EFFECTS OF LATERAL MOVEMENTS ON THE DEFORMATION OF SEDIMENTARY BASINS: A NUMERICAL APPROACH

Transcription

1 EFFECTS OF LATERAL MOVEMENTS ON THE DEFORMATION OF SEDIMENTARY BASINS: A NUMERICAL APPROACH André Brüch Department o Civil Engineering Federal University o Rio Grande do Sul, Porto Alegre RS, Brazil andrebruch@hotmail.com Denise Bernaud Department o Civil Engineering Federal University o Rio Grande do Sul, Porto Alegre RS, Brazil bernaud@ppgec.urgs.br Samir Maghous Department o Civil Engineering Federal University o Rio Grande do Sul, Porto Alegre RS, Brazil samir.maghous@urgs.br ABSTRACT The process o mechanical compaction o a sedimentary basin in ully saturated conditions takes place through water expulsion rom the porous material, thus resulting in grain repacking and volume reduction. The rate o this volume reduction is primarily dependent on the amount and rate o sediment accretion and the permeability o the sediment material. In absence o tectonic-driven deormation, a deposited sedimentary layer compacts as the excess pore-pressure generated by its own weight dissipates progressively. Nevertheless, tectonic loading increases substantially the excess pore-pressure gradient, thus accelerating the compaction process. This work is devoted to the modeling o purely mechanical compaction o a sedimentary basin. Three phases are concurrently or consecutively involved in the latter process: the sediments deposition, its compaction due to gravitational orces and pore-pressure dissipation, and deormation induced by extensional and/or compressive tectonic motion. A speciic computational procedure has been developed to perorm numerical simulations in plane strain conditions via the inite element method. The poromechanical constitutive law is ormulated in the ramework o inite irreversible strains, accounting or hydromechanical and elasticity-plasticity couplings. Comparisons are made or both cases: gravitational compaction only and compaction ollowed by eorts o tectonic origin. Keywords: Sedimentary basin, Finite poroplasticity, Tectonic loading. 1 INTRODUCTION Sedimentary basins are associated with a speciic region o the planet crust that was able to retain an appreciable amount o sediments originated rom destruction o any type o rock. These sediments are transported and deposited in dierent types o environments (continental, marine or intermediate), where they are transormed into rock through natural phenomena involving physical and chemical processes. The study o sedimentary basins is an important issue in the ield o geophysics and geomechanics that seeks understanding the geological history and reconstructing the 1

2 poromechanical history o many regions o the planet. The potential applications include petroleum exploration, reserve assessment and production. They are important aquiers and a large variety o metallic and non metallic minerals can be also ound in this kind o geological ormation. Detection and exploration o all these resources requires sophisticated prediction tools and technical methods, which have been developed in many ways along the past decades. Much o this evolution is due to the oil industry, where a need or knowledge on the subject o oil reservoirs has led to enormous expansion o research on modern sedimentary environments. Today it is possible to make quite detailed predictions or the origin o hydrocarbon and water reservoirs rom a combination o threedimensional seismic relection proiles, electric log signatures and downhole probes [1]. However, the progress in this ield has been hampered by the absence o good models to describe the rheological behavior o the constituent material o the problem. Since it is a multidisciplinary problem, the numerical simulation o all the coupling phenomena that are controlling the basin deormation proves very diicult, leading some authors to give priority to only certain components in the ormulation o their models. In the context o deep oceanic basins, the processes that aect the compaction o sediments can be divided into two main groups: mechanical and chemical. Mechanical compaction is mainly because o the excess pore-pressure dissipation and deormation imposed by tectonics. A load suddenly applied is at irst carried by the pore water (as excess pore-water pressure) and gradually transerred to the sediment structure. The compaction results rom the decrease o pore space through grain repacking and the expulsion o water. The speed o this volume reduction is primarily dependent on the amount and rate o load application and the permeability o the sediment. The mechanical compaction is completed when the excess pore-water pressure is zero and pore-water pressure is solely hydrostatic [2]. Chemical compaction involves dissolution-precipitation mechanisms, generally induced by stress (intergranular pressure-solution). Nevertheless, it is important to note that these are interdependent processes, although mechanical phenomena prevail in the upper layers o sedimentary basins, whereas chemical compaction is dominant in the deeper layers, where stresses and temperatures are higher [3]. The basic models o mechanical compaction are still based on phenomenological relationships relating porosity to eective vertical stress. The concept o porosity versus Terzaghi s eective stress dependence has been early introduced by Hubbert and Rubey [4] and later by Smith [5]. These ideas have been widely adopted and implemented in numerical inite element models that have yielded valuable contributions to the understanding o the evolution o sedimentary basins. Interestingly noting, Gibson [6] can be considered one o the pioneer works that introduced consolidation theory or analyzing sediment compaction. The undamental assumptions o the latter work were: constant sedimentation rate, a single lithology, constant sediment properties and Therzaghi s small strain consolidation theory. The approach was mainly applied to the analysis o consolidation in shallow soil deposits. On the other hand, the lateral movements induced by tectonic events inluence strongly the ormation o sedimentary basins. The rate and manner as the tectonic plates move relatively to each other govern many aspects o the geodynamic environment o sedimentary basins [7]. As regards the speed o the tectonic plates motion, Cloetingh et al. [8] pointed out that 1 mm/yr is a characteristic velocity o oceanic lithospheres, while Assaad [9] indicated that the average movement rate o tectonic plates is around 1 to 2 mm/yr currently. Few works have been recently dedicated to theoretical or numerical modeling o these phenomena. Zhao et al. [1] developed a inite element model to simulate the luid rock interaction in pore-luid saturated hydrothermal sedimentary basins. A numerical model was proposed in [11] that aimed to simulate the distribution o sealoor geotechnical parameters during the growth o a seismically active continental margin. 2

3 Disregarding the chemical aspects, the present work is devoted to purely mechanical modeling o compaction in sedimentary basins by means o numerical simulations perormed in a two-dimensional setting. The inite element approach is developed to simulate the sediments deposition and the mechanical processes involved during the ormation o a sedimentary basin in a saturated environment. One o the major diiculties involving this kind o simulation is connected with the occurrence o large change in porosity throughout the compaction process. The coupled nature o the deormation problem may be understood as ollows: large strains modiy the microstructure, which leads to a change in the poromechanical properties o the sediment material and thus aecting the basins response. This behavior requires that the poromechanical constitutive law be ormulated in the ramework o inite irreversible strains, so the key components or the model are the hydromechanical and elasticity-plasticity couplings. Another speciicity o the present problem is that sedimentary basins simulations deal with open material systems. A inite element technique developed in [12], which is speciically devised or simulating the processes o sediment accretion, is adopted in the present analysis. Particular emphasis is given to the investigation o tectonic-driven deormation in sedimentary basins caused by extensional and compressive movements. The simulations are perormed reasoning on a rectangular geometrical model that is intended to represent an oceanic trench created by pre-depositional divergent tectonics. Then, sediment accumulation occurs over tens o millions o years. Ater the period o deposition and compaction o the sediments resulting rom gravitational orces and pore-pressure dissipation, tectonic movements are applied on the sides o the basin. The sedimentary rock is modeled as a ully saturated poroelastoplastic material undergoing large strains. 2 GOVERNING EQUATIONS At the macroscopic scale, a porous medium can be viewed as the superposition o a solid continuum related to the deormable skeleton and a luid phase occupying the porous space. In this approach, the amount o luid content within an ininitesimal volume o porous material dω t is represented by the porosity. The Lagrangian porosity φ is deined by the ratio between the luid volume in the current coniguration (represented by the superscript ) and the initial total volume, φ = dωt dω, while the Eulerian porosity ϕ quantiies the luid content with respect to the current total volume, ϕ = dωt dωt. Thereore, in order to deine the poromechanical problem under isothermal and quasi-static conditions, two ield equations reerring to momentum and mass balance over the space where the problem takes place must be speciied. By considering the balance o linear momentum, the equilibrium equation or the porous continuum can be obtained: div σ + ρg = (1) where σ is the Cauchy total stress tensor, g is the acceleration o gravity and ρ is the porous material density, deined by the Eulerian porosity, the luid density ρ and the grain density ρ s : ( ϕ) s ρ = ϕρ + 1 ρ (2) The second ield equation is the luid mass balance (3), unction o the iltration vector q deined by Darcy s law (4), where J is the Jacobian o the transormation, p is the pore-pressure and k is the permeability tensor (in case o isotropy, k = k1). d dt ( φ ) + Jdiv( ρ q) = ρ (3) 3

4 ( p + ρ g) q = k. (4) The problem is completely deined only when the geometry and the values o all corresponding ields are speciied at the initial moment. For the boundary conditions in the current coniguration t, partitions o the boundary Ω t o the geometrical domain Ω t are introduced. The directions in which the boundary conditions are applied are deined by the unit normal vector n and two perpendicular directions. The data are indicated by the superscript d. Let ξ be the total displacement vector o a skeleton particle, T be the stress vector and e i be the unit director vectors or the coordinate system (i = 1,2,3). For the mechanical boundary conditions, let S Ti and S ξi be the parts o Ω t where the ith component o the stress and displacement vectors are imposed. Expressions below must be σ.n.e = T = T on S Ti d, and ξ.e i = ξ on S ξi. satisied, where ( ) d i i S i Ti i S ξ = Ω t S Ti ξ S i = For the hydraulic boundary conditions, let S W and S P be the parts o Ω t where the normal component o the luid mass lux and the luid pressure are imposed, respectively. We have: S W S P = Ω t S (5) W P S = (6) d where w.n = w on S W d, and p = p on S P. The macroscopic equations o state o a ully saturated poroelastoplastic material generally assume a total independence o the elastic properties with respect to the plastic behavior. However, in the context o large strains, such an assumption is clearly questionable as the large macroscopic plastic strains are associated with an irreversible evolution o the microstructure, which is responsible or variations o the macroscopic elastic properties o the porous medium [13]. The idea o the constitutive model here presented consists in associate the evolution o the elastic and hydraulic properties o the porous material to its variation o porosity, which is associated to the plastic part o the Jacobian o the transormation. We shall reer to this phenomenon as elasticity plasticity coupling. Let us consider a representative elementary volume (r.e.v.) o the porous medium subjected to a stress state σ and pore-pressure p. Removing this load applied to the initial coniguration dω, the actual volume dω t transorms to a residual coniguration dω u. This transormation between dω t and dω u is reerred to as the elastic part. The variation o the elastic porosity and the plastic porosity are deined as: el φ = dω t dω dω u u dωu dω p φ = (7) dω I F el is the gradient o the homogenous geometric transormation o a skeleton particle between dω u and dω t, and F p is the gradient o the homogenous geometric transormation o a skeleton particle between dω and dω u, the gradient F is given by: el p F = F.F (8) The plastic part o the Jacobian o the transormation J p p p J = dω dω = detf, the variation o porosity is described as ollows: u being deined as p p el φ = φ J φ (9) φ + 4

5 Figure 1 illustrates the decomposition o the gradient F and the variation o porosity experienced by the porous material. Figure 1: decomposition o the gradient o transormation and variation o porosity. el The elastic part o the transormation between dω u and dω t is assumed ininitesimal, F 1. The state equations or linear elasticity are simply given according to Biot s theory or isotropic materials: where σ =C: ε ~ el Bp (1) el el ( φ : ) p= M B ε (11) el ε stands or the ininitesimal elastic strain associated with the elastic sequence B and M are respectively the Biot tensor and Biot modulus, and drained elastic moduli: ( ) el F, C is the ourth order tensor o the ~ C = K 2 µ / µ 1 (12) ~ ~ The main dierence with the usual Biot s theory lies in the act that the state variables el ε and el φ are here deined with respect to the unstressed coniguration. So as the porous medium deorms reducing its porosity, the evolution o the elastic properties (the bulk and shear moduli o the porous material, K and µ) are evaluated by the Hashin-Shtrikman upper bounds [14], unction o the bulk and shear moduli o the solid phase k s and µ s as well as o the Eulerian porosity ϕ : µ ( ϕ) K ( ϕ) s µ s k ( 1 ϕ) s s 4k µ = (13) s s 3k ϕ + 4µ s s ( 1 ϕ)( 9k + 8µ ) = s ( 9 + 6ϕ ) + µ ( ϕ ) (14) 5

6 Under isotropy conditions, classical results o poroelasticity indicate that: = with b( ϕ) B b1 ( ϕ) K = 1 and s k 1 M ( ϕ) b = ( ϕ) ϕ s k The eects o microstructural changes on the evolution o the permeability coeicient o the porous medium k may be modeled by means o the Kozeny Carman ormula: = with ( ϕ) k k1 ( 1 φ ) (15) 3 2 ϕ k = k 3 (16) φ ( ) 2 1 ϕ In the ramework o inite poroplasticity, considering the evolution o the poromechanical properties, the macroscopic rate equations o state take the ollowing rate orm [13]: where D σ p ( ) e J e e e 1 e = σ + σ.ω Ω.σ = C: d d + C:C :σ ~ ~ ~ Dt e σ σ Bp (17) p p φ φ M 1 e ( ) tr p ( ) p = M btr d d + + p Mb C :σ (18) J M ~ 1 { } p = + is the Biot eective stress, Ω is the spin tensor and p p =.( ) d F F is the plastic strain rate. Introducing the plastic potential G(σ ) which depends on σ and p through the Terzaghi eective stress σ = σ + p1, where χ is a non-negative plastic multiplier: sym d p G = χ (19) σ The plastic model used here is the modiied Cam-Clay model [15]. The plastic low rule is associated. The yield surace is unction o the deviatoric stress tensor s and the mean eective stress p deined as: 1 1 s = σ tr( σ)1 p = tr( σ ) (2) 3 3 The plastic criterion is then: 3 2 ( σ,p ) = s:s + M p ( p p ) c cs + c (21) 2 where M cs is the slope o the critical state line and p c is the consolidation pressure, which represents the hardening parameter o the considered model. Its evolution with the volume plastic strains is the hardening law. The latter has been derived rom a micromechanics-based reasoning developed in Barthélémy et al. [16]: p pco 1 φ pc ( J ) = ln 1 p lnφ J (22) As observed in Deudé et al. [17], the main advantage o the above hardening law with respect to classical ones lies in the act that it avoids the development o negative porosities under high isotropic compression. 6

7 3 FINITE ELEMENT DISCRETIZATION Assessment o the poromechanical state requires the determination o the temporal evolution o the geometric transormation as well as the pore-pressure changes. This shall be achieved by solving the boundary value problem deined by the set o governing equations together with the constitutive and complementary equations. The particularity o large strains is that all equations actually reer to the mechanical system in its current coniguration, which is a priori unknown. The inite element procedure used or assessing the evolution o stresses, pore pressures and strains in the porous medium under consideration will be outlined hereater. Full details are provided in Bernaud et al. [13]. The analysis is based on the implementation o the updated Lagrangian scheme [18]. This approach is based on the same procedures used by total Lagrangian ormulations, but instead o being reerred to the initial coniguration, all static and kinematic variables are reerred to the last calculated coniguration, say at time t. The unknown variables are then updated in each step time t. The displacement U o the skeleton particles between t and t+ t is deined as t t t t+ t t U = x x (23) where x (resp. x + ) denotes the coordinate o the particle at time t (resp. t+ t ). The pore pressure dierence at points similar within the skeleton transormation between t and t+ t is t+ t t P= p( x ) p( x ) (24) The discretized orm o the problem is obtained rom weak ormulation o the equilibrium and luid mass balance equations at time t+ t. Six-nodes triangles are used or geometry discretization (igure 2). A piecewise quadratic polynomial unction is adopted to approximate the displacement, while piecewise linear unction is adopted or pore-pressure variations. The resulting system is given below, where K IJ are the global stiness sub-matrices and F I the global orce sub-vectors. U and P are the nodal displacements and pore-pressure dierence, respectively. For a single element, K UU is a matrix, K PU is 12 3, K UP 3 12 and K PP 3 3, resulting in a stiness matrix. KUU K PU U F U = (25) KUP K PP P F P It is emphasized that, or a given coniguration at time t, the system above is highly nonlinear due to the physical non-linearities (plasticity) and geometrical non-linearities (large strains). In particular, vectors F U and F P depend on the unknowns U and P. An iterative method is adopted or solving this system by implementing an appropriate algorithms until it is satisied up to a required tolerance. One speciicity o the problem lies in the act that a sedimentary basin is an open system due to the continuous accretion o material at the top o the basin during sedimentation phase. This requires an appropriate technique to overcome the diiculty o dealing with an open system in the context o inite element method. For this purpose, the activation/deactivation method [12] inspired rom tunnel engineering is used to simulate the accretion process. In the ramework o such method, the real open material system is simulated as ictitious closed one. 7

8 Figure 2: Schematic geometry o the basin and the inite element characteristics. Figure 2 illustrates the basin construction problem, where L corresponds to the sea level and H(t) corresponds to the top o the sediment layer. The evolution in time o the latter must o course correspond to that o the real system. I ρ(z,t) represents the mass density o the sedimented material, the total sediment mass per unit area provided rom the initial moment t = is equal to the mass o the vertical column with unit cross section o equation (26): M (t) = d H(t) ρ ( z,t) Based on this reasoning, the height o a given layer o sediments deposited between the times t = and t = T can be deined using equation (27), where ρ (t) is the sediments initial density at the corresponding time t. H = T () t dz M d(t) dt ρ In act, H represents the thickness o the layer that was deposited in the basin up to time T i the deposited material was rigid. However, while sediments layers are being applied, the already deposited layers are in compaction process. The simulation o the accretion phase takes place subdividing the sedimentation period into n subintervals [t i-1, t i ] with t = and t n = T. During the time increment t i = ti ti 1, the addition o sediments corresponds to a height o H: H i = t t i M ρ i 1 ( t) () t d Beore sediment deposition, all inite element layers constituting the system are attributed the sea water properties. For every advanced subinterval t, the properties o a corresponding layer with thickness H are changed in conjunction with the hydraulic and elastic properties o the deposited material. This process starts at the bottom o the basin (z = ) and continues upwards until the accretion phase ends. dt (26) (27) (28) 8

9 4 COMPUTATIONAL RESULTS The sedimentary basin considered in the numerical simulation is ormed during T = 6 millions years (duration o accretion phase). In addition, the rate o sediment accretion is 9 constant and equal to M d = kg/s per unit area, corresponding to 1 m o sediment thickness per million years in unloaded conditions. In absence o compaction, that is i the sediment material were rigid, the total thickness o the basin would be 6kmat t = T (end o accretion phase). The simulations o the sedimentary basin are perormed considering three distinct phases deined as ollows. Phase (1): corresponds to sediment deposition (ormation o the basin) that extends rom t = and t = T. Phase (2): compaction exclusively due to gravitational orces and pore-pressure dissipation. Phase (3): lateral movement induced by extensional or compressive tectonic events. The initial geometry o the basin is sketched in Figure 3. It consists in a rectangular block o 24 km long by H = 6 km thick. Owing to the symmetry with respect to the vertical plane, only the hal part o the geometrical domain is discretized into inite elements. The inite element mesh consists in 72 triangular elements regularly distributed along 12 horizontal layers, each layer being divided into 6 elements. The mesh corresponds to 1471 total nodes. 3 3 The model data are: initial material density ρ = kg/m, initial porosity φ =.72 3 (taken rom [19]), initial Young modulus E = 1 MPa, initial Poisson s ratio ν =.33, initial Biot coeicient b =.9715, initial Biot modulus 5 M = MPa, coeicient slope o the critical state line M cs = 1.2, initial permeability k = 1 MPa m s, initial consolidation 3 3 pressure p = 1.5 MPa, sea water density ρ = 1 kg/m. co z O x z = 6km T = ρ g( L H) e ; p= ρ g( L H) z z symmetry conditions O layer i x impermeable Figure 3: basin coniguration. impermeable x = 12 km 9

10 The boundary conditions applied to geometric domain are: z = H(t) (upper surace): z = (basin basement): x = 12 km (basin side): IV International Symposium on Solid Mechanics - MecSol 213 = ( ( )) p ρ g( L H ( t) ) T ρ g L H t e z = (29) ξ. e z = qe. z = (3) ξ. e x = qe. x = (31) The above boundary conditions are completed by symmetry conditions at plane x =. 4.1 Gravitational compaction Figure 4 illustrates the compaction law o the sedimentary basin along phases (1) and (2). As it can be seen, the thickness o the basin is about H = 4212 m at the end o accretion phase (T = 6 millions years), which represents a compaction level o 3%. At t = 6T, the thickness o the basin is almost stabilized with H = 2633 m, corresponding to 56% compaction level. Based on this compaction law, ive dierent ages o the basin have been chosen to apply laterally-induced tectonic deormations (i.e., phase (3)). The selected basin ages are indicated in Figure 4 and given in Table 1 together with corresponding basin thickness. Figure 4: Compaction law o the sedimentary basin. Case Height (m) Age (myr) Table 1: selected cases. 1

11 Beore presenting the simulation o tectonic sequences, some results related to phases (1) and (2), which correspond to oedometric compaction, shall be analyzed hereater. The pore-pressure proile is displayed in igure 5 or each reerred case. The hydrostatic pore-pressure proile is drawn as well. It can be seen that although case t = 6T is nearly asymptotic in relation to its compaction history (igure 4), the pore-pressure proile is still ar rom hydrostatic. The Kozeny-Carman ormula used to quantiy the evolution o the permeability coeicient indicates that k when ϕ. This explains the long time required or total dissipation o excess pore-pressure in the lower layers o the basin, i.e. the time required to attain the asymptotic state o the basin. Figure 5: Pore-pressure proiles during gravitational compaction. The porosity proiles are shown in igure 6. As expected, younger sedimentary basins present higher porosities along their height, since excess pore-pressure is continuously dissipated in course o time, leading the sediment layer to compaction as the luid is expelled rom the porous material. The t = 6T case porosity in the lower layers vary rom 7% to 17%. These small values explain the diiculty to continue its gravitational compaction as commented above, since the permeability in these layers are 1 to 1 times lower than its initial value. 11

12 Figure 6: Porosity proiles during gravitational compaction. In classical analysis o soil mechanics, an important parameter is the coeicient o earth pressure Kp, deined as the ratio between the horizontal and vertical eective stresses Kp = σ H / σ V. This parameter is oten considered constant along the depth o a basin. Its estimation allows access to the horizontal eective stress proiles based on the vertical eective stress obtained rom traditional analysis o one-dimensional calculations. Indeed, the obtained values o Kp coeicient beore tectonic motion are constant or all cases along basins depth, except within a thin crust located near the upper surace o the basin as can be seen in igure 7. 12

13 4.2 Tectonic sequences Figure 7: Proiles o coeicient Kp during gravitational compaction. For each one o the ive selected ages, a tectonic loading is applied by imposing at t = T a lateral movement to the basin. In each case, the geometry and hydromechanical ields (stress, pore pressure, porosity and associated poromechanical parameters) resulting rom phases (1) and (2) are considered as the initial coniguration and state o the basin when starting the tectonic loading. The hydromechanical boundary conditions are showed in Figure 8. The lateral right-hand side (resp. let-side) is subjected to a constant horizontal velocity Ve x (resp. Vex). We restrict the analysis to a prescribed velocity magnitude V = 1 mm / year, which alls within the category o slow tectonics. The lateral displacement is applied using time increment o t = 1 year. Tectonic sequences have been simulated in the ive cases deined in Table 1. For each case, the total lateral displacement applied to the basin beore the numerical ailure o the plasticity algorithm was equal to ± 12 m. This means that the total duration o tectonic sequences is about 1.2 million o years. 13

14 z V V O x z=h ( ) T ( ( ) ) z ; ρ ( ( ) ) T = ρ g L H T e p= g L H T z V symmetry conditions O x impermeable Figure 8: Geometrical model and boundary conditions or tectonic simulations. impermeable x = 12 km The irst observation made rom the numerical simulations is that the conigurations reached by the basins at the end o tectonic sequences are almost the same or all considered cases o extensional solicitation. The same can be said or all case o compressive solicitation. However, the inal conigurations in extensional or compressive solicitation are distinct. Hence, or sake o clearness, only the results related to the case 1 will be presented in the sequel. It is recalled that the case 1 is deined by a tectonic loading starting at T =85 Myr and associated to an initial basin thickness HT ( )=375 m. Figure 9 shows the thickness o the basin versus time or T t T Myr. An important eature raised rom the numerical simulations is that the lateral solicitation strongly aects the velocity o the compaction process in both extensional and compressive situations. As a matter o act, ater 1.2 million o years the basin compacted only 1 m under gravitational compaction, while ater the same period it compacted more than 15 m under extensional lateral motion and more than 12 m under compressive lateral motion. The distribution o pore-pressure along the right side o the basin ater 1.2 Myr is displayed in Figure 1 or the case 1. The compressive tectonic motion led to a substantial increase in the pore-pressure proile, reaching about 2 MPa o excess pore-pressure in the basin basement, while the extensional tectonic accelerated the process o dissipation o the excess pore-pressure. 14

15 Figure 9: Inluence o tectonic lateral motion on the compaction law. Figure 1: Pore-pressure proile along the right side o the basin ater 1.2 Myr tectonic loading. Figures 11 and 12 present respectively the porosity and coeicient Kp along the right side o the basin. Even induced by distinct driven mechanisms, the expulsion o pore-luid in both cases led to a signiicant decrease in the sediment layer porosity, reaching the quasi total closure o pores near the basin basement. Regarding coeicient Kp o earth pressure, it turns out that this coeicient is uniorm along the basin thickness or the extensional case, similarly to what has been observed 15

16 under purely gravitational compaction (phases (1) and (2)). In contrast, the distribution along the basin thickness is quite disturbed or the compressive case. Figure 11: Porosity proile along the right side o the basin ater 1.2 Myr tectonic loading. Figure 12: Proile o coeicient Kp along the right side o the basin ater 1.2 Myr tectonic loading. 16

17 5 CONCLUSIONS Starting rom the constitutive model developed by Bernaud et al. [13] in the context o inite poroplasticity, three important phases involved in the mechanical processes o a sedimentary basin ormation were simulated: the sediments accretion phase, its compaction due to gravitational orces and pore-pressure dissipation, and the deormations imposed by compressive and extensional tectonics. From the numerical point o view, the inite element model has been applied to the simulation within a 2D setting o both gravitational compaction and tectonic-induced deormation. The behavior o the basin during the phases o sediment accretion and pore pressure dissipation is irst investigated. Starting rom the coniguration reached by the basin at a given age, tectonic sequences have been then applied to the basin. The tectonic sequences are simulated by applying to the basin lateral extensional or compressive displacements. Even though the numerical simulations have been perormed in the particular situation o slow tectonics, some important eatures that are connected with the induced deormation are emphasized. It is worth noting that the objective o this preliminary analysis is only to investigate the easibility o the 2D modeling and not to provide quantitative insights in the basin deormation under tectonic loading. At this stage, some undamental questions arise regarding the theoretical aspects and the numerical modeling. First, the rictionless boundary condition considered at the basin basement is not very realistic, leading to a more deormable block. A more realistic model or the interace between the basin and the rock basement such as the Coulomb riction law should be implemented. Second, the shape quality o the mesh elements resulting rom compaction (vertical stretching) between t = and t = T that corresponds to the beginning o the tectonic loading phase is rather low: due to oedometric contraction, the elements become thin with high aspect ratio. This is clearly a possible source o numerical inaccuracies and can lead to non convergence o the non-linear algorithm. Third, regarding the simulation o deep oceanic basins, a more comprehensive model should take into account intergranular pressure-solution (IPS) mechanisms, since chemical compaction represents a major mechanism o deormation in the lower layers o this type o sedimentary basins. Fourth, it is also intended to perorm simulations with ractured basins, since they occur in most real cases o sedimentary basins. One should be cautious regarding the conclusions drawn rom the numerical simulation since only very slow tectonics have been considered. It is likely that ast tectonics will induce high pore pressure within the basin. The later will thus deorm under undrained-like conditions, which in turn lead rapidly to substantial increase in the eective stresses controlling the yield ailure. Actually this kind o analysis requires a more robust algorithm to deal with the high non-linear problem. Finally, several issues remain to be addressed on both theoretical and computational viewpoints. In irst line, the development o an eicient numerical tool implementing robust algorithms speciically devised or handling inite poroplasticity problems and parallel computing that allows dealing with high number o degrees o reedom that are involved in a 3D modeling is in progress. REFERENCES [1] Leeder, M.R., 1999, Sedimentology and sedimentary basins: rom turbulence to tectonics, Blackwell Science, Oxord. [2] Taylor D.W., 1948, Fundamentals o soil mechanics, John Wiley, New York. 17

18 [3] Schmidt V.; McDonald D.A., 1979, The role o secondary porosity in the course o sandstone diagenesis, Aspects o Diagenesis, 26: [4] Hubbert M.K.; Rubey W.W., 1959, Role o luid pressure in mechanics o overthrust aulting. I. Mechanics o luid-illed porous solids and its application to overthrust aulting, Geological Society o America Bulletin, 7(2): [5] Smith J.E., 1971, The dynamics o shale compaction and evolution o pore-luid pressures, Mathematical Geology, 3(3): [6] Gibson R.E., 1958, The progress o consolidation in a clay layer increasing with time, Géotechnique, 8(4): [7] Allen P.A.; Allen J.R., 25, Basin analysis: principles and applications, 2nd ed. Blackwell Science, Oxord. [8] Cloetingh S.A.P.L.; Wortel M.J.R.; Vlaar N.J., 1984, Passive margin evolution, initiation o subduction and the Wilson Cycle, Tectonophysics, 19: [9] Assaad F.A., 29, Field Methods or Petroleum Geologists: A Guide to Computerized Lithostratigraphic Correlation Charts Case Study: Northern Arica, Springer, Berlin. [1] Zhao C.; Hobbs B.E.; Walshe J.L.; Mühlhaus H.B.; Ord A., 21, Finite element modeling o luid rock interaction problems in pore-luid saturated hydrothermal/sedimentary basin, Computer Methods in Applied Mechanics and Engineering, 19(18-19): [11] Hutton E.W.H.; Syvitski J.P.M., 24, Advances in the numerical modeling o sediment ailure during the development o a continental margin, Marine Geology, 23(3-4): [12] Bernaud D.; Dormieux L.; Maghous S., 26, A constitutive and numerical model or mechanical compaction in sedimentary basins. Computers and Geotechnics, 33(6-7): [13] Bernaud D.; Deudé V.; Dormieux L.; Maghous S.; Schmitt D.P., 22, Evolution o elastic properties in inite poroplasticity and inite element analysis, International Journal or Numerical and Analytical Methods in Geomechanics, 26(9): [14] Hashin Z., 1983, Analysis o composite materials - a survey, Journal o Applied Mechanics, 5(3): [15] Wood D.M., 199, Soil Behaviour and critical state soil mechanics, Cambridge University Press. [16] Barthelemy, J.F.; Dormieux, L.; Maghous, S., 23, Micromechanical approach to the modelling o compaction at large strains, Computers and Geotechnics, 3: [17] Deudé V.; Dormieux L.; Maghous S.; Barthélémy J.F.; Bernaud D., 24, Compaction process in sedimentary basins: the role o stiness increase and hardening induced by large plastic strains, International Journal or Numerical and Analytical Methods in Geomechanics, 28(13): [18] Bathe K.J., 1996, Finite element procedures, Prentice-Hall, Upper Saddle River. [19] Hamilton E.L., 1959, Thickness and consolidation o deep-sea sediments. Geological Society o America Bulletin, 7(11):