Influence of pressure and density on the rheological properties of rockfills

Abstract

Long-term deformations of rockfill dams can be related to the type of dam, the pre-compaction achieved during the construction of the dam, the history of loading events, the rheological properties of the rockfill material used, the seepage behavior caused by defects of the sealing, the interactions of the dam building with the foundation, and the hydrothermal phenomena of the stressed rockfill material. The present paper investigates the rheological properties of coarse grained rockfill materials using a hypoplastic constitutive model. Particular attention is paid to wetting deformation under different deviatoric loading states and pre-compactions. To quantify the state of weathering a so-called “solid hardness” is used in the sense of a continuum description. It is shown that an appropriate modeling of wetting deformations requires a unified description of the interaction at least between the state of weathering, the stress state, the density and the rate of deformation. The results obtained from the numerical simulations are compared with available experimental data for a rockfill material used in Xiaolangdi earth dam.

Keywords

rockfills / solid hardness / wetting deformation / hypoplasticity / creep

Introduction

Deformations of rockfill dams can be triggered by various events and the corresponding physical and thermo-chemical mechanisms are important for an accurate interpretation of the data obtained from monitoring as well as for numerical modeling. In general it can be distinguished between instantaneous deformations and long-term deformations. The former, for instance, can be initiated by rapid changes of the water level in the reservoir, the change of effective stresses caused by a change of suction of fine grained materials, piping as a result of the seepage-driven internal erosion of solid particles and hydraulic fracturing. Long-term deformations are usually related to the rheological properties of the rockfill material, which mainly depend on the mineralogical composition of the solid material, the grain size distribution, the compaction, the moisture content, the stress state, and the evolution of weathering. For rockfill materials the evolution of weathering caused by chemical weathering or by the intensity and the orientation of micro-cracks has a significant influence on the granular hardness and as a consequence on phenomena such as rockfill creep and collapse settlements, e.g. [1-9]. For rockfills with coarse-grained and uniform particles under stress the forces at the contact areas are much higher than in a well graded granular material. Thus grain abrasion and grain crushing caused by the plastification of contact zones and the progressive development of micro-cracks are usually more pronounced in coarse-grained and weathered rockfills (Fig. 1(a)). For coarse-grained materials capillary effects on the effective stresses are small [8] and they are neglected in the present paper. Single particle crushing tests by Ham et al. [10] show that the compressibility of the grain is higher for the wet grain than for the dry grain as illustrated in Fig. 1(b). The experiments also show that the crushing stress strongly depends on the mineral composition of the grain and the grain size. Usually the crushing strength is higher for smaller grains.

The compressibility of grain aggregates under isotropic loading is also higher for the wet material as illustrated in Fig. 2(a). A higher compressibility can be explained by the degradation of the stiffness of the solid material due to the reaction with water, which may also accompanied by grain abrasion and grain breakage leading to a rearrangement of particles into a denser state. For a pre-compressed material under dry conditions (Fig. 2(b), path A-B) a following wetting causes an additional settlement (Fig. 2(b), path B-C). Depending on the time dependent property of the material wetting can bring about a so-called collapse settlement or it can lead to long-term settlements, which are called creep settlements. For a continuing loading (Fig. 2(b), path C-D) the load-displacement curve follows the curve obtained for the initially wet material [2]. This experimental finding is an important property of weathered and moisture sensitive granular materials as outlined in more detail by Bauer [11].

For granular materials it is experimentally evident that the peak friction angle is not a material constant and it is higher under lower stress levels and for an initially higher packing density of the material. Triaxial compression tests by Li [12] show that for the water saturated material the peak friction angle is much lower than for the dry material (Fig. 3(a)). The results may also be influenced by the pre-compaction of the material and the degree of weathering [2]. Wetting of the material under deviatoric stress states leads to creep deformations, which are higher for a higher mobilized friction angle and a higher lateral stress (Fig. 3(b)). The experimental results indicate that there is an interaction between the stress state, the packing density, the moisture content and the state of weathering. These interactions are also important for the constitutive modeling.

Recently wetting deformations of weathered rockfill materials have been investigated using extended constitutive equations based on the framework of hypoplasticity, e.g., [11,13]. General hypoplastic models for cohesionless granular materials with moisture insensitive stable grains describe the stress rate depending on the current stress, the density and the rate of deformation using a nonlinear tensor-valued function. As the tensor-valued function is incrementally nonlinear in the rate of deformation, an inelastic stress strain behavior and volume strain behavior can be modeled with a single equation as proposed by Kolymbas [14]. The influence of the peak friction angle and the dilatancy behavior on the current pressure level and density can be modeled with respect to a pressure dependent relative density [15]. A consistent embedding of the critical state soil mechanics into hypoplasticity was demonstrated for granular materials like sand for instance by Gudehus [16,17] and Bauer [18,19]. For modeling weathered and moisture sensitive rockfill materials a degradation of the solid hardness depending on the degree of weathering was introduced by Bauer and Zhu [20]. Herein the solid hardness is related to the grain assembly under isotropic compression and does not mean the hardness of a single grain [11]. The degradation of the solid hardness also takes into account the influence of the pressure level on grain plastification and grain crushing in a unified manner. Consequently there is no need to distinguish between so-called collapse deformation and secondary creep. To take into account the influence of the deviatoric stress on the amount of creep deformation and stress relaxation the stress tensor in the corresponding constitutive relation is decomposed into an isotropic part and a deviatoric part [11]. In the present paper the focus is on the influence of the deviator stress and pre-compaction on the amount of wetting deformations. Numerical simulations show that an additional constant introduced to scale the deviatoric part of the stress tensor allows a more accurate prediction of wetting deformations. The capability of the constitutive model proposed is demonstrated by comparing numerical simulations with laboratory tests carried out by Li [12] with a rockfill material used in the Xiaolangdi earth dam.

Throughout the paper the usual sign convention of rational solid mechanics is adopted, i.e., compressive stress and strain are negative. All stresses are effective stresses. Other effects of partly saturated materials like inter-particle capillary forces are negligible for coarse grained rockfill materials.

Solid hardness and pressure dependent limit void ratios

To quantify the solid hardness in the sense of a continuum description the isotropic compression behavior of rockfill materials is considered. In particular for monotonic isotropic compression the relation between the void ratio e and the mean effective pressure p=-({\sigma }_{\mathrm{11}}+{\sigma }_{\mathrm{22}}+{\sigma }_{\mathrm{33}})/\mathrm{3} is approximated using the following exponential function [18,21,22]:

(1)e=e_{\mathrm{0}}\exp \left[-{\left({\displaystyle \frac{\mathrm{3}p}{h_s}}\right)}^n\right].

Herein the constant e_{\mathrm{0}} denotes the void ratio for p\approx \mathrm{0}, h_s has the dimension of stress and n is a dimensionless constant. The quantity of h_s is called solid hardness and related to the grain aggregate and should not be mixed up with the hardness of an individual grain. More precisely, the solid hardness h_s represents the isotropic pressure 3p at which the compression curve in a semi-logarithmic representation shows the point of inflection while the exponent n is related to the inclination of the corresponding tangent as shown in Fig. 4(a). The void ratio e_{\mathrm{0}} for the nearly stress free state is not a material constant. It depends on the arrangement of the grains in the grain skeleton, which is related to the pre-compaction of the material. Generally the void ratio e is defined as the ratio of the volume of the voids, V_v, to the volume of the solid grain, V_s. For weathered rockfill materials the volume of the voids is the sum of the inter-particle void space, V_e, and the volume of the pores of the grains, V_o, i.e., V_v=V_e+V_o, as illustrated in Fig. 1(a). If the density of the solid material is assumed to be constant, the rate of the void ratio can be derived from the balance equation of mass, i.e.,

(2)\dot{e}=(\mathrm{1}+e){\dot{ϵ}}_v.

Herein {\dot{ϵ}}_v denotes the volume strain rate. It can be noted that Eq. (2) also holds in the case of grain crushing. The range of possible void ratios is limited by a maximum void ratio e_i and a minimum void ratio e_d. The values of these limit void ratios are pressure dependent as sketched in the so-called phase diagram of grain skeletons in Fig. 4(b) [17]. The upper bound, e_i, can be related to an isotropic compression starting from the loosest possible skeleton with grain contacts. Thus the compression curve corresponding to the maximum void ratio is relevant for the calibration of the solid hardness h_s and the constant n in Eq. (1). Values of e_d will be achieved by cyclic shearing with very low amplitudes and nearly fixed mean pressure. By contrast, large monotonic shearing leads to a stationary state, which is characterized by a constant stress and constant void ratio. The void ratio in such a limit state, which is called critical void ratio, e_c, also decreases with the pressure p. Gudehus [16] suggested postulating that the maximum void ratio e_i, the minimum void ratio e_d and the critical void ratio e_c decrease with the mean pressure according to

(3){\displaystyle \frac{e_i}{e_{i\mathrm{o}}}}={\displaystyle \frac{e_d}{e_{d\mathrm{o}}}}={\displaystyle \frac{e_c}{e_{c\mathrm{o}}}}=\exp \left[-{\left({\displaystyle \frac{\mathrm{3}p}{h_s}}\right)}^n\right].

Herein e_{i\mathrm{o}}, e_{d\mathrm{o}}, and e_{c\mathrm{o}} are the corresponding values for p\approx \mathrm{0} as shown in Fig. 4(b).

Modeling the degradation of the solid hardness and influence on the limit void ratios

In the present paper the higher compressibility of the wet rockfill material is modeled by using a solid hardness depending on the state of weathering of the material. The process of degradation of the solid hardness can be repeatedly initiated, for instance by continuing infiltration of water into the micro-cracks and pores that penetrate the surface of the weathered grains. In this paper the degradation of the solid hardness is assumed to be irreversible and only the dry state of the material followed by water saturation is considered. To model such a behavior the constant granular hardness h_s in Eq. (1) is replaced by the weathering dependent state variable h_{st}, i.e., Bauer and Zhu [20]:

(4)e=e_{\mathit{0}}\exp \left[-{\left({\displaystyle \frac{\mathrm{3}p}{h_{st}}}\right)}^n\right].

The current value of h_{st} ranges between h_{sw}\le h_{st}\le h_{so}, where the upper limit h_{so} is the solid hardness for the dry material and the lower limit h_{sw} is the final degraded granular hardness when a thermodynamic equilibrium is reached. A lower value of h_{st} means a higher compressibility of the material as illustrated in Fig. 5(a). If a reaction with water takes place, the degradation of the granular hardness is modeled in a simplified manner by the following evolution equation, i.e., Bauer [11]:

(5){\dot{h}}_{st}=-{\displaystyle \frac{\mathrm{1}}{c}}(h_{st}-h_{sw}).

In Eq. (5) the parameter {\dot{h}}_{st} denotes the rate of the solid hardness, h_{st} is the current value of the solid hardness, h_{sw} denotes the value of the solid hardness when the process of degradation is completed, and c has the dimension of time. The value of c scales the velocity of degradation and it can be calibrated from a creep test. During the process of degradation the current value of the solid hardness is larger than the final value, i.e., h_{st}>h_{sw}, so that the rate of the solid hardness is negative, i.e., . Starting the degradation from t=\mathrm{0} and h_{st}(t=\mathrm{0})=h_{so} for the initial state, the integration of Eq. (5) yields the solid hardness h_{st} as a function of the degradation time t:

(6)h_{st}=h_{sw}+(h_{so}-h_{sw})\exp \left(-{\displaystyle \frac{t}{c}}\right).

Eq, (6) describes an exponential decrease of the solid hardness from the initial value h_{so} down to the final value h_{sw} with an increase of the degradation time. As the solid hardness is a function of the degradation time, the time derivative of Eq. (4) reads

(7)\dot{e}=ne{\left({\displaystyle \frac{\mathrm{3}p}{h_{st}}}\right)}^n\left[{\displaystyle \frac{{\dot{h}}_{st}}{h_{st}}}-{\displaystyle \frac{\dot{p}}{p}}\right].

Herein \dot{e}, {\dot{h}}_{st} and \dot{p} denote the time derivatives of e, h_{st} and p, respectively. Assuming a constant grain density the following relation for the volume strain rate, {\dot{ϵ}}_v, under isotropic compression can be derived, i.e. substituting Eq. (7) into Eq. (2) yields,

(8){\dot{ϵ}}_v={\displaystyle \frac{\dot{e}}{\mathrm{1}+e}}={\displaystyle \frac{ne}{\mathrm{1}+e}}{\left({\displaystyle \frac{\mathrm{3}p}{h_{st}}}\right)}^n\left[{\displaystyle \frac{{\dot{h}}_{st}}{h_{st}}}-{\displaystyle \frac{\dot{p}}{p}}\right].

From the right-hand side of Eq. (8), it can be concluded that the volume strain rate depends on the current state of e, p and h_{st}, and also on their corresponding rates. In the special case that during the degradation of h_{st} the pressure is kept constant, i.e., \dot{p}=\mathrm{0}, the material creeps and the volumetric strain rate in Eq. (8) reduces to

(9){\dot{ϵ}}_v={\displaystyle \frac{ne}{\mathrm{1}+e}}{\left({\displaystyle \frac{\mathrm{3}p}{h_{st}}}\right)}^n{\displaystyle \frac{{\dot{h}}_{st}}{h_{st}}}.

Eq. (9) indicates that during creep the volumetric strain rate {\dot{ϵ}}_v is proportional to the rate of the solid hardness, {\dot{h}}_{st}, and it is also influenced by the pressure p and the current void ratio e. Under constant volume, i.e., {\dot{ϵ}}_v=\mathrm{0}, Eq. (8) yields for stress relaxation

(10)\dot{p}=p{\displaystyle \frac{{\dot{h}}_{st}}{h_{st}}}.

Under mixed boundary conditions and for {\dot{h}}_{st}\ne \mathrm{0} the material can undergo both volume changes and stress changes, which is described with Eq. (8) in a unified manner. It is obvious that with a degradation of the granular hardness according to relation (6) the pressure dependent limit void ratios and the critical void ratio obtained from relation (3) are lower for , which is illustrated in Fig. 5(b).

Hypoplastic model for general stress paths

For general stress paths the history dependent solid hardness and limit void ratios proposed in Section 2 were embedded in the hypoplastic model by Gudehus [16] and Bauer [18] as outlined in more detail by Bauer [11]. In the version by Gudehus [16] and Bauer [18] the solid hardness is assumed to be constant and the stress rate is described by a nonlinear tensor valued function depending on the current void ratio e, the effective Cauchy stress tensor \sigma and the rate of deformation tensor \dot{ϵ}. With respect to the normalized quantities {\widehat{\sigma }}_{ij}={\sigma }_{ij}/{\sigma }_{kk}, {\widehat{\sigma }}_{ij}^{\ast }={\widehat{\sigma }}_{ij}-{\delta }_{ij}/\mathrm{3}, and the Kroneker delta {\delta }_{ij} the constitutive equations for the components of the objective stress rate can be represented as:

(11){\stackrel{\circ }{\sigma }}_{ij}=f_s\left[{\widehat{a}}^{\mathrm{2}}{\dot{ϵ}}_{ij}+\left({\widehat{\sigma }}_{kl}{\dot{ϵ}}_{kl}\right){\widehat{\sigma }}_{ij}+f_d\widehat{a}\left({\widehat{\sigma }}_{ij}+{\widehat{\sigma }}_{ij}^{\ast }\right)\sqrt{{\dot{ϵ}}_{kl}{\dot{ϵ}}_{kl}}\right].

Herein the scalar factors f_s and f_d depend on the stress, relative densities and the solid hardness. Function \widehat{a} is related to the stress limit condition in critical states, i.e. for a simultaneous vanishing of the stress rate and the volume strain rate f_d = 1 and Eq. (11) reduces to [21]

(12)\widehat{a}=\sqrt{{\widehat{\sigma }}_{ij}^{\ast }{\widehat{\sigma }}_{ij}^{\ast }}.

In the present paper function \widehat{a} is adapted to the stress limit criterion by Matsuoka and Nakai [23], which can be represented as [24]:

(13)\widehat{a}={\displaystyle \frac{\sin {\phi }_c}{\mathrm{3}+\sin {\phi }_c}}\left[\sqrt{{\displaystyle \frac{(\mathrm{8}/\mathrm{3})-\mathrm{3}\left({\widehat{\sigma }}_{kl}^{\ast }{\widehat{\sigma }}_{kl}^{\ast }\right)+g\sqrt{\mathrm{3}/\mathrm{2}}{\left({\widehat{\sigma }}_{kl}^{\ast }{\widehat{\sigma }}_{kl}^{\ast }\right)}^{\mathrm{3}/\mathrm{2}}}{\mathrm{1}+\sqrt{\mathrm{3}/\mathrm{2}}{\left({\widehat{\sigma }}_{kl}^{\ast }{\widehat{\sigma }}_{kl}^{\ast }\right)}^{\mathrm{1}/\mathrm{2}}}}}+\sqrt{\left({\widehat{\sigma }}_{kl}^{\ast }{\widehat{\sigma }}_{kl}^{\ast }\right)}\right],\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}g=-\sqrt{\mathrm{6}}{\displaystyle \frac{{\widehat{\sigma }}_{kl}^{\ast }{\widehat{\sigma }}_{lm}^{\ast }{\widehat{\sigma }}_{mk}^{\ast }}{{\left({\widehat{\sigma }}_{pq}^{\ast }{\widehat{\sigma }}_{pq}^{\ast }\right)}^{\mathrm{3}/\mathrm{2}}}}.

Herein {\phi }_c denotes the intergranular friction angle, which is defined in the critical state under triaxial compression.

The dilatancy behavior, the peak stress ratio and strain softening depend on the density factor f_d, which represents a relation between the current void ratio e the critical void ratio e_c and the minimum void ratio e_d, i.e.,

(14)f_d={\left({\displaystyle \frac{e-e_d}{e_c-e_d}}\right)}^{\alpha },

where \alpha is a constitutive constant. It can be noted that in contrast to the well-known relative density in soil mechanics the current void ratio in Eq. (14) is related to the pressure dependent critical void ratio and the minimum void ratio. In Eq. (11) the stiffness factor f_s is proportional to the current state of the granular hardness, h_{st}, and also depends on the mean pressure p, i.e.,

(15)f_s={\left({\displaystyle \frac{e_i}{e}}\right)}^{\beta }{\displaystyle \frac{h_{st}(\mathrm{1}+e_i)}{n\left({\widehat{\sigma }}_{kl}{\widehat{\sigma }}_{kl}\right)e_i}}{\left[{\displaystyle \frac{\mathrm{8}{\sin }^{\mathrm{2}}{\phi }_c}{{(\mathrm{3}+\sin {\phi }_c)}^{\mathrm{2}}}}+\mathrm{1}-{\displaystyle \frac{\mathrm{2}\sqrt{\mathrm{2}}\sin {\phi }_c}{\mathrm{3}+\sin {\phi }_c}}{\left({\displaystyle \frac{e_{i\mathrm{0}}-e_{d\mathrm{0}}}{e_{c\mathrm{0}}-e_{d\mathrm{0}}}}\right)}^{\alpha }\right]}^{-\mathrm{1}}{\left({\displaystyle \frac{\mathrm{3}p}{h_{st}}}\right)}^{\mathrm{1}-n}.

Herein, \beta is a constitutive constant. In Eqs. (14) and (15) the maximum void ratio e_i, the minimum void ratio e_d and the critical void ratio e_c depend on the pressure and the solid hardness according to Eq. (1) and Eq. (3).

To take into account creep and stress relaxation the constant solid hardness h_{so} is replaced by the state quantity {\mathit{h}}_{\mathit{s}\mathit{t}} and a term depending on the rate of the solid hardness, {\dot{h}}_{st}, is added to the right-hand side of Eq. (11). The extended hypoplastic model proposed by Bauer [11] reads

(16){\stackrel{\circ }{\sigma }}_{ij}=f_s\left[{\widehat{a}}^{\mathrm{2}}{\dot{ϵ}}_{ij}+\left({\widehat{\sigma }}_{kl}{\dot{ϵ}}_{kl}\right){\widehat{\sigma }}_{ij}+f_d\widehat{a}\left({\widehat{\sigma }}_{ij}+{\widehat{\sigma }}_{ij}^{\ast }\right)\sqrt{{\dot{ϵ}}_{kl}{\dot{ϵ}}_{kl}}\right]+{\displaystyle \frac{{\dot{h}}_{st}}{h_{st}}}\left({\displaystyle \frac{{\sigma }_{kk}}{\mathrm{3}}}{\delta }_{ij}+\kappa {\sigma }_{ij}^{\ast }\right),

where {\sigma }_{ij}^{*}={\sigma }_{ij}-{\sigma }_{kk}{\delta }_{ij}/\mathrm{3} denotes the deviatoric part of the stress tensor. In earlier versions factor \kappa on the right-hand side of Eq. (16) was assumed either to be zero [25] or equal to one [13].

Investigations by Fu [26] and Bauer and Fu [27] show that the deviatoric stress can have a significant influence on the amount of stress relaxation and creep deformation. Herein factor \kappa can also depend on the loading history in a more complex manner. As detailed investigations are still missing, factor \kappa is assumed to be a constant in the present paper. The calibration of \kappa can be carried out for instance based on the inclination of the volume strain curve obtained from a creep test under constant deviatoric stress. When the degradation of the solid hardness has been completed, i.e., for {\dot{h}}_{st}=\mathrm{0}, the corresponding solid hardness is h_{sw}. Then the last term on the right-hand side of Eq. (16) becomes zero and the rate independent hypoplastic model in Eq. (11) is recovered.

Comparison of numerical simulations with experiments

The performance of the constitutive model proposed for weathered rockfill materials is demonstrated by comparing the results obtained from the numerical simulation of triaxial compression tests with the corresponding experiments carried out by Li [12]. All experiments with slightly weathered broken sandstone were performed under drained conditions. In the numerical simulations the influence of the specific weight of the solid grains and of the water is neglected. The effective grain stress is assumed to be equal to the total stress prescribed at the boundary of the specimen.

The hypoplastic model proposed in Section 3 includes 11 constants. For the initially dry material the following values for the constitutive constants involved were obtained: {\phi }_c=\mathrm{40}°, h_so = 47 MPa, n=\mathrm{0.3}, e_{i\mathrm{o}}=\mathrm{0.59}, e_{c\mathrm{o}}=\mathrm{0.48}, e_{d\mathrm{o}}=\mathrm{0.20}, \alpha =\mathrm{0.18} and \beta =\mathrm{2.50}. After water saturation the additional constitutive constants for modeling the degradation of the solid hardness are: h_sw = 11.5 MPa, \kappa =\mathrm{0.7} and c=\mathrm{3} days. More details about the calibration of the hypoplastic constitutive constants can be found for instance in [18,28,29]. In the present paper the same set of constitutive constants is used for all numerical simulations of triaxial tests under both low and high lateral stresses. The solid hardness is the only parameter which differs for the dry material (h_so = 47 MPa) and for the water saturated material (h_sw = 11.5 MPa). In particular, the numerical results together with the experimental data are shown for a lateral stress of -100 kPa in Fig. 6 and for a lateral stress of -1000 kPa in Fig. 7.

As can be seen in Fig. 6(a), the deviatoric stress ({\sigma }_{\mathrm{11}}-{\sigma }_{\mathrm{33}}) and the volumetric strain {ϵ}_v against the axial strain {ϵ}_{\mathrm{11}} are different for the dry and the water saturated materials. The compaction at the beginning of deviatoric loading is significantly higher for the water saturated material, while the maximum deviatoric stress is higher for the dry material. Moreover, under subsequent loading dilation appears, but it is considerably lower for the saturated material, which can be attributed to the more pronounced particle disintegration. The comparison of Fig. 6(a) with Fig. 7(a) shows that, for a higher lateral stress, the deviatoric stress is also higher and it is reached for a larger vertical compression of the specimen. At the beginning of deviatoric loading the compaction is also higher but with subsequent loading the dilatancy is less pronounced as for the case of the lower lateral stress.

For the stressed material the degradation of the solid hardness from h_{so} to h_{sw} is accompanied by creep or stress relaxation depending on the boundary conditions, the packing density and the stress state of the material. In the present numerical and experimental investigations the degradation is initiated by water saturation of the initially dry material. First isotropic compression and then deviatoric loading are applied to the dry specimen. Then the specimen is saturated under constant stress, which initiates a time dependent degradation of the solid hardness according to Eq. (5). The creep behavior of the specimens under different lateral stresses and for different deviatoric stress states are shown in Figs. 6(b)–6(d) and Figs. 7(b)–7(d). As can be seen, the axial creep deformation is more pronounced for a higher deviatoric stress while the volume strain curve is steeper under a lower deviatoric stress. The volumetric creep paths are almost linear and also in good agreement with the experimental data for both the lower and the higher lateral pressure.

Conclusions

The long-term behavior of weathered rockfill materials may be strongly influenced by crack propagation within the individual particles, grain abrasion and grain breakage. Under high stresses the degradation of the solid hardness can be accelerated when the moisture content changes, which leads to effects called collapse settlements and secondary creep deformations. With respect to a solid hardness depending on the state of weathering creep and stress relaxation can be modeled in a unified manner and there is no need to distinguish between primary and secondary deformations. The state of the solid hardness also has an influence on the pressure dependent limit void ratios and the critical void ratio. In the hypoplastic constitutive model proposed the current void ratio is related to the pressure dependent maximum void ratio, the minimum void ratio and the critical void ratio, so that the incremental stiffness depends on the current density of the material, the pressure level and the state of weathering. As a consequence the peak friction angle, dilatancy or contractancy is also influenced by a change of the solid hardness. To model the influence of the amount of creep depending on the deviatoric stress a refined modeling is suggested in the present paper. Creep deformation initiated by the saturation of the initially dry material is simulated at different confining pressures and deviatoric stresses. The comparison of the numerical results obtained from the extended hypoplastic model are in good agreement with experimental data for a rockfill material used in the Xiaolangdi earth dam.

References

[1] Brauns J, Kast K, Blinde A. Compaction effects on the mechanical and saturation behaviour of disintegrated rockfill. In: Proceedings of the International conference on Compaction. Paris, 1980, 1: 107–112

[2] Kast K. Mechanisches Verhalten von Granitschuettungen. In Veroeffentlichungen des Institutes fuer Bodenmechanik und Felsmechanik der Universitaet Fridericiana in Karlsruhe, Heft 125, 1992

[3] Biarez J, Hicher P Y. Influence de la granulometrie et de son evolution par ruptures de grains sur Ie comportement mecanique de materiaux granulaires. Revue française de genie civil, 1(4): 607–631, 1997

[4] Nobari E S, Duncan J M. Movements in dams due to reservoir filling. In: Proceedings of the ASCE Specialty conference on Performance of Earth and Earth-supported Structure. Lafayette: Purdue University, 1973, 797–815

[5] Alonso E, Oldecop L A. Fundamentals of rockfill collapse. In: Proceedings of the 1st Asian Conf. on Unsaturated Soils. Rahardjo H, Toll DG, Leong EC, eds. Rotterdam: Balkema Press, 2000, 3–13

[6] Oldecop L A, Alonso E. Theoretical investigation of the time-dependent behaviour of rockfill. Geotechnique, 2007, 57(3): 289–301

[7] Hu W, Frossart E, Hicher P Y, et al. A new method to evaluate the mechanical behavior of granular material with large particles: Theory and validation: In: Proceedings of the 2nd Int. Conf. on Long Term Behaviour of Dams. Bauer, Semprich and Zenz, eds. Graz: Publisher Graz University of Technology, 2009, 437–478

[8] Alonso E, Cardoso R. Behaviour of Materials for Earth and Rockfill Dams: Perspective from Unsaturated Soil Mechanics. In: Proceedings of the 2nd Int. Conf. on Long Term Behaviour of Dams Bauer, Semprich and Zenz, eds. Graz: Publisher Graz University of Technology, 1–38, 2009

[9] Klammer D, Dietzel M. Weathering of Natural Minerals and Rocks – Effect of Composition and Structure of Solids and Solution Chemistry. In: Proceedings of the 6th Int. Conf. on Dam Engineering. Pina, Portela and Gomes, eds. Lisbon, Portugal, 2011

[10] Ham T G, Nakata Y, Orense R, et al. Influence of water on the compressive behavior of decomposed granite soil. Journal of Geotechnical and Geoenvironmental Engineering, 2010, 136(5): 697–705

[11] Bauer E. Hypoplastic modelling of moisture-sensitive weathered rockfill materials. Acta Geotechnica, 2009, 4(4): 261–272

[12] Li G X. Triaxial Wetting Experiments on Rockfill Materials Used in Xiaolangdi Earth Dam. Research Report from Tsinghua University, 1988

[13] Bauer E, Fu Z, Liu S. Hypoplastic constitutive modeling of wetting deformation of weathered rockfill materials. Frontiers of Architecture and Civil Engineering in China, 2010, 4(1): 78–91

[14] Kolymbas D. An outline of hypoplasticity. Archive of Applied Mechanics, 1991, 61: 143–151

[15] Wu W, Bauer E. A hypoplastic model for barotropy and pyknotropy of granular soils. In: Proceedings of the International Workshop on Modern Approaches to Plasticity. Elsevier, 225–245, 1993

[16] Gudehus G. A comprehensive constitutive equation for granular materials. Soil and Foundation, 1996, 36(1): 1–12

[17] Gudehus G. Physical Soil Mechanics, Advances in Geophysical and Environmental Mechanics and Mathematics. Springer-Verlag Berlin-Heidelberg, 2011

[18] Bauer E. Calibration of a comprehensive hypoplastic model for granular materials. Soil and Foundation, 1996, 36(1): 13–26

[19] Bauer E. Constitutive modelling of critical states in hypoplasticity. In: Proceedings of the 5th International Symposium on Numerical Models in Geomechanics. Pande and Pietruszczak, Balkema Press, 15–20, 1995

[20] Bauer E, Zhu Y. Constitutive modelling of pressure, density and moisture content on the mechanical behaviour of rockfill materials. In: Proc. of the 4th Int. Conf. On Dam Eng.. Wieland, M.RenaQ.Tan J S Y, eds. Nanjing: Balkema Publishers, 2004, 129–146

[21] Bauer E. Constitutive modelling of critical states in hypoplasticity. In: Proceedings of the Fifth International Symposium on Numerical Models in Geomechanics. NUMOG-V, Davos, Switzerland, Balkema, 15–20, 1995

[22] Bauer E. The critical state concept in hypoplasticity. In: Proceeding of the 9th Int. Conf. on Computer Methods and Advances in Geomechanics. IACMAG 97, Wuhan, China, 1997, 691–696

[23] Matsuoka H, Nakai T. Stress-strain relationship of soil based on the “SMP”. In: Proceedings of Specialty Session 9, IX Int. Conf. Soil Mech. Found. Eng. Tokyo, 1977, 153–162

[24] Bauer E. Conditions for embedding Casagrande’s critical states into hypoplasticity. Mechanics of Cohesive-Frictional Materials, 2000, 5(2): 125–148

[25] Fu Z, Bauer E. Hypoplastic constitutive modeling of the long term behaviour and wetting deformation of weathered granular materials. In: Proceedings of the 2nd Int. Conf. On Long Term Behaviour of Dams, Bauer, Semprich and Zenz, eds. Graz: Publisher Graz University of Technology, 437–478, 2009

[26] Fu Z Z. Hypoplastic constitutive modelling for wetting deformation of granular materials and its application in Engineering. Dissertation for the Doctoral Degree. Nanjing: Hohai University, 2011 (in Chinese)

[27] Bauer E, Fu Z. Modeling of weathered and moisture sensitive granular materials. In: Proceedings of the 9th International Workshop on Bifurcation and Degradation in Geomaterials. Bonelli S Dascalu C, Nicot F, eds. Springer Series in Geomechanics & Geoengineering, 2011, 333–338

[28] Herle I, Gudehus G. Determination of parameters of a hypoplastic constitutive model from properties of grain assemblies. Mechanics of Cohesive-Frictional Materials, 1999, 4(5): 461–486

[29] Bauer E, Tantono S F, Niemunis A, et al. Modelling the Disintegration of Weathered and Partly Saturated Grains of Rockfill Material. In: Proceedings of the 3rd Asian Conference on Unsaturated Soils, Beijing: Science Press, 2007, 335–340

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