Influence of backfill on coal pillar strength and floor bearing capacity in weak floor conditions in the Illinois Basin

International Journal of Rock Mechanics & Mining Sciences 76 (2015) 55–67

Contents lists available at ScienceDirect

International Journal of Rock Mechanics & Mining Sciences journal homepage: www.elsevier.com/locate/ijrmms

Influence of backfill on coal pillar strength and floor bearing capacity in weak floor conditions in the Illinois Basin T. Kostecki n, A.J.S. Spearing Southern Illinois University, Carbondale, IL, USA

art ic l e i nf o

a b s t r a c t

Article history: Received 6 April 2014 Received in revised form 22 November 2014 Accepted 28 November 2014 Available online 18 March 2015

This paper discusses the current theoretical design equations associated with foundation design in the Illinois Basin, as well as the benefits of utilizing high density backfill in a numerical model, to improve pillar and floor stability. Based upon the results, Vesic’s bearing capacity solution for a two layered soil tends to underestimate the true bearing capacity of a foundation, especially at higher friction angles and when footings are placed in close proximity. Minimizing the distance between adjacent foundations has shown an improvement in the ultimate bearing capacity of a foundation; however, placing the foundations in too close proximity has shown the foundations may behave as a single foundation and undergo appreciable settlement. A 10–40% increase in pillar strength and ultimate bearing capacity can be expected when a cohesive fill is used between 25 and 75% fill of the mined height, respectively. The non-cohesive nature of the simulated backfill showed little influence on increased pillar strength, even at higher fill ratios. It was determined, that as the shearing resistance, tensile strength and stiffness of the backfill are reduced, increases in coal pillar strength is due more to the confinement aspect of an underground mine rather than the strength properties of the material itself. A methodology for analyzing the plastic flow characteristics of a coal pillar and a footing using FLAC3D has also been presented herein. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Coal Room and pillar Backfill Fireclay Underclay

1. Introduction This paper directly relates to the numerical investigation of an immediate weak floor, a coal pillar and the support consisting of backfill represented as a confining material. In particular, this study will focus on the Illinois Basin which consists of Illinois, Indiana and Western Kentucky. The Illinois Basin is major coal producer in the U.S. where nearly one hundred thousand short tons of underground coal were produced in 2013 [1]. This research was conducted mainly because of the ever-restrictive legislation posed on coal mines in the United States by the Environmental Protection Agency (EPA). More specifically, the EPA have proposed new legislation which is predicted to increase the conventional surface disposal cost for coal mines in the future [2]. Additionally, public opposition to surface waste disposal hinders the ability to obtain surface disposal permits in a timely fashion. Surface disposal is the primary means of coal waste disposal in the United States, therefore the most practical, but not yet cost effective option for the future, will probably be underground disposal of

n

Corresponding author. E-mail address: [email protected] (T. Kostecki).

http://dx.doi.org/10.1016/j.ijrmms.2014.11.011 1365-1609/& 2015 Elsevier Ltd. All rights reserved.

waste as the form of high density (paste) backfill [3]. In this case, coal waste can constitute either washing plant tailings or combustion by-products such as fly or bottom ash. Currently use of high density backfill is not a routine operation for underground coal mines in the U.S. but has been used quite regularly in longwall coal mines in Germany and Poland for several decades [3]. Further, this paper considers backfill disposal in underground coal mines located primarily in the Illinois Basin of the United States. Total mineable reserves for the Illinois Basin are estimated at nearly 14.4 billion tons [4]. More importantly, the majority of underground coal mines in the major mineable coal seams in the Illinois Basin are associated with a weak immediate floor termed underclay, fireclay or clay-stone which is very friable and variable in nature. Generally underclay has been studied and analyzed from the basis of soil mechanics because of its behavior to that of a clayey soil. Most importantly, underclay can cause serious instability issues in the short-term including pillar punching, loss of entry, pillar sloughing and roof problems and subsidence in the longterm [5]. This issue is typically mitigated via oversized pillars, which significantly results in reduced extraction in room and pillar mines. Since no theoretical methods exist, to the authors’ knowledge, regarding the design of such a scenario concerning the pillar, backfill

56

T. Kostecki, A.J.S. Spearing / International Journal of Rock Mechanics & Mining Sciences 76 (2015) 55–67

and immediate floor interaction, and deriving such a relationship would be impractical or rigorous at best; a heuristic approach with numerical modeling was deemed most appropriate to observe this problem. This paper will discuss the shortcomings of current and theoretical design equations associated with foundation design in the Illinois Basin and the potential benefits of utilizing backfill as a confining agent to coal pillars in a numerical model. The results are presented in a pragmatic and useable manner for future design.

qf loor ¼ cNC sc

2. Theoretical background Classical foundations engineering credo is concerned with the satisfaction of two criteria: designing against shear failure in the soil and minimizing excessive displacements or settlement of the foundation. Shear failure is associated with the term of ultimate bearing capacity, which is the load per unit area of a foundation at which shear failure in the soil occurs [6]. Foundation design as a whole has been largely geared and implemented more in civil engineering practice than any of the other engineering sciences, and for good reason. However, situations arise in underground mining where the classical foundations principles and those same theoretical relationships are necessary for the design of underground foundations. This situation occurs in the Illinois Basin, where underground coal mines in the major mineable coal seams (i.e. Herrin, Danville and Springfield Seams) are underlain by a weak immediate fireclay floor. To date, limited research has been conducted regarding the influence of the weak immediate floor in Illinois Basin Mines. This is surprising considering the influence weak floor has on pillar stability. The most recent work was presented by Gadde [5] in 2009, where he provided a comprehensive study of the underclay floor in the Illinois basin. Within his study he developed the Vesic– Gadde equation for use in design of Illinois Basin Mines and presented the most detailed, and practically useful, numerical modeling to date. The difference between this body of work and Gadde’s work is that no research regarding backfill and its influence to pillar and floor strength was conducted. Multiple other researchers presented studies [7–14], but the majority of work all occurred prior to 1991. Although all of these studies collectively contain the majority of field and theoretical studies, Gadde’s work in 2009 takes advantage of the advances in numerical modeling that have occurred since the earlier research. Gadde’s work is therefore referenced multiple times throughout this paper and often compared. This is primarily for calibration purposes within the numerical modeling itself, as well as to present a second look at how results of similar models may differ when different users try to simulate the same problem. 2.1. Prandtl’s semi-infinite homogenous bearing capacity approximation Of the numerous theoretical approximations for foundation design, one of the earliest approximations is the Prandtl’s approximation for a continuous foundation resting on a weightless semiinfinite homogenous soil. This can be expressed by: qc
strip ¼ cN C

of the bearing capacity of as little as 10% and, for example, the inclination factors play little role in the bearing capacity as most coal seams in the U.S. are relatively flat lying. In contrast to Prandtl’s approximation for a strip footing shown in Eq. (1), underground foundations are generally square or rectangular and a more applicable design equation is the shape-corrected Prandtl solution shown in Eq. (2). The approximation for the bearing capacity of a footing with length and width resting on a semi-infinite soil can be approximated as:

ð1Þ

where c is the soil cohesion and Nc is the normalized bearing capacity factor for cohesion which is based on the effective friction angle of the soil. As stated by Gadde [5], these factors, excluding the shape correction factor for cohesion (sc), are either negligible for a real coal mine scenario, in the Illinois Basin, or are often difficult to obtain, and are often times not considered in calculations. This is because these factors only cause an under-estimation

ð2Þ

where sc represents the shape-correction factor dependent on the footing dimensions, Nq and Nc. 2.2. Vesic’s non-homogenous bearing capacity approximation One of the disadvantages of Prandtl’s solution is that actual mining pillar foundations are not semi-infinite and homogenous in extent. There exists some non-homogeneity of the floor underlying a coal pillar (i.e. multiple layers). Vesic’s [15] approximation for a non-homogenous soil is therefore more appropriate for design purposes, and is expressed by: qf loor ¼ c1 N m

ð3Þ

For the most part, Vesic’s approximation has been the most popular methodology for pillar design in the Illinois Basin for years and is used as the method for governing approval purposes. This may not be the best approach; bearing in mind this approximation is only valid when [5]: no adjacent footings/pillars exist, angle of internal friction of both layers is zero, does not consider c-phi soils (cohesive and frictional soils), both soil layers are homogenous, does not consider different aspect ratios of the footing (square, rectangular and strip), does not consider two layered soils, is only valid for failure criteria of the Mohr–Coulomb model and when no volume change/dilation occurs in the post-failure state. 2.3. Effect of adjacent footings The majority of fundamental theoretical approximations for bearing capacity don’t consider the influence of an adjacent footing on the calculated bearing capacity. This has been widely researched in foundations engineering with the pioneering research being conducted by Stuart [16]. Within his study he considered two continuous rough footings within close proximity on granular soils. He determined that a reduction in spacing of adjacent footings may not only increase the ultimate bearing capacity of the footing but can also negatively cause an increase to the settlement in that region, if spaced too closely together. He further defined an interference coefficient that showed an increase at close spacing and a decrease with increasing distance. Multiple other studies formed similar conclusions [17–24]. 2.4. Gadde’s research To better represent a realistic coal mine scenario, Gadde [5] developed an adaption to Vesic’s approximation, known as the Vesic–Gadde approximation. Gadde’s work is fairly new to the industry; but it is gaining popularity as it is geared for foundation and pillar design where a weak immediate floor is present, and was developed based off numerous field studies conducted in the Illinois Basin. Ultimately, Gadde’s work found that the Vesic–Gadde approximation was a much better predictor for floor bearing capacity conditions in the Illinois Basin than any of the de facto approximations, including Vesic’s. The Vesic–Gadde solution is expressed in the similar form as Eq. (3); however, the cohesion of the immediate and

T. Kostecki, A.J.S. Spearing / International Journal of Rock Mechanics & Mining Sciences 76 (2015) 55–67

main floor is approximated by its moisture contents in separate equations. Generally, a floor safety factor is approximated by a traditional strength–stress ratio shown below: qf loor FSF ¼ σp

ð4Þ

where qfloor is the load bearing capacity of the floor, found from Eq. (5), and σp is the vertical stress on a pillar, approximated by traditional tributary area theory. The load bearing capacity can be determined by multiplying the cohesion of the immediate floor (c1) by a normalized bearing capacity factor (Nm) found from Eq. (6): qf loor ¼ c1 N m

ð5Þ

i
h 2 KN nC N nC þ β
1 ðK þ 1ÞN nC þ ð1 þKβÞN nC þ β
1      N m ¼ 
K ðK þ 1ÞN nC þ K þβ
1 ðN nC þβ N nC þβ
1
ðKNnC þβ
1ÞðN nC þ 1Þ

ð6Þ where β is a unit-less punching index given by, B the width, L the length of the coal pillar, and H the height of the immediate floor: β¼

BL ½2ðB þ LÞH

ð7Þ

N nc ¼ sc N c

ð8Þ

The parameter Nnc is a bearing capacity factor related to the bearing capacity factor for homogeneous semi-infinite soil (Nc) given by Eq. (13) and a shape correction factor (sc) given by Eq. (12). The parameter K is the ratio of the undrained shear strength of the stronger main floor (c2) given by Eq. (10) and to the weaker immediate floor (c1) given by Eq. (11). Eqs. (10) and (11) are for Eastern Shelf coal mines in the Illinois Basin. Separate equations, given by Gadde (5) are presented for Western Shelf coal mines. The friction angle of the immediate floor is defined by (φ) in the following equations and the moisture content of the immediate floor is defined as MCif and the moisture content of the main floor is defined as MCmf: K¼

c2 c1

c2 ¼

8931eð
0:368MC mf Þ 2

ð9Þ

4164eð
0:2MC if Þ N c sc

  B Nq sc ¼ 1 þ L NC c1 ¼

N C ¼ cot ϕ½N q
1 N q ¼ eπ

tan ϕ

 tan 2

ð10Þ

57

3. Model set-up 3.1. Methodology The popular numerical modeling package of FLAC3D 5.0 was utilized throughout the following body of work. Since this problem is representative of a three part system – pillar, floor and backfill – it is obvious that trying to model, and interpret and analyze the response of the system as a whole by using an “all at once” approach is very difficult and impractical. Therefore a “one-factorat-a-time” approach was adopted initially until each particular factors effect on the models response was apparent and understood. Thereafter multiple factors were varied at a time in order to analyze their interaction effect on the models response. All of the modeling was conducted qualitatively and presented in a normalized fashion. By normalizing the results, it is not necessary to present the total stress of the pillar or the floor. Instead, if a ratio of a modeled to theoretical value is determined, the actual stress capacity of the pillar, floor or both can be determined by multiplying a calculated theoretical value to the modeled value within this paper. This will give a value of stress in terms of bearing capacity or pillar capacity. Once the total stress, in terms of the bearing and pillar capacity is known, the lower of the two capacities will represent the governing component of failure of the system as a whole (i.e. pillar or floor).

3.2. Grid generation The coordinate system is represented by the x- and y-axes in the horizontal plane and the z-axis in the vertical plane, shown in Fig. 1. The footing is square and was modeled as half the width in both the x and y directions. For this example an arbitrary footing dimension of 1 ft was chosen (i.e. 6 in. (B) in the model). The advantage of quarter symmetry was also exploited in the problem. Therefore Fig. 1 is, in essence, an infinite array of footings and rooms where the influence of an adjacent footing is negligible. The origin of the model is located at the center of the footing at the intersection point of planes x, y and z. The model extents were five times the footing width, from the edge of the footing, in all directions. This is to assure

ð11Þ ð12Þ ð13Þ

ϕ 451 þ 2

ð14Þ

In summary, populated approximations are used for estimating the bearing capacity of a soil, based on sometimes unrealistic assumptions, and are often not suitable for the design of underground pillar foundations. Vesic’s approximation for floor bearing capacity is widely accepted as the popular choice for floor design in the Illinois Basin. It has been found that the adaptive Vesic– Gadde approximation is much more appropriate for floor design but has yet to gain the attention it deserves. The theoretical approximation by Vesic is currently the most popular means for design, probably because of its robust and rapid calculation scheme; however the limitations of the approximation itself make it an ersatz to more up-to-date approaches, such as routine numerical models.

Fig. 1. Generated mesh density for calibration study showing the simulated footing (B) as well as distance to boundary (5B).

58

T. Kostecki, A.J.S. Spearing / International Journal of Rock Mechanics & Mining Sciences 76 (2015) 55–67

no interaction effect of model boundaries and adjacent footings for the initial model.

3.3. Meshing scheme and loading rate The mesh density adopted is also shown in Fig. 1. Adopting a mesh density, along with an appropriate loading rate, plays a critical role in the calibration results, especially when attempting to model quasi-static loading conditions of a coal mine pillar and footing. For this particular problem the loading options considered were either stress controlled or strain controlled. As recommended in [25a,b], it is easier to control the test and obtain a good load versus displacement graph when a strain-controlled load is used. Further, it can become difficult to control the model as the applied load reaches the collapse load. Therefore a displacement rate of 1.0E
5 in./step was selected. This loading rate was selected because it produced theoretical results within a reasonable tolerance. Selecting a slower loading rate made the model run times too lengthy and did not improve the accuracy of the results. The loading occurred essentially by a platen in the region outlined as the footing, represented by 0.5B, in Fig. 1. The footings were loaded until the limit load was reached, meaning until the maximum load on the footing occurred. This was observed via a load–displacement curve generated by a FISH function. From there the average footing pressure at failure could be observed. More loosely stated, the FISH function was designed to calculate the Nc factor of Eqs. (1) and (2) or the Nm factor of Eq. (3), depending on the scenario which was modeled (i.e. semiinfinite or finite immediate floor scenario). FISH is a language used within FLAC3D mainly to implement user defined functions and variables beyond the traditional code in FLAC3D. A uniform mesh was adopted and each zone was assigned a 1  1  1 dimension in the x, y and z directions, respectively. This uniform mesh prevented abrupt jumps in zone sizes or ‘long, thin zones’ which could be developed in a graded meshing scheme, especially around the furthest-most boundaries of the model. Additionally, this simplified the model for later studies, which involved implementation of backfill around a pillar. To check the validity of the meshing scheme, mainly to ensure that the results of the model were not affected significantly by a finer meshing scheme, the model was run with an increased zone density. The zones were arbitrarily increased in all directions and the limit load was observed in each case. The results are shown in Table 1, where a 2% difference in footing load was found with a three-fold increase in the number of zones. The limit load was observed next and compared with the theoretical Prandtl shape corrected bearing capacity solution represented by Eq. (2). From Table 1, a 5–7% difference in the results of the models and the theoretical approximation were found. Therefore this loading rate and mesh density were determined as sufficient for the remaining studies because theoretical solutions were produced within a reasonable tolerance and an increased zone density showed little effect on the overall response of the model, as shown in Table 1.

3.4. Boundary conditions The x- and y-boundaries around the entire model were roller boundaries. Therefore displacements and velocities were restricted normal to those planes. The z-boundary plane in the furthest most coordinate direction was pinned, therefore restricting displacements both normal and parallel to the plane. A few test models were generated to determine which boundary conditions were most appropriate. It was observed that the boundaries posed little effect on the calculated bearing capacity except when the room width was small compared to the pillar/footing width. In this case, the smooth boundaries on the x- and y-planes produced more conservative estimates, in comparison to theoretical approximations, therefore they were deemed most appropriate. This will be discussed further in Section 4.1. Next, it was of interest to determine the influence of roughness of the footing base compared to the theoretical approximations. Gadde [5] reported the majority of his modeling as a smooth footing because he showed no significant difference between the rough and smooth footing. In fact, Gadde concluded the boundary conditions between a coal pillar and the floor are normally not known, and based on his results; a smooth footing was a more conservative estimate of the bearing capacity and hence “erred on the safer side” which is always desirable. Previously in 1982, Griffiths analyzed that the roughness of the footing will influence the bearing capacity factor for soil weight (Nγ) more than the bearing capacity factor for cohesion (Nc). As mentioned earlier, in a coal mine situation, the bearing capacity factor Nγ is usually ignored. To confirm this, a simple model was run comparing the rough and smooth footings. A smooth footing is allowed to move freely in the x- and y-directions during loading, whereas for a rough footing, the x- and y-velocities and displacements are restricted. For this scenario the limit load of the footing was observed for both cases and compared to known theoretical solutions and to similar results presented by Gadde [5]. The results are tabulated in Table 2 and shown in Fig. 2. The results are presented in a normalized manner, relative to the theoretical approximations for Vesic’s Nc factor. For this scenario, properties were chosen that represented an underclay floor in the Illinois Basin at 8% moisture content, cohesion of 150 psi and a Poisson’s ratio of 0.35. The shear and bulk modulus and tensile strength were determined, based on the moisture content, from equations derived by Gadde [5] for underclay. The bulk modulus was 17,300 psi, the shear modulus was 5800 psi, and the tensile strength was 63 psi. The model was ran at varying friction angles from 01 to 351 as this range represents the friction angle values encountered in the Illinois Basin for underclay floors.

Table 2 Ratio normalized bearing capacity factor for cohesion (Nc) to theoretical value. Friction angle

Ratio Nc for smooth footing/ theoretical Nc

Ratio Nc for rough footing/ theoretical Nc

Ratio Nc for smooth footing/ theoretical Nc reported by Gadde [5]

Ratio Nc for rough footing/ theoretical Nc reported by Gadde [5]

0 5 10 15 20 25 30 35

1.0 1.1 1.1 1.1 1.2 1.3 1.4 1.5

1.1 1.2 1.2 1.3 1.5 1.6 1.7 1.9

1.0 1.0 1.0 1.0 1.0 1.0 1.0 –

1.0 1.0 1.0 1.0 1.0 1.0 1.0 –

Table 1 Model strength compared to the shape corrected Prandtl strength for increased zone density. Zones

Ratio of model strength to the shape corrected Prandtl Strength

Effect at increased zone density

84,640 156,800 217,800 261,360

1.05 1.06 1.07 1.07

1.00 1.01 1.02 1.02

T. Kostecki, A.J.S. Spearing / International Journal of Rock Mechanics & Mining Sciences 76 (2015) 55–67

59

Table 3 Comparison of the model strength to Gadde’s results and the shape corrected Prandtl strength. Friction angle

Ratio of model strength to shape corrected Prandtl strength

Ratio of model strength to shape corrected Prandtl strength by Gadde [5]

5 10 15 20 25 30 35

1.07 1.10 1.15 1.20 1.28 1.40 1.54

0.96 0.97 1.01 1.06 1.11 1.19 –

Fig. 2. Plot of the ratio of the modeled normalized bearing capacity to the theoretical value for a rough and smooth footing.

Based upon these observations Gadde’s [5] conclusion is validated, which is that smooth footing will represent a more conservative estimate of the bearing capacity. Therefore unless specifically mentioned, the remaining modeling in this study will simulate a smooth footing. 3.5. Material properties and failure criteria Adopting the appropriate material properties and failure criteria is vital to the reliability of results that are obtained. To reiterate, this study focuses on three parts: coal pillar, the pillars weak floor and backfill portion. This represents a broad range of materials that can behave quite differently, particularly in the post-failure states. For instance, from physical testing conducted on coal samples, coal will exhibit either a strain softening or hardening response in the post-failure state [26,27] and therefore may not be best represented by the same failure criteria as a underclay floor which may undergo elastic-plastic behavior. Therefore, the Mohr Coulomb Elastic Plastic behavior was selected for all materials for two reasons. First, in order to adopt a strain softening response in the coal pillar, some known material performance from laboratory tests must first be conducted. This material performance is then calibrated to the zone sizes selected within the model. This limits the capabilities of the model as size dependent properties now exist. In contrast, no calibration to zone sizes is needed and no size dependent properties are employed when utilizing the Mohr–Coulomb criterion, thereby further simplifying the model [28]. Second, because there are no size dependent properties, the results can be reported in a normalized fashion and can be extrapolated to represent much larger dimensional scenarios. 3.6. Shape correction factor Next a footing where the friction angle was simulated at 51 increments from 51 to 351, was compared to Gadde’s [5] work and Prandtl’s theoretical approximate for bearing capacity shown in Eq. (2). The same material properties as discussed previously were used for the analysis. From the results given in Table 3 a generally good match between the theoretical Prandtl’s solution of Eq. (2) and the modeled bearing capacity strength is achieved up to about 151. Contrary to Gadde’s results, it seems the Prandtl solution provides a conservative estimate of the bearing capacity at all friction angles and an ultra-conservative estimation at higher friction angles. The reason could be because of the mesh density, loading rate or properties. Gadde used a much finer and graded meshing scheme, which seems to be the controlling factor at first glance. Otherwise it was deemed that the models produced theoretical solutions within a reasonable tolerance.

Fig. 3. Comparison of modeled bearing capacity factor Nc to theoretical value at varying friction angles with fixed and smooth boundaries and varying Fw/Rw ratios.

4. Results and discussion 4.1. Effect of pillar spacing The effect of footing spacing on the bearing capacity model was studied next, as it was known from past research [16] that the effect of footings and/or pillars in close proximity increases the bearing capacity. Therefore the modeled bearing capacity was compared to the theoretical bearing capacity value. Four footing-to-room width (Fw/Rw) ratios were simulated: 1.5, 2.0, 3.0 and 6.0. These ratios were chosen as they cover the majority of Fw/Rw ratios found in Illinois Basin Coal Mines [5] and because these were the only allowable ratios accommodated using the current grid without adjusting the meshing scheme and/ or footing size. In a similar fashion, the footing was loaded until the limit load of the footing was reached using the aforementioned loading rate. For all the previous models to this point, the boundary conditions (fixed/pinned or smooth/roller) of the furthest most X- and Yplanes had little effect on the bearing capacity of the model because the planes were located far away from the loaded footing. However, when the furthest most X- and Y-planes were located in close proximity, the boundary conditions were observed to have a significant effect on the calculated bearing capacity. Therefore the bearing capacity was not only observed with changing Fw/Rw ratios, but also with smooth and fixed boundary conditions on the X- and Y-planes. Furthermore, the models were observed at friction angles from 0 to 351. The results are shown in Fig. 3 and the following conclusions were drawn. As observed previously, Vesic and Prandtl’s theoretical estimate of the bearing capacity seems to underestimate the true bearing capacity of the footing, especially at higher friction angles. The boundary conditions played an important role in the modeled bearing capacity as well, as very different values were obtained between the fixed and smooth boundaries. In particular,

60

T. Kostecki, A.J.S. Spearing / International Journal of Rock Mechanics & Mining Sciences 76 (2015) 55–67

when the boundaries were fixed at a Fw/Pw ratio equal to 6, the modeled bearing capacity never reached the limit load, even after a million model steps. This seems to suggest that the ultimate bearing capacity was either infinitely strong, or the footings in close proximity were acting equivalently to a single footing and underwent excessive settlement whilst never reaching the limit load. Considering that past research regarding adjacent strip footings on granular soil, in close proximity Stuart [16] observed the latter of the two conclusions. Overall, smooth/roller boundaries represented a more conservative estimate for further modeling. Lastly, an increase of the Fw/Rw ratio played a significant role on the modeled bearing capacity especially at higher friction angles (25–351). For friction angles between 01 and 201 the influence of the adjacent footing definitely plays a significant role but is much less pronounced than at higher friction angles. 4.2. Effect of a finite floor thickness All previous models to this point were run under the conditions of a semi-infinite immediate floor which does not accurately reflect a realistic scenario. Therefore the effect of a finite immediate floor thickness was analyzed. Since this now incorporates a two layered medium below the footing, the modeled bearing capacity factor is now represented by the Nm factor as opposed to Nc factor in all of the previous cases. These factors were explained in Eqs. (3) and (2), respectively. From past research [5] it was determined the following ratios could be found in relation to Illinois Basin Coal Mines; Immediate floor friction angle φ1 and the underlying main floor friction angle φ2 vary between 01 and 351; the cohesion of the main floor c2 and the cohesion of the immediate floor can be well represented by a c2/c1 ratio between 2 and 5; the thickness of the immediate floor (H) in comparison to the footing width (B) can be accurately represented by a B/H ratio of 4 in the minimum case and 40 in the maximum case; the Fw/Rw ratios from the previous models were 1.5 and 6.0 in the extreme cases. Combining these factors, twenty four models were run to determine the effect of each on the simulated bearing capacity of the footing relative to the theoretical estimate by Vesic. Table 4 was generated where only the extreme values of each ratio were run to minimize the total number of models. In conclusion, at higher friction angles of the immediate floor (φ1) and main floor (φ2) (i.e. 351), Vesic’s estimate of the bearing capacity is highly underestimated (13–23 times Vesic’s estimate). As the B/H (width of the footing/height of the immediate floor) ratio increases, and when the immediate floor was simulated at 0 degree friction angle, Vesic’s solutions tends to underestimate the true bearing capacity from 10% to 50%. At higher friction angles (351), and when the footings are in close proximity (Fw/Rw ¼6.0), the limit load was never reached. This is shown by the greater than (4) symbol shown in Table 4. The most likely mechanism occurring seems to be that which was determined by Stuart [16] since the same response was not found when the Fw/Rw ¼1.5. That is, when footings are placed too close in proximity they behave as a single foundation and the settlement greatly increases. 4.3. Pillar and backfill modeling The effect of backfill on pillar strength is addressed in the following section. For this, a cohesive and a non-cohesive backfill were simulated. The material properties of the backfill, coal and main floor are shown in Table 5, and were found from Wang, et al. [27] which was a modeling study on the influence of roadway backfill on pillar strength. The main floor was simulated as an elastic material so to alleviate any interaction effect. The floor was

Table 4 Ratio of Nm modeled bearing capacity factor to Nm theoretical for a finite floor thickness. φ1

φ2

c2/c1

0 0 0 0 35 35 0 0 0 0 35 35 0 0 0 0 35 35 0 0 0 0 35 35

0 0 35 35 35 35 0 0 35 35 35 35 0 0 35 35 35 35 0 0 35 35 35 35

2 2 2 2 2 2 2 2 2 2 2 2 5 5 5 5 5 5 5 5 5 5 5 5

B/H

40.00 40.00 40.00 40.00 40.00 40.00 4.00 4.00 4.00 4.00 4.00 4.00 40.00 40.00 40.00 40.00 40.00 40.00 4.00 4.00 4.00 4.00 4.00 4.00

Fw/Rw

Ratio of Nm model/ Vesic Nm theoretical

1.50 6.00 1.50 6.00 1.50 6.00 1.50 6.00 1.50 6.00 1.50 6.00 1.50 6.00 1.50 6.00 1.50 6.00 1.50 6.00 1.50 6.00 1.50 6.00

1.0 1.1 1.9 1.8 17.9 417.9 0.9 0.9 0.9 0.9 17.8 417.8 1.5 1.4 1.5 1.4 13.7 413.7 0.9 0.9 0.9 0.9 23.0 423.0

Table 5 Material properties chosen for the quarter pillar model [3]. Coal pillar properties (psi and 1)

Backfill properties (psi and 1)

NonCohesive cohesive

Cohesion Friction angle Poisson’s ratio Young’s modulus Dilation angle Tensile strength Shear modulus Bulk modulus

Cohesion Friction angle Poisson’s ratio Young’s modulus

0 42 0.2 2900

148 36 0.3 159,541 6 6 61,362 132,951

Dilation angle Tensile strength Shear modulus Bulk modulus

Main floor properties (psi and 1)

17 150 40 0 0.4 0.4 81,946 15,557

8 0

10 15

0 63

1261 1381

29,267 136,577

5,762 17,286

simulated as underclay material with the same properties as in the previous models. An 8% moisture content of the main floor was arbitrarily chosen. Using this moisture content, the bulk modulus, shear modulus and tensile strength could all be determined from equations for an underclay material located in the Herrin 6 seam as derived by Gadde [5]. A pillar width (Pw) was chosen which corresponded to the footing width in the previous modeling studies. Although this pillar width is not a realistic pillar size, the model followed the Mohr–Coulomb failure criteria, so there are no size dependent properties, such as when a strain-softening or hardening material is simulated. In Fig. 4, Rw represents half of the total room width. The pillar was simulated four zones in height because this works well with the 0–100% fill ratios at 25% increments. Therefore, the model represents a pillar width/ pillar height ratio of 1.5. The model extents were five times the pillar width in the z-coordinate direction. Such a distance was chosen in the z-direction so to neutralize any effects which may be attributed from the floor material. In effect this isolates the pillar and backfill interaction. An immediate roof was not simulated for a few reasons. First, if the immediate roof was

T. Kostecki, A.J.S. Spearing / International Journal of Rock Mechanics & Mining Sciences 76 (2015) 55–67

61

Table 6 Normal and shear stiffness properties of the simulated interfaces [3]. Cohesive backfill Interface ID Location kn (psi) ks (psi) Interface ID Location kn (psi) ks (psi)

Interface 1 Interface 2 Pillar & floor Backfill & floor 249,689 1755,993 249,689 1755,993 Non-cohesive backfill Interface 1 Interface 2 Pillar & floor Backfill & floor 249,689 30,621 249,689 30,621

Interface 3 & 4 Pillar & backfill 2147,674 2147,674 Interface 3 & 4 Pillar & backfill 30,621 30,621

times the equivalent stiffness of the stiffest adjacent zone. 


K þ 4=3G kn & ks ¼ 10  Δzmin

ð15Þ

where K and G are the bulk and shear moduli, respectively and Δzmin is the smallest width of the adjacent zone in the normal direction to the plane. On the other hand, if a much softer material exists within the model the interfaces should be based upon the much softer material in the model as behavior is largely governed by the softer material. By adopting this methodology, the normal and shear stiffness properties for the interfaces are tabulated in Table 6. 4.4. Pillar and backfill implementation and results

Fig. 4. Example of the generated grid for the quarter pillar model at 25% fill [3].

simulated than the model would need to be interpreted with consideration of non-uniform pillar loading. Because this model does not consider non-uniform loading across the pillar, the question arises whether the current model could be useful for actual pillar stability cases where non-uniform loading occurs. Based on past research studies, namely Gadde [5], it was determined that non-uniform loading across the pillar showed negligible effect to the overall bearing capacity, aside from some localized failures. In terms of pillar stability, a uniform pillar load seems more conservative, as opposed to guessing arbitrary increases in loading magnitudes to different regions of the pillar. Additionally, studies such as Wang et al. [27], which make no effort towards a non-uniform loading condition, still provide useful results, which can be extracted for pillar stability studies. Second, it was desired to observe the effects of pillar confinement due to the backfill based on strength characteristics of the backfill alone, implementing the immediate roof would constitute another factor within the model, which should be analyzed separately. Now that the model has multiple materials interacting (backfill, pillar and floor), four interfaces were generated to simulate movement along the intersecting planes. Since no properties of the interface were known, [29] offers the following recommendations for approximating the shear (ks) and normal stiffness (kn) of the interfaces. If the behavior between two different materials of is governed by the stiffer of the two materials, the shear (ks) and normal stiffness (kn) of the interface can be interpreted as ten

The ultimate goal was to observe the behavior of coal pillar strength at varying backfill percentages. This was of interest for both a cohesive and non-cohesive fill. In order to monitor the coal pillar strength, the average pillar stress and average pillar strain were monitored within the coal pillar, via a FISH subroutine. Loading followed the same magnitude (1.0E
5 in./step) as in the footing models, except the loading platen was now located at the top of the pillar. The model was stepped until the pillar stress–strain curve normalized and reached its ultimate load. An example of a stress– strain curve for a 50% cohesive fill, for a Pw/Rw ratio of 1.5, is shown in Fig. 5. The ultimate loads of the pillars at varying Pw/Rw ratios for a cohesive and non-cohesive backfill were modeled and are tabulated in Table 7. The results were presented in a normalized manner, mainly for qualitative purposes. An unconfined pillar (0% fill) represents the baseline value. For example, if the pillar strength at a 0% confinement was 2000 psi and the pillar strength at 50% fill was 4000 psi, then the normalized pillar strength ratio would be 1.0 for 0% fill and 2.0 for 50% fill. Adopting the aforementioned methodology, the results for all scenarios were tabulated in Table 7. From the results the noncohesive fill attributed to zero increase in pillar strength overall, except at 100% fill and at a Pw/Rw ¼6. This is not surprising considering the non-cohesive fill has zero shearing or tensile resistance and a low stiffness. In this instance, the model was ran for over 5 million steps and showed no indication of failure, therefore the ( 460.0) value indicates the value at which the model was stopped. The other non-cohesive backfill models reached their ultimate load in fewer than 200,000 steps. Overall, it was deemed that the non-cohesive fill was only useful at high Pw/Rw ratios of 6 and at 100% fill, in which case the pillar was indestructible. This does not indicate the non-cohesive fill cannot attribute to increase pillar strength however. In a recent study [27], it was shown that a non-cohesive fill does increase the coal pillar strength at increased fill ratios. In their study they simulated the floor, pillar and roof however. Therefore the strength of the

62

T. Kostecki, A.J.S. Spearing / International Journal of Rock Mechanics & Mining Sciences 76 (2015) 55–67

Fig. 5. Plot of avg. pillar stress versus avgrage pillar strain for a coal pillar with 50% cohesive fill and a Pw/Rw ¼1.5 [3].

Table 7 Normalized pillar strength results at varying percent confinements and pillar to room width ratios for a cohesive and non-cohesive backfill [3]. % Pw/ Confinement Rw

0 25 50 75 100 0 25 50 75 100 0 25 50 75 100 0 25 50 75 100

1.5 1.5 1.5 1.5 1.5 2 2 2 2 2 3 3 3 3 3 6 6 6 6 6

Non-cohesive fill

Cohesive fill

Normalized pillar strength ratio

Normalized pillar increase ratio

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 460.0

1.0 1.1 1.3 1.4 2.4 1.0 1.1 1.3 1.4 2.9 1.0 1.1 1.2 1.4 4.1 1.0 1.1 1.2 1.4 4 60.0

non-cohesive fill, attributed to increased pillar strength, must be associated more with the confinement aspect of the fill, rather than the strength properties of the fill itself. Physical modeling [3] showed how the influence of fill strength can influence the overall pillar strength. Contrary to [27], they make no mention of an interface between the pillar and backfill, which could be an error within their modeling, as this would have most likely caused significant over estimation of the non-cohesive fill results attributed to coal pillar strength and lead to the discrepancies. On the other hand, the cohesive fill increased the pillar strength at increased fill percentages as well as at increased Pw/Rw ratios. Additionally, at a Pw/Rw ¼ 6 and 100% fill the model was stopped after five million steps, similar to the non-cohesive fill model. This also indicated an indestructible pillar at a high Pw/Rw ratio. Owing to the previous footing models however, placing the pillars in close proximity, along with a weak floor, would seem to cause the footings to behave has a single foundation, in which case appreciable settlement would occur in these entries. Moreover, it seems impractical to think a panel would be filled to 100%, so cases of 100% at high Pw/Rw ratios may be unrealistic. Contrary to the noncohesive results, the cohesive nature of the cohesive fill, increased the pillar strength overall. This is most likely attributed to its significant increase in shearing, tensile resistance and increased stiffness. All in all, it seems the only significant increase in pillar strength can be expected, due to the strength properties of the fill itself, when the shearing resistance, tensile strength and stiffness are increased and the fill percent is anywhere greater than 50% fill. In this case the increase in pillar strength can be expected to be at least 20% greater than an unconfined coal pillar. Fig. 6 displays all of the average pillar stress versus average pillar strain curves at varying fill percentages. The failure regions were next observed via the plasticity state plot to better describe the influence of an adjacent pillar and the regions undergoing plastic flow. Plasticity state plots can be used to determine which zones have, or are currently undergoing shear and tensile failure. Shear-p and tension-p indicate plastic flow in the past and zones which no longer satisfy the yield criteria and shear-n and tension-n indicate active plastic zones. For this, Fig. 7a–e will be used as an example and represent a quarter pillar geometry confined at 50% cohesive fill at a Pw/Rw ratio of 1.5. Both sides of the pillar are shown in each perspective to capture a complete view of the pillar.

Fig. 6. Plot of all of the avg. pillar stress versus the average pillar strain for all coal pillars modeled with a cohesive backfill [3].

T. Kostecki, A.J.S. Spearing / International Journal of Rock Mechanics & Mining Sciences 76 (2015) 55–67

The elastic-perfectly plastic behavior for this pillar is shown in Fig. 5. Points A–E specified along this yield curve in Fig. 5 corresponds to the plasticity state plots shown in Fig. 7a–e. For example Fig. 7a was extracted from the model when point A on the yield curve was reached. The points were chosen in the following manner: before loading began (point A; after 0 steps), at two arbitrary points along the elastic region of the yield curve (points B and C; after 16,650 and 35,200 steps, respectively), at the yield point of the pillar (point D; after 54,900 steps) and at the ultimate load of the pillar (point E; after 85,000 steps). Similarly, Fig. 8a–e are plasticity state plots for a Pw/ Rw ¼6, which were extrapolated at the same step numbers as Fig. 7a–e (0, 16,650, 35,200, 54,900, and 85,000 steps). The most important point to remember is that the stress–strain curve for Fig. 8a–e (i.e. Pw/ Rw ¼6 and 50% cohesive fill) does not correspond to the same stress– strain curve as in Fig. 5. Instead, Fig. 8a–e represents the failure the pillar and backfill undergo after the same amount of displacement as a pillar with a Pw/Rw ¼1.5 (i.e. Fig. 7a–e). Based upon the plots in Fig. 7a–e the following observations were made. In Fig. 7a the system is in equilibrium and no shear or tensile failure is occurring. In Fig. 7b, loading has progressed to point B in

63

Fig. 5. At this point shear failure (shear-n) initializes within the backfill at the pillar corner. Tensile failure (tension-n) initializes at the bottom of the pillar along the symmetry planes. For Fig. 7c, loading has further progressed to point C in Fig. 5. Shear failure (shear-n) onsets at the pillar corner and to a greater extent within the backfill. For Fig. 7d, the pillar now begins to yield and shear failure remains the dominant failure mechanism throughout the pillar and backfill. Although the pillar has yielded the core of the pillar remains intact. With Fig. 7e, the ultimate load of the pillar has been reached and the entire regions have now undergone some form of failure. Next, similar plasticity state plots were extrapolated for a Pw/Rw ¼6 at 50% fill. The plots in Fig. 8a–e corresponds to the same step numbers (displacements) as Fig. 7a–e but not the same stress strain plot as in Fig. 5. Based upon the plots in Fig. 8a–e the following observations were made. For Fig. 8a, the system is in equilibrium and no shear or tensile failure is occurring. With Fig. 8b, the pillar has undergone the same magnitude of displacement as in Fig. 7b. At this point the system shows no obvious zones of failure in shear or tension, whereas in the Fig. 7b shear failure had initiated within the backfill at the pillar corner. In

Fig. 7. (a) Plasticity state plot of a coal pillar at 50% confinement, Pw/Rw ¼1.5 and corresponding to point A in Fig. 5. (b) point B in Fig. 5, (c) point C in Fig. 5, (d) point D in Fig. 5, (e) point E in Fig. 5.

64

T. Kostecki, A.J.S. Spearing / International Journal of Rock Mechanics & Mining Sciences 76 (2015) 55–67

Fig. 8. (a) Plasticity state plot of a coal pillar at 50% confinement, Pw/Rw ¼6.0 and corresponding to point A in Fig. 5. (b) Point B in Fig. 5, (c) point C in Fig. 5, (d) point D in Fig. 5, (e) point E in Fig. 5.

Fig. 8c and within the backfill, all zones are undergoing some magnitude of shear failure (shear-n) and the pillar remains intact throughout. For Fig. 8d, the same amount of displacement as in Fig. 7d has occurred. At this point the backfill continues to show all zones undergoing some magnitude of shear failure (shear-n). At this point the pillar remains intact throughout. In contrast, the pillar in Fig. 7d had already yielded at the pillar edges. Finally, in Fig. 8e, the pillar shows failure in shear at the pillar ribs and tensile failure at the base of the pillar. In comparison to a Pw/Rw ¼1.5 at 50% fill, the pillar core remains intact whereas the aforementioned has displayed failure throughout. This behavior indicates that for two coal pillars undergoing the same amount of displacement, the pillars spaced with an adjacent pillar in close proximity (Pw/Rw ¼ 6) indicates a more stable pillar core under the same percent confinement. Also, the failure mechanism tends to be governed by shear failure which initiates at the pillar corners and then propagates to pillar ribs. 4.5. Pillar, backfill and floor implementation In the previous studies either the immediate and main floor was modeled without the influence of the pillar or backfill, or the pillar and

backfill were modeled atop an elastic homogenous floor to eliminate any interaction effect. Additionally, all gravitational effects were neglected up to this point which allowed for approximation of the ultimate bearing capacity by neglecting the Nq and Nγ factors. This section will discuss the results of a model which incorporates the mechanisms of the immediate floor, pillar and backfill. In the previous section it was determined that the non-cohesive fill played little role on increasing the pillar strength therefore it was not included in the following section to help minimize the model runs. Additionally, gravitational effects were incorporated; because of this, a surcharge (Nq) now acts upon the immediate floor and the soil weight (Nγ) can no longer be neglected in the approximation of the bearing capacity. The following scenarios were modeled based upon known conditions encountered in the Illinois Basin: Immediate (φ1) and main floor (φ2) were again ran at 01 and 351; cohesion of the main floor (c2) and the cohesion of the immediate floor (c1) varied between 2 and 5; footing/pillar base to immediate floor thickness (B/H) ratios of 4 and 40; Pillar to room width (Pw/Rw) ratios of 1.5 and 6.0; Confinement of 0–100% at 25% increments. Both the limit load of the footing and the ultimate load of the pillar were monitored and are compared in Table 8.

T. Kostecki, A.J.S. Spearing / International Journal of Rock Mechanics & Mining Sciences 76 (2015) 55–67

In all cases, improvement in pillar strength and the ultimate bearing capacity are shown as the percent confinement increases. As previously mentioned however, since 100% fill is most likely not a practical fill range, it seems that a 10–40% increase in pillar strength and bearing capacity is more realistic based upon the following models. The pillar spacing effect definitely tends to have the largest influence on the ultimate bearing capacity and the ultimate pillar strength within these models. In the cases of 100% fill where the Pw/Rw ratios are high it seems that the foundations are again behaving as a single foundation as shown in the footing studies. This is a factor which should be analyzed further to determine and optimum spacing range. 4.6. Softening effects on pillar and floor properties Though this paper does not consider the effects of softening on the pillar and floor, studies [27] have already been conducted which show the influence of cohesive and non-cohesive fill on a roadway coal pillar. Their studies showed up to 120% increase in pillar

65

strength for cohesive fill and up to 35% increase in strength with pillars confined with non-cohesive fill at 90% fill ratios and pillar heights of 10 m. For pillar heights of 5 m, a 60% increase in pillar strength with pillars confined with cohesive fill, and 20% increase in pillar strength for non-cohesive backfill. Additionally, the softening showed little change in peak strength for coal pillars modeled with strain-softening properties. The greatest increase in strength was found in the post-failure region when the pillar began to harden. This goes to show, that simulation with Mohr–Coulomb properties is appropriate when considering changes due to peak strength of the pillar, but cannot accommodate for changes in strength to a coal pillar in the post-failure state. Minimal studies to date have been conducted which consider strain-softening properties of the immediate floor, mainly because of the lack of real in-situ properties of underclay’s in general. Some modeling studies by Gadde [5] were conducted where the immediate floor was water “softened” by decreasing the Mohr– Coulomb properties gradually, hence weakening the floor in the presence of water. Barring the lack of research in this area, it is the

Table 8 Results of backfill, pillar and immediate floor models. φ1

φ2

c2/c1

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 35 35 35 35 35 35 35 35 35 35 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 0 0 0 0 0 0 0 0 0 0 35 35 35 35 35 35 35

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

B/H

40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00

Pw/Rw

% Confinement

Immediate floor Ultimate load

Pillar Ultimate load

1.50 1.50 1.50 1.50 1.50 6.00 6.00 6.00 6.00 6.00 1.50 1.50 1.50 1.50 1.50 6.00 6.00 6.00 6.00 6.00 1.50 1.50 1.50 1.50 1.50 6.00 6.00 6.00 6.00 6.00 1.50 1.50 1.50 1.50 1.50 6.00 6.00 6.00 6.00 6.00 1.50 1.50 1.50 1.50 1.50 6.00 6.00

0 25 50 75 100 0 25 50 75 100 0 25 50 75 100 0 25 50 75 100 0 25 50 75 100 0 25 50 75 100 0 25 75 50 100 0 25 50 75 100 0 25 50 75 100 0 25

1.0 1.1 1.3 1.4 2.6 1.0 1.1 1.2 1.4 44.2 1.0 1.1 1.3 1.4 2.6 1.0 1.1 1.2 1.4 47.6 1.0 1.1 1.3 1.4 2.6 1.0 1.1 1.2 1.4 47.6 1.0 1.1 1.3 1.4 1.9 1.0 1.1 1.2 1.4 46.2 1.0 1.1 1.3 1.4 1.9 1.0 1.1

1.0 1.1 1.3 1.4 2.5 1.0 1.1 1.2 1.4 4 5.3 1.0 1.1 1.3 1.4 2.5 1.0 1.1 1.2 1.4 4 6.5 1.0 1.1 1.3 1.4 2.5 1.0 1.1 1.2 1.4 4 6.5 1.0 1.1 1.3 1.4 1.7 1.0 1.1 1.2 1.4 4 5.3 1.0 1.1 1.3 1.4 1.7 1.0 1.1

66

T. Kostecki, A.J.S. Spearing / International Journal of Rock Mechanics & Mining Sciences 76 (2015) 55–67

Table 8 (continued ) φ1

φ2

c2/c1

0 0 0 35 35 35 35 35 35 35 35 35 35 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 35 35 35 35 35 35 35 35 35 35 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 35 35 35 35 35 35 35 35 35 35

35 35 35 35 35 35 35 35 35 35 35 35 35 0 0 0 0 0 0 0 0 0 0 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 0 0 0 0 0 0 0 0 0 0 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35

2 2 2 2 2 2 2 2 2 2 2 2 2 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

B/H

4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00

Pw/Rw

% Confinement

Immediate floor Ultimate load

Pillar Ultimate load

6.00 6.00 6.00 1.50 1.50 1.50 1.50 1.50 6.00 6.00 6.00 6.00 6.00 1.50 1.50 1.50 1.50 1.50 6.00 6.00 6.00 6.00 6.00 1.50 1.50 1.50 1.50 1.50 6.00 6.00 6.00 6.00 6.00 1.50 1.50 1.50 1.50 1.50 6.00 6.00 6.00 6.00 6.00 1.50 1.50 1.50 1.50 1.50 6.00 6.00 6.00 6.00 6.00 1.50 1.50 1.50 1.50 1.50 6.00 6.00 6.00 6.00 6.00 1.50 1.50 1.50 1.50 1.50 6.00 6.00 6.00 6.00 6.00

50 75 100 0 25 50 75 100 0 25 50 75 100 0 25 50 75 100 0 25 50 75 100 0 25 50 75 100 0 25 50 75 100 0 25 50 75 100 0 25 50 75 100 0 25 50 75 100 0 25 50 75 100 0 25 50 75 100 0 25 50 75 100 0 25 50 75 100 0 25 50 75 100

1.2 1.4 4 7.4 1.0 1.1 1.3 1.4 2.6 1.0 1.1 1.2 1.4 4 7.6 1.0 1.1 1.3 1.4 2.6 1.0 1.1 1.2 1.4 4 7.5 1.0 1.1 1.3 1.4 2.6 1.0 1.1 1.2 1.4 4 7.6 1.0 1.1 1.3 1.4 2.6 1.0 1.1 1.2 1.4 4 7.6 1.0 1.1 1.3 1.4 1.9 1.0 1.1 1.2 1.4 4 7.4 1.0 1.1 1.3 1.4 1.9 1.0 1.1 1.2 1.4 4 7.4 1.0 1.1 1.3 1.4 2.6 1.0 1.1 1.2 1.4 4 7.6

1.2 1.4 46.4 1.0 1.1 1.3 1.4 2.5 1.0 1.1 1.2 1.4 46.5 1.0 1.1 1.3 1.4 2.5 1.0 1.1 1.2 1.4 46.5 1.0 1.1 1.3 1.4 2.5 1.0 1.1 1.2 1.4 46.5 1.0 1.1 1.3 1.4 2.5 1.0 1.1 1.2 1.4 46.5 1.0 1.1 1.3 1.4 1.7 1.0 1.1 1.2 1.4 46.4 1.0 1.1 1.3 1.4 1.7 1.0 1.1 1.2 1.4 46.4 1.0 1.1 1.3 1.4 2.5 1.0 1.1 1.2 1.4 46.5

T. Kostecki, A.J.S. Spearing / International Journal of Rock Mechanics & Mining Sciences 76 (2015) 55–67

author’s recommendation that further studies need to be conducted on determining in-situ properties of under-clays before accurate modeling studies can be conducted. 5. Conclusions Based on the following body of work the following conclusions can be made. Vesic’s approximation for bearing capacity, which is by far the most popular design equation for governing purposes for mines in the Illinois Basin, tends to underestimate the total bearing capacity of a footing especially at higher friction angles and when multiple footings are in close proximity. This conclusion was also validated by Gadde [5]. Minimizing the distance between adjacent foundations has shown an improvement in the ultimate bearing capacity of a foundation. However, placing the foundations too close (Pw/Rw ¼6) has shown the foundations may behave as a single foundation and undergo appreciable settlement. The magnitude of settlement and optimum pillar spacing need to be researched further. A 10–40% increase in pillar strength and ultimate bearing capacity has been observed when a cohesive fill is used between 25% and 75% fill, respectively. Therefore at least 25% fill is recommended to show any such influence on the ultimate strength of the surrounding pillar or floor materials. A fill range of 75–90% will need to be investigated further as modeling 100% fill may be impractical. The non-cohesive nature of the simulated backfill showed little influence on increased pillar strength, even at higher fill ratios. It was determined, that as the shearing resistance, tensile strength and stiffness of the fill are reduced, and material relies more and more on the confinement aspect of an underground mine rather than the strength properties of the material itself. Therefore higher fill ratios will be needed to show any influence on increased pillar strength. Shear failure tends to be the governing failure mechanism occurring at the pillar corners first and thereafter propagating to the pillar ribs. Finally, a methodology for analyzing the plastic flow characteristics of a coal pillar and a footing using FLAC3D has also been presented herein. This same methodology can be adopted for other users interested in analyzing mechanisms such as floor heave or failure regions for routine numerical models. Acknowledgments The authors greatly appreciate the funding from the Illinois Department of Commerce and Economic Opportunity through the Illinois Clean Coal Institute. References [1] U.S. Energy Information Administration. Annual coal report, 〈http://www.eia. gov/coal/annual/pdf/acr.pdf〉; 2013 (December 2013). [2] Spearing AJS, Benton D, Kostecki T, Hirschi J. The potential of using coal washing plant waste as a backfill in room and pillar mines In: The 32nd

67

international conference on ground control in mining (ICGCM). Morgantown, WV; 2013. p. 1–8. [3] Spearing AJS, Hirschi J. The conceptual design and financial implications of a room and pillar mine using paste fill. Illinois Clean Coal Institute Project: 12/3A-1. [4] Fiscor S. The Illinois Basin supply-side story. Coal age. 06 Jan 2012. 〈http:// www.coalage.com/index.php/features/1605-the-illinois-basin-supply-side-s tory.html〉 2012 (13 Feb. 2014). [5] Gadde MM. Weak floor stability in the Illinois Basin underground coal mines. (PhD thesis). Morgantown, WV: University of West Virginia; 2009. [6] Das M. Principles of foundation engineering. 6th ed. Samford: Thompson Canada Ltd.; 2007. p. 121. [7] Speck R. A comparative evaluation of geologic factors influencing floor stability in two illinois coal mines. (PhD thesis). Rolla: University of Missouri; 1979. p. 265. [8] Rockaway JD, Stephenson, RW. Investigation of the effects of weak floor conditions on the stability of coal pillars. Report No. BUMINES-ofr-12-81; 1979. [9] Chugh YP. Laboratory characterization of the immediate floor strata associated with coal seams in Illinois. Final report to mine subsidence research program, Illinois State Geological Survey; 1986. [10] Chugh YP. In situ strength characteristics of coal mine floor strata in Illinois. Final report to mine subsidence research program, Illinois State Geological Survey; 1986. [11] Shankar S. Geotechnical properties of immediate floor strata from an Illinois coal mine. (PhD thesis). Carbondale, IL: Southern Illinois University; 1987. [12] Tandon S. Field strength-deformation characteristics of immediate floor strata in Illinois coal mines. (PhD thesis). Carbondale, IL: Southern Illinois University; 1987. [13] Chandrashekhar K. Effects of weak floor interaction on underground roomand-pillar coal mining. (PhD thesis). Carbondale, IL: Southern Illinois University; 1990. p. 345. [14] Jayanti S. A finite element analysis of bearing capacity of coal pillars on weak floor strata. (PhD thesis). Carbondale, IL: Southern Illinois University; 1991. [15] Vesic AS. Bearing capacity of shallow foundations. In: Winterkorn HF, Fang H, editors. Foundation engineering handbook. Van Nostrand Reinhold, Co.; 1975. p. 121–47. [16] Stuart JG. Interference between foundations, with special reference to surface footings in sand. Géotechnique 1962;12(1):15. [17] Das BM, Larbi-Cherif S. Bearing capacity of two closely spaced shallow foundations on sand. Soil Found 1982:1–7. [18] Graham J, Raymond GP, Suppiah A. Bearing capacity of three closely spaced footings on sand. Geotechnique 1984;34(2):173–82. [19] Jao M, Wang MC, Chou HC, Lin CJ. Behavior of interacting parallel strip footing. Electron J Geotech Eng 2002;7:000. [20] Kumar J, Ghosh P. Ultimate bearing capacity of two interfering rough strip footings. Int J Geomech 2007;7(1):53–62. [21] Kumar J, Ghosh P. Upper bound limit analysis for finding interference effect of two nearby strip footings on sand. J Geotech Geol Eng 2007;25(5):499–507. [22] Kumar J, Kouzer KM. Bearing capacity of two interfering footings. Int J Numer Anal Methods Geomech 2007;32(3):251–64. [23] Kumar J, Bhoi MK. Interference of two closely spaced strip footings on sand using model tests J. Geotech Geoenviron Eng ASCE, 135; 2009. p. 595–604. [24] Lee J, Eun J. Estimation of bearing capacity for multiple footings in sand. J Comp Geotechnol Eng 2009:1–9. [25a] Itasca Consulting Group Inc. FLAC3D. (Fast Lagrangian Analysis of Continua in 3-dimensions), Version 5.0. Minneapolis; 2012. [25b] Itasca Consulting Group Inc. FLAC3D. (Fast Lagrangian Analysis of Continua in 3-dimensions), User’s guide. 5th ed. Minneapolis, MN; October 2012. Section 3. p. 48; 105; 109; 114–115. Print. [26] Singh R, Sheorey PR, Singh DP. Stability of the parting between coal pillar workings in level contiguous seams. Int J Rock Mech Min Sci 2002;39:9–39. [27] Wang H, Poulsen BA, Shen B, Xue S, Yadong J. The influence of roadway backfill on the coal pillar strength by numerical investigation. Int J Rock Mech Min Sci 2011;48:443–50. [28] Dzik E. Personal Communication; 2012. [29] Itasca Consulting Group Inc. FLAC3D. (Fast Lagrangian Analysis of Continua in 3-dimensions), Theory and Background. 5th Ed. Minneapolis; October 2012. Section 2. p. 11–13.