Three-dimensional settlement analysis of a primary crusher station at a copper mine in Chile

Transcription

1 Three-dimensional settlement analysis of a primary crusher station at a copper mine in Chile B. Méndez Rizzo Associates Chile S.A., Santiago, Chile D. Rivera Rizzo Associates Inc., Pittsburgh, PA, USA ABSTRACT: A copper mine located in Northern Chile at 3000 m above sea level is expanding its operations. Accordingly, the mine is planning the construction of a new primary crusher station of around 36 m height. The crusher station will be surrounded by the Rom Pad backfill on three of its side walls, thus making its settlement distribution a key aspect to consider in the design and operation of the crusher facilities. A FLAC 3D model was developed to study the foundation settlement response, accounting for a detailed three-dimensional geometry. The model included site 3D topography, stratigraphy and construction sequence. Material properties were obtained from a geotechnical exploration campaign specifically tailored for the project. 1 INTRODUCTION As part of the mine s expanding copper production, the construction of a new primary crusher station is being planned. The station building will be about 36 m high and will serve as a retaining element on three of its faces to support the Rom Pad fill, which will be delimited on its front face by 29 m high MSE walls. The expected stress to be induced by the MSE walls over the soil next to the crusher building is over 600 kpa, while the stress exerted by the mat building foundation is around 350 kpa. This high soil stress is an important issue to be analyzed, along with the three-dimensional interaction between the MSE walls, Rom Pad and building station. An important 3D effect is anticipated in the settlement spatial distribution under the foundation mat. Moreover, the Rom Pad backfill will impose very high soil loads over the crusher building, which will contribute to the development of differential settlements. Also, the geometrical distribution of the construction works induces three-dimensional effects that must be taken into account in order to model the foundation settlement distribution realistically. Accordingly, a detailed FLAC 3D (Itasca 2009) model was developed to analyze the problem and compute the maximum differential settlements expected at the end of the construction. The construction stages were included in the numerical simulations, to approximate the induced stress paths in the non-linear foundation soils. 2 MODEL GEOMETRY AND BOUNDARY CONDITIONS 2.1 Geometry The extension of the zone involved in the project is very large, as seen in Figure 1. The actual area included in the analysis was limited to a section of 280 m 350 m with variable depth down to 100 m. Figure 1 shows the full Rom Pad backfill, which will be built in two stages: the first stage consists of the Rom Pad construction up to the boundary shown with a broken bold line in Figure 1, and marked as Zone A in Figure 2. The second stage will be the construction of the backfill between the first stage of the Rom Pad, the crusher station and MSE walls (Zone C in Fig. 2). This second construction stage of the Rom Pad will be called final fill from now on.

2 Rom Pad boundary for the first construction stage Rom Pad fill Excavation for conveyor system 280 m MSE walls Crusher station 350 m Modeled zone Figure 1. Plan view of the project and actual zone modeled. A A 1.6d MSE Walls B C d B Terrain level 5.7B B 3d B 5.5B Figure 2. Plan view of the numerical model in FLAC 3D. A The MSE walls will be used to define the front boundary of the Rom Pad, as shown in Figure 1. The actual model developed in FLAC 3D for the analysis is shown in Figure 2, where zones A and C are as described above, and zone B is the excavation for the conveyor system that will transport crushed material. The model s plan dimensions, shown in Figure 2, were selected to comply with two conditions: in the short direction (280 m), the whole excavation works required to allocate the station building, Rom Pad final backfill (Zone C) and the space for the conveyor system should be included in the model. For the long dimension (350 m), the criterion was that Zone C should be sufficiently far apart from both the front and back boundaries. This was accomplished by locating the back model boundary a distance 2.6d from the back wall of the crusher building (see Fig. 2) and the front model boundary a distance 3d from the same point. The distance d is the largest size of Zone C in the model s long dimension, as shown in Figure 2. The purpose of this criterion was to avoid boundary effects over the soil pressures exerted on the back wall of the crusher building, which will influence foundation settlements. Dimensions shown in Figure 2 are as follows: width of mat foundation, B = 23 m, length of final fill behind the building, d = 60 m. General dimensions of the overall geometry are depicted in the isometric view of the model at the final construction stage, shown in Figure 3. Each color represents either a material type or a construction stage. This will be detailed in the following sections. A view of cross sections A and B is shown in Figures 4 and 5, respectively. It can be seen in Figure 4 that the distance between the building foundation to the sloping rock stratum varies along the foundation length, L (42 m). Note that this distance is smaller than 2L. Accordingly, it is expected that the settlements will be constrained by the rock stratum and will vary due to its three dimensional inclination, as can be seen in Figures 4 and 5 were the rock slope is shown for the two cross sections.

3 30 m 67 m 40 m 10 m 70 m 24 m Figure 3. Isometric view of the 3D model. Structural backfill Crusher station building Terrain level m Excavation to allocate the conveyor system L 0.7L 0.6L 0.5L Rom Pad second construction stage Rom Pad first construction stage Rock base Figure 4. View of cross section A. Crusher station Structural backfill MSE Walls Rom Pad second construction stage Rom Pad first construction stage B B Rock base Figure 5. View of cross section B. 2.2 Boundary conditions Roller boundary conditions were assigned to each model outer face, i.e. the boundaries were restrained only in the direction normal to each face, as shown in Figure 6. The distance from the area of analysis (location of the crusher building) to the model boundaries is large enough so that boundary locations do not affect the solution. This can be observed in Figures 7 through 9, where different views of the stress increment distribution due to foundation loading are presented (over 500 kpa were applied to the mat, as shown in Fig. 7). Figure 7 shows a threedimensional view of stress increment. The influence area of foundation loading can be seen in this Figure. It is interesting to note in Figure 7 how the stress increment reaches the rock stratum with only a small fraction of the maximum stress induced over the foundation area. This can be observed better in Figures 8 & 9, where a view of cuts A and B is presented in terms of maxi-

4 mum stress percentage. Figure 8 shows that the maximum stress increment develops at the back of the mat, close to the excavation boundary. This maximum stress concentration (depicted as 100% in Fig. 8) corresponds to the minimum distance between the mat slab and the rock stratum (see Fig. 4), i.e. the soil is more confined in this zone, thus settlement is constrained, consequently inducing high stress levels. Figures 8 & 9 show that stress increment at the boundaries is between zero and five percent of the maximum stress, thus revealing that model boundaries are located sufficiently far away from the area of interest, namely the area of the mat foundation. Accordingly, it was concluded that no boundary effects are induced into the area of interest of the model. Figure 6. Model boundary conditions. Figure 7. Three-dimensional view of stress increment distribution (in Pascals). Figure 8. Percentage of maximum stress distribution along cut A.

5 Figure 9. Percentage of maximum stress distribution along cut B. 3 MATERIAL PROPERTIES AND CONSTITUTIVE MODELS The project of the crusher station involves excavations in natural soils, backfilling and embankment construction. Accordingly, both natural soils and backfill materials were geotechnically characterized. The properties for the mat foundation and the crusher station building are also presented. 3.1 Natural soil characterization A geotechnical exploration campaign was performed to characterize the site. The campaign included geophysical testing (downhole, seismic refraction and refraction microtremor method), laboratory testing, in-situ plate bearing testing, SPT, exploration pits and drilling down to the rock stratum with core sampling. The exploration campaign aimed to characterizing both the geotechnical units and their spatial distribution over the site. From the results of the geotechnical exploration, four geotechnical units were interpreted, as described below: Superficial loose silts. This layer is only about 30 cm thick and will be removed during construction. Accordingly, this soil was not included in the geotechnical profile used for the analysis. Stratum I. This layer contains a gravelly-silty sand with a maximum particle size of 3. The particles are angular and the fines are non plastic. This stratum corresponds to dense soil. Stratum II. This layer contains a sandy-silty gravel with a maximum particle size of 1. This stratum corresponds to dense soil. Stratum III. Moderately weathered Sandstone rock. The rock is slightly fractured. Its RQD increases with depth from about 53 % up to 88 %. Stratum IV. Unweathered rock with RQD over 90 % The spatial distribution of these strata was determined mainly from geophysical exploration and drilling data. The thickness of each stratum immediately underneath the foundation of the crusher station is as follows: 10 m for Stratum I, 24 m for Stratum II, 21 m for Stratum III and 34 m for Stratum IV. The variable thickness of all strata can be seen in Figures 3 through 5. The superficial loose silt stratum was not considered in the numerical model. Also, only one rock stratum (Stratum III) was taken into account for simplicity, as rock strains are assumed to be negligible due to its high stiffness inferred from geophysical surveys. The strength material properties were assigned based on triaxial testing of disturbed samples, the results of in-situ plate bearing tests and in-situ soil conditions. Due to the type of soils encountered in-situ, it was considered that the Mohr-Coulomb constitutive model was a good approximation for modeling the soil strength. Accordingly, a Mohr-Coulomb constitutive model was used for Stratum I and Stratum II, while a linear elastic material model was assigned to the rock stratum. To achieve a better approximation to soil stiffness variation with confining stresses, the Young s modulus for Strata I and II was modified through a FISH function. This function reproduced the in-depth soil static-stiffness variation obtained from geophysical testing. The

6 static moduli were estimated for the shear strain range, based on G máx (shear modulus for small strains) geophysical estimations (Ishihara, 1996). Equation 1 shows the soil Young s modulus variation with octahedral stress for Strata I and II. (1) where E S = soil Young s modulus in MPa, oct is the octahedral stress, and k 0 are the soil volumetric weight and at rest soil pressure coefficient for each stratum, respectively. As mentioned before, Equation 1 was calibrated using all the available data gathered in the exploration campaign, including plate bearing test results for the shallow soils. Equation 1 assumes the medium and minimum principal stresses are equal, and uses Jaky s formula to estimate k 0. The static strength and deformability material properties at the center of each stratum are shown in Table 1. The properties for the base rock were held constant throughout the analyses. Table 1. Strength and elastic natural soil material properties for numerical static analyses. *E s k 0 Constitutive Material (kg/m 3 ) ( ) (MPa) Model Stratum I Mohr-Coulomb Stratum II Mohr-Coulomb Rock base Linear Elastic * Values at center of strata 3.2 Backfill material characterization Preliminary results from laboratory testing were available for these materials. Accordingly, the properties for backfill materials were estimated based both on those results and upon engineering judgment along with local experience with the soils available in the project area. It was considered that all backfill materials are granular and compacted up to 95% of its maximum dry density according to regular construction standards. Typical compacted soil properties were assumed for these materials, as shown in Table 2. Backfill materials were divided in two groups: F1 is the group for the Rom Pad backfill and the final fill material and F2 includes the fill used for the unreinforced portion of the MSE walls and structural fill materials. The Rom Pad material (first construction stage of Rom Pad) was modeled with a linear elastic constitutive model. This model was adopted because the Rom Pad backfill yielding analysis is not a priority for the project, as this embankment is allowed to accommodate large strains without posing any risks to the operation of the crusher station. The key aspect of the Rom Pad is its weight, as this is crucial for settlement magnitude and spatial distribution. Equation 2 shows the general form for the of Young s modulus variation with octahedral stress for the backfill material groups. Table 2. Strength and elastic backfill material properties for numerical static analyses. Backfill Material Material *E s E 0 k 0 Constitutive group (kg/m 3 ) ( ) (MPa) (MPa) Model Rom Pad F Linear Elastic Final fill F Mohr-Coulomb Unreinforced MSE wall F Mohr-Coulomb Structural fill F Mohr-Coulomb * Values at center of strata

7 (2) where E 0 is the minimum Young s modulus related to the minimum expected octahedral stress, 0, is the exponent shown in Table MSE wall material properties Since the purpose of the analysis was not to evaluate the stability and behavior of the MSE walls, they were accounted for in a simplified manner. Accordingly, the MSE walls were modeled as high stiffness blocks, in accordance with the usual external global stability analysis of such reinforced soil masses. The assigned values for the Young s modulus of the MSE elements were chosen based on the basic mechanics of reinforced earth, i.e. bearing in mind that MSE walls are a composite material combining the compressive and shear strengths of compacted granular fill with the tensile strength of horizontal, inextensible reinforcements (Anderson et al. 2012). The inextensible reinforcement prevents large lateral strains to develop within the MSE wall, i.e. the MSE system behaves similar to a laterally constrained material. For this reason, it was assumed that the constrained Young s modulus was adequate to model the reinforced soil block of the MSE wall. This modulus was estimated based on a typical value of the shear wave velocity for high grade compacted fills (330 m/s). This approach was adopted considering that usually the MSE wall design is based on small-moderate shear strains, as implied by the maximum allowable value of the internal soil friction angle permitted by the AASHTO specifications (op. cit.). The vertical faces of the MSE walls pose a complex modeling issue if the soil reinforcement is not explicitly accounted for, because of the material failure of such vertical faces when considering a material failure criterion. Hence, to avoid such modeling problems, and since it was not intended to analyze the MSE walls themselves, a linear elastic constitutive model was used for the MSE wall elements. 3.4 Mat foundation The mat foundation was accurately modeled both in its geometry and properties. Accordingly, the corresponding assigned material properties were those of reinforced concrete. However, it was not intended to compute mechanical elements within the slab, but to capture its stiffness. Hence, solid elements with linear elastic behavior were used for this purpose. 3.5 Crusher station building For simplicity, the building was modeled as a single solid volume, i.e. equivalent material properties had to be set in order to adequately represent its stiffness. The equivalent properties were computed from the actual building flexural stiffness. A linear elastic constitutive model was used for the building. 4 SEQUENCE OF ANALYSIS The in-situ geostatic stress field in the model was achieved through initial equilibrium under gravitational loads. After that, the construction sequence adopted for the analysis was as follows: I. Rom pad construction. This stage was divided in two steps. II. Excavation. This stage considers all the excavations involved in the project. III. Mat foundation. In this stage the mat foundation is set in place. IV. Crusher station and MSE walls. This stage was divided in three steps. V. Final fill. This fill was modeled in two stages. A view of the sequence of analysis is presented in Figure 10.

8 Initial equilibrium I. Rom Pad construction (two steps stage) II. Excavation III. Mat foundation IV. Crusher station and MSE walls (three steps stage) V. Final fill (two steps stage) Figure 10. Construction sequence considered in the analysis. 5 RESULTS ANALYSIS Results are presented for both settlement distribution and sub-grade modulus under the building mat foundation. Before settlement results are presented, a brief discussion on the mesh accuracy verification is presented in the following section. 5.1 Mesh accuracy verification The accuracy verification was deemed adequate because the mesh used for the analyses is tetrahedral-based. Accordingly, it is well known that tetrahedra, when used in the frame-work of plasticity, do not provide for enough modes of deformation (Itasca, 2009), and even exhibit an overly stiff response compared to what is expected from theory for particular situations. For the case analyzed in this paper, an overall elastic response was expected, because of the high strength soils present on site (foundation soils with 40 of friction angle). Consequently, a tetrahedral mesh was expected to provide accurate enough settlements results for engineering purposes. However, in order to improve the accuracy in plasticity calculation, it is recommended to use the nodal mixed discretization (NMD) approach (op. cit.). Therefore, results were compared for both cases, with and without NMD, in terms of settlements and geostatic vertical stresses (directly related to settlements). The purpose of the comparison was to determine the impact of the NMD both on accuracy and computing time, as to decide if its use was justified for the dynamic analysis phase of the problem (not presented in this paper).

9 Depth (m) Depth (m) A comparison between computed geostatic vertical stresses is presented in Figure 11(a) for the cases of with and without NMD ( NMD and, respectively). It can be noted in this figure that the difference between cases is negligible, as it is always less than 10 %. Since the stress comparison between cases was satisfactory, a further comparison between analytical and numerical stress (without NMD) was warranted. Results are depicted in Figure 11(b), where it is noted that numerical results match quite well the theoretical values. When settlements are compared between cases (below the center of foundation mat), it is observed from Figure 12 that results are very similar for both cases, showing differences well below 10 %. Settlements computed using NMD ( Z NMD ) proved to be slightly larger (up to 7 % in the whole foundation area, as observed from a contour plot) than those computed without NMD ( Z). This difference is not significant from the engineering point of view, as it falls in the range of uncertainty commonly implied in soil properties. On the other hand, the difference observed in computing time between the NMD and without NMD cases was over 100 %. Since the stress and settlement comparison between cases was satisfactory, and the stress comparison for numerical and analytical stresses was also adequate for engineering purposes, it was concluded that the mesh was accurate enough to serve the modeling purposes of the particular problem. Further, because the differences between NMD and without NMD cases were not significant, and the increment in computing time from one to another was over 100 %, it was chosen not to use the NMD option for this case. The selection was made bearing in mind the time required for the dynamic analysis phase, as this was a critical step in the time available to model the project. It is worth mentioning that the mesh geometry was optimized to be useful for both static and dynamic calculations, in order to reduce computational time and keep the detailed 3D geometry simultaneously. The optimization criterion was based on static stress comparison, free-field seismic site response and computing time with/without NMD. Site response results are not presented herein since they are out of the scope of this paper. NMD / V Vertical stress E E E E E Analytical, vertical stress 5.00 V (Pa) FLAC3D vertical stress (without NMD) Stratum I Stratum I Foundation depth Foundation depth Stratum II Stratum II Rock stratum Rock stratum (a) (b) Figure 11. (a) Normalized geostatic vertical stress with and without NMD, (b) numerical versus analytical geostatic stresses.

10 Depth (m) Z NMD / Z Settlements under foundation center Foundation depth Stratum I Stratum II Rock stratum Figure 12. (a) Normalized settlements with and without NMD (values computed underneath the center of foundation mat). The use of a single model for static and dynamic computations was a key feature for the project analysis stage, as this permitted to keep the costs and analyses time within a reasonable range in order to incorporate to the project an advanced numerical tool like FLAC 3D. By analyzing results presented in Figure 11, it can be seen that numerical stresses are on the conservative side, and that the difference between analytical and numerical values is rather small. Accordingly, it was considered that the model was adequate for engineering purposes. 5.2 Settlement results The results presented herein consider only the effective loads induced on the foundation soil by construction stages III through V. Hence, all the previous displacements induced by the Rom Pad backfill construction and excavation are not considered. However, the loading history is accounted for in the soil modulus distribution, according to the constitutive model used for each material, as stated in section 3. This approach was taken because during the project execution, all the settlements induced before the building construction will be leveled off in order to achieve the terrain elevations considered for the project. Also, due to the type of soil, long term settlements are not expected. Therefore, no previsions were taken in this regard. It is worth highlighting that the Mohr-Coulomb model with stress dependent soil modulus was used only for the effective loading stages. Since predicting settlements during previous stages was not a goal of the analyses, those stages considered elastic soil model with stress dependent modulus. A general view of the 3D settlement distribution at the foundation level (Strata I and II) is shown in Figure 13 (displacements shown in meters). A clear view of the area of influence can be seen in Figure 13, which consists of the mat foundation, the crusher building, MSE walls and final fill. It can also be noted that small differential settlements develop under the loaded area in the direction along the short dimension of the foundation mat. This is because the soil strata have variable thickness, as well as the final backfill and MSE walls, as seen in Figure 5. Also, the weight of the final fill behind the building causes differential settlements. However, the dif-

11 ferential settlement at the bottom of the excavation is less than one centimeter in a distance over 20 m along the short mat dimension. Results presented in Figure 13 clearly show the threedimensional effect in the settlement spatial distribution. A view of settlement distribution along cross section A (see Fig. 2) is shown in Figure 14. It is seen in this Figure that differential settlements develop in the direction of the long mat dimension, around 3 4 cm in magnitude. These settlements take place due to the surcharge induced by the final fill behind the building. However, the differential settlement distributes over the 42 m length foundation, thus giving a mat rotation between radians. This rotation is considered adequate for the crusher station when compared to similar projects were the maximum foundation rotation is set to radian (Canteros & Clemente 2011). It is interesting to note from Figure 14, that soil settlements reached down to the rock stratum, which slopes in the long mat dimension, thus contributing to the observed foundation rotation developed due to the weight of the Rom Pad backfill and the building weight distribution. Settlements along cross section B are presented in Figure 15. It is noted from these results that settlements under the mat are nearly uniform on the short dimension of the mat. Settlements directly under the mat foundation will be discussed later on this section. Taking a closer look to the foundation area, Figure 16 depicts the settlement distribution on Stratum II under the mat foundation area. Results show that the differential settlements are around 3 cm in the long mat dimension. In the short mat dimension, it is observed that the maximum settlements developed under the mat foundation are larger on one side of the mat, thus revealing a small rotation over that direction. However, the differential settlement observed is very small, between 2 3 mm, and should not pose any complications for the operation of the crusher station. This result coincides with those of Figure 15, where settlement distribution under the mat showed a nearly uniform distribution. Figure 13. General 3D view of settlement distribution over the loaded area. Figure 14. Settlement distribution on Strata I and II over cross section A.

12 Figure 15. Settlement distribution on Strata I and II over cross section B. MSE wall Rom Pad MSE wall Figure 16. Settlement distribution under the mat foundation (on Stratum II). 5.3 Sub-grade modulus distribution A simple methodology is proposed in this work to obtain sub-grade moduli distributions using a FISH function. Sub-grade modulus is used for detailed soil-structure interaction models where the goal of such analyses is to compute mechanical elements within the structure. Accordingly, the value used for the sub-grade modulus is very important in order to adequately account for the soil in the structural analysis. Several simplified analytical methodologies are available for this purpose in the related technical literature. However, those solutions are based on ideal conditions which include regular problem geometry and ideal soil behavior. The methodology proposed herein is based on the basic definition of sub-grade modulus: stress divided by settlement. However, the soil stress used in sub-grade modulus computation can include soil non linearity effects, stress path, geometrical effects and foundation stiffness. Further, this methodology can be used to obtain a soil moduli distribution for any desired model state, either at the end or during the construction stage. The details of the methodology used for sub-grade moduli computation is described next. Sub-grade modulus, K, were computed via a FISH function developed for that purpose. Based on material group, element location and face normal data, the function first selected all the elements under the mat foundation, as shown in Figure 17. Afterwards, a value of sub-grade modulus for each soil element was computed as the quotient of the vertical soil stress at the centroid of the element, zz, and the average vertical displacement of the nodes of the element face in contact with the foundation, U z. Figure 17 depicts the latter criterion, which was applied to all the elements under the foundation, thus obtaining a spatial distribution of sub-grade modulus. Only the final stage of the construction was considered for simplicity. However, the FISH function developed can be invoked at any other stage to obtain the associated sub-grade modulus distribution.

13 MSE wall Results are shown in Figure 18, where a sub-grade modulus distribution is depicted. The values shown in Figure 18 are presented in kn/m 3. It is seen that an average value for the loaded area would be around 7500 kn/m 3, while much higher values are seen around the edges, as expected. It can also be observed that the upper part of the distribution has higher values when compared to the central and lower zones. This is because of the building weight distribution and to the influence of the Rom Pad fill. The sub-grade modulus distribution is intended to be used in future detailed structural analyses for the crusher station building, to account for the foundation soil in the structural models. U z = (U z1 + U z2 + U z3 )/3 K = zz /U z U z3 U z zz (centroid) Normal vector U z2 U z Figure 17. Criterion used for computing sub-grade modulus under the mat foundation. Rom Pad MSE wall Figure 18. Sub-grade modulus distribution under mat foundation. 6 FINAL REMARKS A detailed three-dimensional geometry was set up in a FLAC 3D numerical model for the crusher station at a Copper mine in Chile. The model developed included stress-dependent soil modulus, non-linear soil behavior and the modeling of construction sequence. The high level of induced stress over foundation soils did not pose any problems on differential settlements. It is important to highlight that the obtained settlement rotation results include the effect of soil-foundation interaction, three-dimensional geometry effects, topography and stratigraphy spatial distribution, as well as the effect of the Rom Pad fill, which showed to have a major influence on settlement results.

14 Under such considerations, a spatial distribution for foundation settlement was obtained from model results, showing that maximum differential settlements should be on the order of 3 cm, and expected foundation rotations are around radians. These values are considered adequate when compared to similar projects in Northern Chile, which are currently operating. The settlement distribution under the mat foundation was used to compute a sub-grade modulus distribution for the soil-mat system. This was accomplished through a FISH function developed specifically for this purpose. The methodology coded into the FISH function considered the quotient of the vertical stress of each zone under the mat, and the average vertical displacement of the nodes of the zone face in contact with the mat. This methodology allows computing a sub-grade modulus distribution for any stage of the model, thus obtaining different sets of subgrade modulus for detailed further soil-structure interaction analyses. ACKNOWLEDGEMENT The authors wish to acknowledge the comments of the reviewers, which enriched the contents of the paper. REFERENCES Anderson, P.L., Gladstone R.A., & Sankey, J.E State of the practice of MSE wall design for highway structures; Proceedings of the Geocongress 2012, state of the art and practice in geotechnical engineering, Oakland, March ASCE. Canteros C.G. & Clemente J.L.M Settlement behavior of new primary crusher foundation; Proceedings of the Geo-Frontiers Congress 2011, Advances in geotechnical Engineering, Dallas, March ASCE. Ishihara, K Soil behavior in earthquake geotechnics. New York: Oxford University Press. Itasca Consulting Group, Inc FLAC 3D Fast Lagrangian Analysis of Continua in 3 Dimensions, Ver Minneapolis: Itasca.