evaluated by the OCR ratio. These two effects of the overconsolidation are

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disjointed and should be evaluated separately even if due to the same overconsolidation process.

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Acknowledgements

This research has been achieved during the PhD studies of A. Bretschneider at the Department of Earth

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Sciences and at the Research Center CERI on "Prediction, Prevention and Control of Geological Risks" of the University of Rome "La Sapienza". The authors would like to thank the ENI S.p.A. for the supply of

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materials used in physical modelling, and the students A Rocca, A Barra and C Fortunato that have prepared their Master degree theses in the frame of this research with activities of geological surveying, geotechnical

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testing and physical modelling.

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ACCEPTED MANUSCRIPT Leroueil, S., 2001. Natural slopes and cuts: movements and failure mechanisms. Géotechnique, 51(3), 197243. Maffei, A., 1998. Studio delle Deformazioni Gravitative Profonde di Versante. Analisi del comportamento dei

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materiali e definizione dei principali parametri di resistenza. M.Sc. Degree Thesis, Department of Earth

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Sciences, Sapienza University of Rome.

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Malatesta, A., Zarlenga, F., 1986. Evoluzione paleogeografico-strutturale plio-pleistocenica del basso bacino romano a nord e a sud del Tevere. Mem. Soc. Geol. It. 35, 75–85.

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Marra, F., 1993. Stratigrafia ed assetto geologico-strutturale dell’area romana compresa tra il Tevere ed il Rio Galeria. Geologica Romana 29, 515–535.

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geologia di Roma. Il centro storico. Mem. Descr. Carta. Geol. d’It., 50, 49–112. Marra, F., Rosa, C., 1995b. Carta geologica del centro storico di Roma in scala 1:10000. In Funiciello, R.

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Matheson, D.S., Thomson, S., 1973. Geological implications of valley rebound. Can. Geothech. J. 10, 961977. Mayne, P.W., Kulhawy, F.H., 1982. K0-OCR relationships in soil. Journal of Geotechnical Engineering, 108, 851-872. McTingue, D.F., Mei, C.C., 1981. Gravity-induced stresses near topography of small slope. J. Geophys. Res., 86, 9268-9278. Meyerhof, G. G., 1976. Bearing capacity and settlement of pile foundations. 11th Terzaghi Lecture. J. Geotech. Eng. Div. ASCE 102, No. GT3, 197–228. Michalowski, R.L., 2005. Coefficient of Earth pressure at rest. J. of Geotech. and Geoenv. Eng. DOI: 10.1061/ASCE1090-0241 2005.

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ACCEPTED MANUSCRIPT Mitachi, T., Kitago, S., 1976. Change in undisturbed strength characteristics of a saturated remoulded clay due to swelling. Soils. Found. 16(1), 45–58. Potts, D.M., Dounias, G.T., Vaughan, P.R., 1990. Finite element analysis of progressive failure of Carsington

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embankment. Géotechnique, 40(1), 79-101.

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Potts, D.M., Kovacevic, N., Vaughan, P.R., 1997. Delayed collapse of cut slopes in stiff clay. Géotechnique 47(5), 953–982.

th

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Ramberg, H., 1981. Gravity, Deformation and the Earth’s Crust in Theory, Experiments and Geological Applications. Academic Press, London.

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Savage, W.Z., Swolfs, H.S., Powers, P.S., 1985. Gravitational stresses in long symmetric ridges and valleys. Int. J. Rock. Mech. Min. Sci. Geomech. Abstr. 22(5), 291-302. Schmidt, B., 1966. Discussion of ‘Earth pressures at rest related to stress history’ by Brooker & Ireland

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(1965). Can. Geotech. J., 3(4), 239-242.

Shohet, D.C., 1995. Prediction of in situ stresses in clay soils from the measurement of undrained shear

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strength, plasticity index and vertical effective stress. Proc. Inst. Civ. Engrs. Geotech. Eng. 113(4), 206–214. Simpson, B., 1992. Retaining structures: displacement and design, Géotechnique, 42(4), 541–576.

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Sivakumar, V., Doran, I.G., Graham, J., Navaneethan, T., 2001. Relationship between K0 and overconsolidation ratio: a theoretical approach. Géotechnique, 52(3), 225-230. Sivakumar, V., Navaneethan, T., Hughes, D., Gallagher, G., 2009. An assessment of the earth pressure coefficient in overconsolidated clays. Géotechnique, 59(10), 825-838. Vaughan, P.R., 1994. Assumption, prediction and reality in geotechnical engineering, Géotechnique, 44(4), 573-609. Viyalov, S.S., 1986. Rheological Fundamentals of Soil Mechanics, Elsevier, New York.

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ACCEPTED MANUSCRIPT FIGURE CAPTIONS

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Fig. 1 a) Schematic representation of the stress field within a slope: in the external sector stress indicators

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are distorted and the K0 tends towards the Ka; in the internal sector the stresses are in a geostatic condition; b) the K0 values discussed in this paper are referred to the portion of the p-q plane which includes all the K

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lines with origin in (0,0) and <f

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Fig. 2 Location of the study sites: Monte Mario hill, Rome; Lubriano, northern Latium

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Fig. 3 Geological map of the Monte Mario hill, circles indicate the boreholes location

Fig. 4 a) Geological setting of the Lubriano southern slope, geological map and sections; b) schematic

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stratigraphy of the boreholes (S1 and S2) and location of the pressuremeter tests (P1 and P2)

Fig. 5 Synoptic chart showing logs of natural unit weight n, natural water content w%, porosity and saturation degree of the Lubriano clays. It is clear the geotechnical stratification of the geological contact

Fig. 6 a) Sketch of the scaled physical model reproducing the rigid on ductile materials overlapping; b) samples of the artificial materials used in this experiment, on the left the G200 ductile material, on the right the C5 brittle material

Fig. 7 a) The model is contained in a box. Iron props bound the sides of the box to avoid horizontal deformations; b) load cells internal disposition on two levels 21 and 32 cm from the bottom respectively (2x vertical exaggeration); light grey sensors measure vertical stresses, heavy grey sensors measure horizontal stresses

22

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Fig. 8 Example of stress vs. time plot. Data are referred at both the model’s setup and the secondary

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consolidation of the artificial materials. Sensors numbers are referred to the sketch of Fig. 7b

Fig. 9 Load-unload tests: stress vs. time data (for sensors numbers see fig. 7b) and images of different test

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stages

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Fig.10 Range of variation for the K0 coefficient in OC clays on the basis of the here presented results. Dotted lines indicate the different evolution of the parameter in cases of rapid or slow incision of the slope. The

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variations are analyzed both in a short and a long time period. The variations are compared with the K0

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evolution in physical modeling, which occurred by viscous creep deformations only.

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Pressuremeter test

Depth (m)

’h (Pa)

’v (Pa)

S106/02

25

2.56×105

3.94×105

S102/01

40.5

2.41×105

S102/02

48

3.9×105

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Table 1 Data from pressuremeter tests performed in Monte Mario (Rome)

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K 0.65

4.55×105

0.53

5.39×105

0.72

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mean S102 0.63

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Table 2 Data from pressuremeter tests performed in Lubriano

Depth (m)

’h (Pa)

’v (Pa)

K

P1

32.50

2.85×105

4.50×105

0.63

P2

46.30

5.09×105

7.67×105

0.67

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Pressuremeter test

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ACCEPTED MANUSCRIPT Table 3 Mechanical properties of the real lithologies considered for this experiment and of artificial materials used in the physical modelling experiment

c



Pa

°

Pa

Pa*s

tuffs

13

1×109

0.25

38

clays

20

4×107

0.25

30

C51

17.3

3.32×106

0.25

G200

15.6

6.3×104

0.22

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kN/m3

5×105

3.3×104

22

1.38×105

5

2.5×103

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Maffei (2002)



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

SC

E

1.00×1014

1.00×107

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1



Table 4 Scaling ratios applied in the physical modelling experiment. * density ratio; g* gravity ratio; L*

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length ratio; * stress ratio; E* deformability ratio; * viscosity ratio; ˙* strain rate ratio; t* time ratio

Model Nature value

Model/Nature value

value

Model/Nature

ratio

G200

Clay

ratio

Density

kg/m3 1730

1300

 ~

1.33

1560

2000

 ~

0.78

Gravity

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value

Model Nature

m/s2

9.81

9.81

g* ~

1

9.81

9.81

g* ~

1

Length

m

0.13

40

L* ~

3.25×10-3

114

0.37

L* ~

3.25×10-3

Stress

Pa

 ~

4.33×10-3

 ~

2.53×10-3

Deformability Pa

E* ~

3.2×10-3

 ~

1.6×10-3

Parameter

C5

Tuff

1×107 1×1014  ~

1×10-7

Viscosity

Pa·s

Strain rate

s-1

˙ ~

1.27×104

Time

s

t*

7.9×10-5

~

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ACCEPTED MANUSCRIPT Table 5 Results of the loading-unloading tests, identified by Roman numerals; the K0 values are related to

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the different couples of load cells as displayed in the Fig. 6b

k 2/1

k 6/5

k 8/7

k 10/9

k 14/13

k 16/15

I

0.63

0.65

1.01

0.60

0.56

0.52

II

0.64

0.42

0.72

0.52

III

0.64

0.52

0.74

0.52

IV

0.64

0.55

0.75

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test

0.58

0.52

0.58

0.53

0.57

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0.52

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0.53

0.60

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Mean value for the whole model

26

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TE D

MA N

US

CR

IP

T

Figure 1

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CE P

TE D

MA N

US

CR

IP

T

Figure 2

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MA

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RI P

T

Figure 3

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PT

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MA

NU

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RI P

T

Figure 4

30

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AC

CE P

TE D

MA N

US

CR

IP

T

Figure 5

31

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PT

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MA

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T

Figure 6

32

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Figure 7

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Highlights  Analysis of the coefficient of lateral stress at rest for overconsolidated clay deposits  Different stress-strain evolution of an artificial cuts vs. natural slopes  Hypothesys about the evolution during the time of this parameter

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