Open Pit Design Analysis

Introduction

Forge Aggregates have had a design submitted by Andrews Surface-Design LTD for one of their open pit operations in the UK. West Country Minerals have been asked to provide a design check report as an independent third party. This report aims to analyse the critical slope design in the north face of the proposed workings. The design details of the pit will be 75m deep with 15m vertical bench intervals. Bench widths will be 10m standard with 20m for haulage roads.

All benches are affected by multiple bedding planes dipping to the South. The design is also impacted by steep dipping discontinuities striking sub-parallel to the slope face, however information provided has shown this is limited to only one slope. The area has moderate rainfall with limited seismicity. This report will outline the analysis for the stability of the entire slope. The stability of individual benches will also be analysed using plane failure analysis. The software used will be discussed further in the report.

Andrews Surface-Design LTD have provided geotechnical data for the structural mapping of discontinuities in the pit, the table below shows the bedding plane data. They have emphasised possible planar failure along the North face. The table below shows laboratory test data on the siltstone rock mass. For the report piezometric levels are assumed to be 3 on the Hoek & bray piezometric cross sectional table.

UCS (σc) GSI Hoek & Brown, mi

Disturbance factor, D

Unit weight of rock, ϒr

60 MPa 55 7 1 25 kN/m3

Table 1: Rock mass properties provided by laboratory testing by Andrews Surface-Design LTD

Orientation Bedding friction angle, ɸ Bedding cohesion, cDip 35° towards 180° 32° 40 kN/m2

Table 2: Bedding plane analysis provided by Andrews Surface-Design LTD

The recommended factors of safety for the whole slope, and individual benches have been provided by Forge Aggregates and are outlined in the report. The data calculated in RocLab and RocPlane will be used to compare with recommended FOS values in order to evaluate the suitability of the slope design. The variable factor of safety between benches is down to the effect of the piezometric surface, seismicity, tension crack size and the location of the haulage road with the effect of truck weight.

Design Considerations – Kinematic Analysis This section utilises the data provided in tables 1 and 2 combined with RocScience (Dips) analytical software. Kinematic analysis focuses on planar, wedge and toppling failure. All stereograms are presented in Appendix A.

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West Country Minerals

A. Planar FailureStereogram 1 (Appendix A) shows the analysis for planar failure using DIPSv6 software. The software confirms the potential for planar failure. The region of failure is highlighted red on the stereonet, this region sits outside the friction cone but within the daylight envelope. The criteria for instability are as follows:

- Slope dip exceeds dip of potential failure planes- Potential slip plane is within the daylight envelope- The potential slip plane dip exceeds the angle of friction- The dip direction of the sliding plane lies within +/- 20 degrees of the slope dip

direction.

Analysis shows that there are 43 of 150 critical bedding planes within the zone of instability resulting in a 28.67% chance of failure. All bedding planes are marked as one meter with dip direction to the South. The limits of +/- 20 degrees for the sliding plane is set in kinematic analysis.

B. Toppling FailureRock geometry governs the likelihood for direct toppling. The other form of toppling, flexural is the result of a function of slope angle, friction angle and the dip of discontinuities. Comparative analysis of stereograms 2 and 3 (Appendix A) demonstrate a greater potential for direct toppling (6.05%) as opposed to flexural toppling (5.3%). Notably, stereogram 3 shows that intersecting joint sets (Joint set 2) dipping south east and bedding planes dipping south would be the cause of this failure mode occurring.

C. Wedge FailureStereogram 4 (Appendix A) represents the kinematic analysis carried out with respect to wedge failure potential. It is clear that within the friction cone, located at the centre of the stereogram, there is a high concentration of bedding planes that spread as far as into the zone of pit slope (yellow area). From DIPSv6, the likelihood of wedge failure is very high, 37.64%.

From the analyses performed above, it may be deducted that wedge and planar failure modes may occur. Toppling failure is predicted to be the lowest of all examined above. It must be mentioned, that DIPSv6 does not account for groundwater conditions and may produce averaged data, yet it is a good tool to indicate potential failure mechanisms.

Design considerations – Whole slope analysis (RocPlane)In this section of the report, both whole slope angle and factor of safety for the whole slope is determined through circular failure analysis. RocLab and Slide software are manipulated to perform the latter. Notably, disturbance factor was chosen as 1.0 due to the blast damage of the slope.

A. Overall slope angleTo determine overall slope angle, simple manipulation of data was required in Slide software. More specifically, the toe of the slope was given the basic coordinates of (0, 0) and the crest of the slope was calculated to (77.3, 75.0) using known vertical bench heights and bench widths. From this, simple trigonometry has been applied, the overall slope angle is determined as following:

Equation 1: tan (∅ )=Opposite(O)Adjacent (A )

where O = 75m and A = 77.3m

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Equation 2: (∅ )=tan−1( 7577.3 )=44 .13 °

B. Circular failure analysisCohesion (c) and angle of friction (°) values are not provided and therefore RocLab software is used to determine these (Appendix B shows the Mohr-Coulomb fit). The subsequent results are c = 0.432 MPa and friction angle, phi = 34.28°.

Further, Slide software was used to represent the cross section of a 75 m Northern slope face in which the worst case scenario of piezometric surface is shown (Figure 1).

Importantly, Hoek and Bray charts were examined in order to estimate the factor of safety (FOS or F). Three charts of five were considered applicable for the given conditions. The worked example below (Figure 2) for the analysis utilises Hoek and Bray Chart 3. Table 3 provides the values of factor of safety for Charts 2 and 4.

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Figure 1: Cross section showing piezometric surface of the 75 m slope face looking towards West with added length, width and height annotations

Figure 2: Chart 3 manipulated to determine F as part of circular failure

cyHF

To determine F: c

Y × H× tan∅ where

C = 0.432 MPa Phi = 34.28⁰ H = 75mY = 25 KN/m3 = 0.025 MN/m3 (rearranged to keep the units same in the equation)

Therefore: 0.432

0.025×75× tan(34.28)=0.338

0.338 is located on the circumference of the chart 3.

Vertical line drawn from the edge of the chart to intercept x axis. Values read: x axis = 0.102 y axis = 0.320

Therefore:

cyHF

Rearranged: c

YH 0.102=F

Therefore: F= 0.4320.025×75×0.102

=2.26

AB

CD

Table 3: Results for the analysis of Hoek and Bray charts 2 & 4.

Overall circular slope failure at the top is not predicted based on the results obtained from circular failure analysis. The factor of safety is much higher than 1 in all three charts examined and also higher than the recommended F=1.6 as set by Forge Aggregates. For the purposes of accuracy an average of the three charts has been taken in order to gain a FOS of 2.22. Chart 3 is considered the best suited for the conditions of the slope. With both the preferred chart result and the average result it can be seen that for the current conditions circular failure is unlikely to occur for the North slope. A further analysis using Slides data interpretation tool can be seen in Appendix D, the result of the simulation concurs with the Hoek and Bray charts as the computer model predicts a FOS of 2.478. It must be noted that over time, conditions can change and will affect the FOS. Data for seismicity and piezometric levels should be recorded regularly in order to simulate whole slope FOS every 3 years.

C. Bench stability analysisThe diagram shown in Figure 1 highlights 5 benches. However Forge Aggregates have specified that stability analysis should be done for 4 benches known as A, B, C and D. Bench B is the haul road bench with bench A being adjacent below and C adjacent above, bench D is the top bench. Therefore there is no analysis for the bench at the base of the pit.

RocPlane software calculates a FOS by utilising input parameters of rock geometry, strength and the forces acting upon the rock. The forces include the water pressure, truck pressure and seismicity. Each bench has a target FOS set by Forge Aggregates with bench B and C having a factor of safety of 1.6. This is because of the haul road location on B and the slope adjacent to the haul road on C. A and D have FOS set at 1.3. The inputs for calculation are outlined in Appendix C. The calculation force of the truck is noted below. Its assumed at worst case scenario that for a bench width of 20m with a tension crack 10 m from the edge only one full truck will be affecting the potential for failure. This is because even in worst case only one full truck will be driving on the haul road of that bench at one time, despite the empty truck coming the other way, it will be the other side of the tension crack therefore not affecting failure.

Force of truck=( mass×gTruck length )

1000=0.268MN /m

Mass = 300t

Gravity (g) = 9.81

Truck length = 11m

A number of case scenarios were run in the software with variances for seismicity and bolt strength simulated. Outlined on page 5 are a series of 5 cases for bench A. 3 scenarios were specified by Forge Aggregates whilst the extra cases are a result of further analyses deemed necessary by West Country Minerals. The remaining cases are found in Appendix D with the 2D views for examples in Appendix E. Each bench has 5 cases.

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Chart C (MPa) Unit Weight, Y (MN/m3)

H (m) Friction angle, phi (⁰)

c/YH tan(Ө)

Tan (Ө)/F y axis

c/YHF) x axis

F

2 0.432 0.025 75 34.28 0.338 0.28 0.10 2.34 0.432 0.025 75 34.28 0.338 0.32 0.11 2.1

Table 4: Results of cases for bench A, using RocPlane analysis

The simulated analysis shows for bench A that no support would not only fail to meet the target factor of safety but produce a FOS<1. Therefore under standard conditions bench A is very likely to have slope failure. The effect of adding the bolt to stabilise the slope increases the FOS above 1 but a higher tension of 400 KN/m is required in order to reach target FOS. If seismicity is simulated for the bench at a coefficient of 0.05 then a further increase in bolt tension will be required. The simulation shows 500 KN/m bolt tension is sufficient in this scenario with a FOS of 1.38.

D. Influence of SeismicityThe influence of ground vibrational waves on the rock mass is shown to decrease the FOS for the slope. This is because seismic waves disturb the rock mass and encourage movement of blocky material and can induce planar failure. For the worst case scenarios a coefficient of 0.075 has been used. In the location of the design there is limited seismicity. Appendix E shows for cases with no water pressure of truck weight (Bench D) that seismicity has impact on the FOS however it is easily counted by the tension bolts.

E. Influence of Truck WeightThe force of the truck has been calculated in this section subsection C. As discussed the possibilities of two trucks passing fully loaded on one side of the tension crack is impossible due to their dimensions. Therefore it is safe to assume that the worst case scenario of force is one fully loaded truck at 300t. The truck force does impact FOS case 7B and 8B show that the addition of the truck in the same conditions lowers FOS by 0.08. Therefore when a truck force is added additional support may be necessary.

F. Influence of Tension CrackThe tension crack for the benches is able to lie anywhere between 0-10m along the top of the bench. However this study has averaged the position to the middle of the bench at 5m and 10m for the haul road. The position of the tension crack has little influence, a difference of 5m in case 6B and 7B shows a FOS difference of 0.03. Therefore further study is not required.

G. D. Influence of Tension Bolt The addition of the tension bolt is shown to improve factor of safety (See Appendix E and Table 4). This is because the Position and angle of the bolt provide a force opposing the planar or block movement in the slope. The higher the tension in the bolt the more force applied and therefore the less likely the chance of failure resulting in a higher FOS. All bolts modelled are 10m in length.

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Case Bench b (tension crack)

Trucks (yes(y)/No(n))

Zw/Z α (seismicity) T (bolt tension)

Target FOS

FOS

1 A 5 n 0.75 0 0 1.3 0.972 A 5 n 0.75 0 200 1.3 1.173 A 5 n 0.75 0 400 1.3 1.424 A 5 n 0.75 0.05 400 1.3 1.265 A 5 n 0.75 0.05 500 1.3 1.38

Discussion and ConclusionThe analysis conducted by West Country Minerals has aimed to provide comments and amendments for the slope design submitted to Forge Aggregates by Andrews Surface-Design LTD. The recommendations above fulfil this aim. It should be noted that all analysis conducted in this report is not without limitation and judgement.

The analysis of kinematic failure mechanisms using Dips software is limited to averaging data and not highlighting individual events sufficiently. There also a need to account for impact of water pressure and persistence that is not met by the software or stereograms in general.

The analysis through Hoek-Bray charts for whole slope failure relies heavily on engineering judgement for the chart selection. Then there is risk of human error when calculating FOS this way, but through data simulation analysis a comparison has been made and shown that the charts are within a 10% value of FOS compared with the simulation. The truck weight is assumed and therefore the force of the truck calculated is an assumption.

Further analysis should be taken into account through a sensitivity analysis for truck weight changes. This report however focused on worst case scenario which is applicable for FOS calculations. The final limitation to highlight is the positioning of the tension bolt in the RocPlane software. This is engineering judgement and may vary between cases resulting in changes (likely minute) to the FOS value.

A summary of the key findings:

- Planar and wedge failure are the dominant failure mechanisms that are likely to occur with smaller risk of toppling.

- The orientation and dip of the slope are critical, Likely changes may impact stability.- The entire slope stability is sufficient and is unlikely to fail at an average FOS of 2.22.- A change in slope angle will impact the FOS, further sensitivity analysis is required if

design changes are made to slope angle.- Truck weight and seismicity show strong impact on FOS. - Addition of tension bolts have the greatest impact on FOS.

Recommendations Bench A will require 500 KN/m tension bolts at 15 degrees angle and 10m length

spaced evenly to account for any changes to seismic coefficient. Bench B will require 600 KN/m tension bolts with the same parameters of A to ensure

sufficient protection against failure from truck force and seismic combination. Bench C will require 400 KN/m tension bolts spaced evenly at proposed angle and

length to ensure protection against failure for potential seismic changes. Bench D will require 200 KN/m tension bolts along the bench in order to protect

against failure mechanisms onset by seismicity.

For the whole slope it is recommended that a hydrogeological assessment take place in order to better quantify the piezometric levels. Drainage of the water will reduce water pressure and increase the rock mass shear strength. The likelihood is an increase in whole slope FOS and individual bench FOS. Further study should be made in order to correctly establish these details. Furthermore as touched on earlier in the report, regular recording of seismicity and ground water level should be taken in order to establish accurate simulation models produced in slice.

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Appendix A – Dips Analysis

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Stereogram 1: planar failure projection

Stereogram 4: wedge failure projection

Stereogram 3: flexural toppling failure projection

Stereogram 2: Direct toppling failure projection

Appendix B – RocLab Analysis

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Appendix C – Input Parameters for Bench Stability Analysis

Input Symbol Mean ValueUnit weight of rock (kN/m3) r 25

Unit weight of water (kN/m3) w 10Bench Height (m) H 15

Crest to tension crack (m) b 5

Bench Face angle (deg) φf 70

Dip of failure plane (deg) φp 35

Bolt inclin. from horiz(deg) β 15Bolt Tension (kN/m) T 0

Failure plane cohesion(kPa) c 40Failure plane friction (deg) ϕ 32

Water level ratio zw/z 0.75Earthquake coefficient α 0

Appendix D – Slide Analysis

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Figure 3: Slide interpretation

Appendix E – Case simulations for RocPlane Analysis (tables)

Case Bench b (tension crack)

Trucks (yes(y)/No(n))

Zw/Z α (seismicity) T (bolt tension)

Target FOS

FOS

1 A 5 n 0.75 0 0 1.3 0.972 A 5 n 0.75 0 200 1.3 1.173 A 5 n 0.75 0 400 1.3 1.424 A 5 n 0.75 0.05 400 1.3 1.265 A 5 n 0.75 0.05 500 1.3 1.386 B 5 n 0.50 0 400 1.6 1.657 B 10 n 0.50 0 400 1.6 1.688 B 10 y 0.50 0 400 1.6 1.609 B 10 y 0.50 0.05 400 1.6 1.3810 B 10 y 0.50 0.05 600 1.6 1.6211 C 5 n 0.25 0 300 1.6 1.6712 C 5 n 0.25 0 400 1.6 1.8513 C 5 n 0.25 0.05 400 1.6 1.6614 C 5 n 0.25 0.05 300 1.6 1.4915 C 5 n 0.25 0.075 600 1.6 1.8516 D 5 n 0.00 0 0 1.3 1.3517 D 5 n 0.00 0 200 1.3 1.6118 D 5 n 0.00 0.05 0 1.3 1.2319 D 5 n 0.00 0.05 200 1.3 1.4620 D 5 n 0.00 0.075 200 1.3 1.39

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Appendix F – Example case simulations for RocPlane

Analysis (2D View)

Figure 4: Case 2A 2D RocPlane View

Figure 5: Case 8B 2D RocPlane View

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Figure 6: Case 12C 2D RocPlane View

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Figure 7: Case 16D 2D RocPlane View

Appendix F – SWedge

Figure 8: Example of SWedge software with FOS for design. Unused with no analysis.

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