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 retain-ing 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 founda-tion 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 im-portant 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 dis-tribution of the construction works induces three-dimensional effects that must be taken into ac-count in order to model the foundation settlement distribution realistically. Accordingly, a de-tailed 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.

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 sta-tion 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 de-sign and operation of the crusher facilities. A FLAC

3D model was developed to study the foun-

dation 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.

Continuum and Distinct Element Numerical Modeling in Geomechanics -- 2013 -- Zhu, Detournay, Hart & Nelson (eds.) Paper: 02-01 ©2013 Itasca International Inc., Minneapolis, ISBN 978-0-9767577-3-3

Figure 1. Plan view of the project and actual zone modeled.

Figure 2. Plan view of the numerical model in FLAC

3D.

The MSE walls will be used to define the front boundary of the Rom Pad, as shown in Fig-

ure 1. The actual model developed in FLAC3D

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 condi-tions: 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 in-cluded 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 locat-ing 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.

280 m

35

0 m

Modeled zone

Rom Pad fill

Excavation for

conveyor system

Crusher station

MSE walls

Rom Pad boundary for the

first construction stage

d

1.6d

3dB

C

A

MSE Walls

Terrain level

A

A

BB

5.5B5.7B B

2

Figure 3. Isometric view of the 3D model.

Figure 4. View of cross section A.

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 re-strained 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 present-ed (over 500 kPa were applied to the mat, as shown in Fig. 7). Figure 7 shows a three-dimensional 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-

70 m

24 m

10 m

67 m

40 m

30 m

Crusher station building

Rom Pad first

construction stage

Rom Pad second

construction stage

Excavation to allocate

the conveyor system

Rock base

Terrain level

Structural backfill

L

0.6L 0.5L0.7L

35.60 m

Structural backfill

Crusher station

Rom Pad first

construction stage

Rom Pad second

construction stage

MSE Walls

B

B

Rock base

3

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, conse-quently 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.

4

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 embank-ment 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 in-cluded 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 spa-tial 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 crush-er 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 en-countered in-situ, it was considered that the Mohr-Coulomb constitutive model was a good ap-proximation 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 stress-es, 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

5

static moduli were estimated for the 10-1

– 100 shear strain range, based on Gmáx (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 ES = soil Young’s modulus in MPa, oct is the octahedral stress, and k0 are the soil vol-umetric 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 as-sumes the medium and minimum principal stresses are equal, and uses Jaky’s formula to esti-mate k0.

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. __________________________________________________________________________________________________________

*Es k0 Constitutive Material (kg/m

3) ( ° ) (MPa) Model

__________________________________________________________________________________________________________

Stratum I 1910 38 56 0.38 Mohr-Coulomb Stratum II 2070 40 114 0.36 Mohr-Coulomb Rock base 2120 - 4272 - 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 engineer-ing judgment along with local experience with the soils available in the project area. It was con-sidered 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 as-sumed 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 with-out 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 materi-al groups. Table 2. Strength and elastic backfill material properties for numerical static analyses. __________________________________________________________________________________________________________

Backfill Material Material *Es E0 k0 Constitutive group (kg/m

3) () (MPa) (MPa) Model

__________________________________________________________________________________________________________

Rom Pad F1 1910 - 130 35 - 0.45 Linear Elastic Final fill F1 1910 36 130 35 0.41 0.45 Mohr-Coulomb Unreinforced MSE wall F2 1910 38 200 60 0.38 0.50 Mohr-Coulomb Structural fill F2 1910 38 257 60 0.38 0.50 Mohr-Coulomb __________________________________________________________________________________________________________

* Values at center of strata

6

(2)

where E0 is the minimum Young’s modulus related to the minimum expected octahedral stress, 0, is the exponent shown in Table 2.

3.3 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 mod-eled 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 maxi-mum 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 con-sidering 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 prop-erties 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 fol-lows: 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.

7

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 tetra-hedral-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 com-pared 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).

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)

8

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 ob-served from Figure 12 that results are very similar for both cases, showing differences well be-low 10 %. Settlements computed using NMD (ZNMD) 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 particu-lar 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 pre-sented herein since they are out of the scope of this paper.

(a) (b)

Figure 11. (a) Normalized geostatic vertical stress with and without NMD, (b) numerical versus analytical geostatic stresses.

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Dep

th (m

)

NMD/V

Vertical stress

Stratum II

Stratum I

Foundation depth

Rock stratum

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

0.00E+00 2.00E+05 4.00E+05 6.00E+05 8.00E+05

Dep

th (m

)

V (Pa)

Analytical, vertical stress

FLAC3D vertical stress (without NMD)

Stratum II

Stratum I

Foundation depth

Rock stratum

Foundation depth

Rock stratum

9

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 ac-counted 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 de-pendent 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-

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

45.00

0.00 0.20 0.40 0.60 0.80 1.00 1.20

Dep

th (m

)

ZNMD/Z

Settlements under foundation center

Stratum I

Stratum II

Foundation depth

Rock stratum

10

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 three-dimensional 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 dimen-sion, 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 0.0007 - 0.001 radians. This rotation is considered adequate for the crusher station when compared to similar projects were the max-imum foundation rotation is set to 0.003 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 max-imum settlements developed under the mat foundation are larger on one side of the mat, thus re-vealing 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 un-der 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.

11

Figure 15. Settlement distribution on Strata I and II over cross section B.

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 con-ditions which include regular problem geometry and ideal soil behavior. The methodology pro-posed 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 dur-ing the construction stage. The details of the methodology used for sub-grade moduli computa-tion 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 cen-troid of the element, zz, and the average vertical displacement of the nodes of the element face in contact with the foundation, Uz. 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 func-tion developed can be invoked at any other stage to obtain the associated sub-grade modulus distribution.

MSE wall

MSE wall

Rom

Pad

12

Results are shown in Figure 18, where a sub-grade modulus distribution is depicted. The val-ues 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/m3, while much higher values are seen around the edges, as ex-

pected. 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 anal-yses for the crusher station building, to account for the foundation soil in the structural models.

Figure 17. Criterion used for computing sub-grade modulus under the mat foundation.

Figure 18. Sub-grade modulus distribution under mat foundation.

6 FINAL REMARKS

A detailed three-dimensional geometry was set up in a FLAC3D

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.

Normal

vector

Uz1zz

(centroid)

23

1

Uz2Uz3

Uz

Uz = (Uz1 + Uz2 + Uz3)/3

K = zz/Uz

MS

E w

all

Rom Pad

MS

E w

all

13

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 0.0007 - 0.001 radians. These values are consid-ered adequate when compared to similar projects in Northern Chile, which are currently operat-ing.

The settlement distribution under the mat foundation was used to compute a sub-grade modu-lus distribution for the soil-mat system. This was accomplished through a FISH function devel-oped 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 displace-ment 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 sub-grade 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. 2012. State of the practice of MSE wall design for high-way structures; Proceedings of the Geocongress 2012, state of the art and practice in geotechnical en-gineering, Oakland, March 25-29. ASCE.

Canteros C.G. & Clemente J.L.M. 2011. Settlement behavior of new primary crusher foundation; Pro-ceedings of the Geo-Frontiers Congress 2011, Advances in geotechnical Engineering, Dallas, March 13-16. ASCE.

Ishihara, K. 1996. Soil behavior in earthquake geotechnics. New York: Oxford University Press. Itasca Consulting Group, Inc. 2009. FLAC

3D – Fast Lagrangian Analysis of Continua in 3 Dimensions,

Ver. 4.0. Minneapolis: Itasca.

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