Impact of deformable materials and convergence on the 

transverse load capacity of mine ventilation stoppings 

T. J. Batchler & T. M. Barczak 

National Institute for Occupational Safety and Health, Pittsburgh Research Laboratory, Pittsburgh PA 

ABSTRACT: Deformable materials are sometimes added to ventilation stopping constructions to prevent damage 

caused by convergence in coal mines. However, adding deformable materials can significantly reduce the capacity 

of a stopping to resist transverse loading. As part of its mining health and safety program, the National Institute 

for Occupational Safety and Health (NIOSH) has conducted research on the effect of various materials with 

different deformation properties on the transverse loading capability of a stopping wall. Based on a three-point 

hinge method of failure, a half-wall method of testing in the NIOSH Mine Roof Simulator was used to simulate 

full-scale wall behavior. This simulated the fracture initiation and eventual failure of the stoppings from 

transverse loading. The impact of the modulus of elasticity of various deformable materials was examined in this 

study. A polystyrene foam block with a low modulus of elasticity, which is commonly used as a deformable 

material, was shown to degrade the transverse load capacity of the stopping by as much 95%. Other materials 

with higher modulus of elasticity preserved more of the transverse load capacity of the stopping, but were not able 

to absorb as much convergence. This paper presents the results of a parametric study that quantifies the impact of 

various deformable materials in block stopping construction under transverse load conditions. 

Disclaimer: The findings and conclusions in this report have not been formally disseminated by the National 

Institute for Occupational Safety and Health and should not be construed to represent any agency determination or 

policy. 

1 Introduction 

Ventilation stoppings are airflow control devices, typically 

dry-stacked concrete block walls, erected between intake 

and return airways to direct ventilating air throughout the 

working sections of underground coal mines. The Code of 

Federal Regulations (CFR) requires ventilation stoppings 

to meet a certain minimum transverse load, but they often 

fail to meet these criteria due to convergence loading. 

Under the freestanding load conditions, 2 kPa (39 psf) is 

designated in the preamble to the CFR as the minimum 

required transverse load capacity. In order to prevent 

premature failure from convergence, deformable materials 

are incorporated into the stopping construction. Currently, 

the most commonly used material is an expanded 

polystyrene foam, formed into squeeze blocks or planks, 

that are sandwiched between one or more courses of a 

block stopping. Figure 1 shows a 1.2-m (4-ft) wide section 

of a stopping wall with a 5-cm (2-in) thick foam plank 

placed between the top two courses of block, showing the 

wall before and after failure during a laboratory test. Figure 

2 compares the response of the wall for vertical loading. 

As seen in figure 2, the foam increases the displacement at 

which wall failure occurs, thereby increasing the capability 

of the wall to accommodate the roof-to-floor closure of the 

mine entry. 

Although the foam is effective in enhancing the yield 

capability of the wall and extending the service life of the 

stopping in response to the closure of the mine opening, 

what does it do to the transverse load capacity of the 

stopping? Before addressing that question, it is important 

to understand how the transverse load capacity of a 

Foam Layer Foam Layer squeezed from 

convergence 

stopping is assessed. The current CFR evaluates transverse 

loading of stoppings under freestanding loading conditions 

in accordance with ASTM E-72 specifications (Barczak 

and Batchler, 2006). In this condition, the transverse load 

capacity for dry-stacked stopping constructions is primarily 

Figure 1. Two-inch-thick foam plank used to reduce the 

stiffness and extend the life of a block stopping by 

allowing the wall to absorb some deformation prior to 

failure. Only vertical loading is applied in this test. 
 

 

 

determined by the tensile strength of the sealant applied to 

the face of the stopping (see figure 3). Deformable 

materials are typically not included in these evaluations, 

but would not make much difference in this test protocol 

since the compressive forces developed within the 

freestanding wall are minimal and little damage would 

occur to them during the transverse load application. A 

new protocol has been developed that evaluates the 

transverse resistance of stoppings using equivalent arch 

loading conditions (Barczak and Batchler, 2006). The arch 

loading to approximate transverse loading is highly 

dependent upon the compressive forces developed within 

the wall as the wall arches between the mine roof and floor 

from the application of transverse pressure. In this 

condition, any deformable material in the wall can 

significantly degrade the transverse load capacity of the 

stopping. Using the protocol developed to simulate a threehinge arch arrangement, the foam material decreased the 

transverse loading capacity of a representative stopping 

made from solid concrete masonry block by 95% (24.4 to 

1.3 kPa or 510 to 28 psf), as shown in figure 4. 

This example clearly demonstrates that under arch 

loading conditions, which are believed to be representative 

of the loading conditions that occur in the mine (Barczak, 

2005), the application of deformable materials to enhance 

the yield capability and survivability of the stopping due to 

convergence must be properly designed to preserve the 

transverse load capacity. The purpose of this paper is to 

determine the relationship between the modulus of 

elasticity of the deformable material and the transverse 

load capacity of the stopping under arch loading 

conditions. 

VERTICAL DISPLACEMENT, in 

0.0 0.5 1.0 1.5 2.0 2.5 3.0 

0 

222 

444 

666 

888 

1,110 

1,332 

1,554 

1,776 

VERTICAL LOAD, kN 

VERTICAL LOAD, kips 

No deformable 

51-mm (2-in) thick 

foam deformable 

400 

350 

300 

250 

200 

150 

100 

50 

0 

0.0 12.7 25.4 38.1 50.8 63.5 76.2 

VERTICAL DISPLACEMENT, mm 

Figure 2. Comparison of a block stopping wall’s response 

to vertical loading with and without a foam, deformable 

layer. 

C

o

m

pr

e

s

i 

Wall 

Stopping 

Sealant 

(shown only 

on backside)
 Transverse 

Load 

Figure 3. In freestanding evaluation, the sealant provides 

the main resistance to transverse loading. 

 

3 

LATERAL DISPLACEMENT, inches 

0 0.5 1 1.5 2 2.5 

0 

222 

444 

666 

888 

1,110 

1,332 

1,554 

1,776 TRANSVERSE PRESSURE, kN 

TRANSVERSE PRESSURE, psf 

No deformable material 

5-cm (2-in) thick foam 

deformable material 

300 

250 

200 

150 

100 

50 

0 

0.0 12.7 25.4 38.1 50.8 63.5 76.2 

LATERAL DISPLACEMENT, mm 

Figure 4. Under arch loading conditions, foam layer can 

severely degrade transverse load capacity of a stopping. 

This figure shows the results of the MRS transverse 

loading tests of a stopping with and without a foam layer. 

2	 Evaluation of Transverse Pressure under Arch 

Loading Conditions 

Ventilation stoppings bridge the gap between the mine 

floor, roof, and pillars providing a restrained boundary 

condition. When a transverse pressure acts against the face 

of a stopping, the wall deflection is restrained by the mine 

roof and floor abutments creating a three-hinge arch. In 

order to simulate this arching mechanism, a half-wall 

section of a stopping is placed in the NIOSH’s Mine Roof 

Simulator (MRS) (see figure 5). The half-wall is then 

hydraulically clamped to a fixed vertical height. The upper 

platen remains fixed in place as the lower platen moves 

horizontally, causing the wall to rotate. As the base of the 

wall is forced to move horizontally, hinge points and 

deformation zones are created at the ends of the wall on 

opposite sides, consistent with the arch loading 

mechanism. The horizontal force applied to the ends of the 

half-wall is measured and is equated to the transverse load 

acting on the wall (see figure 6) (Barczak, 2005). 
 

 

 

 

 

MRS UPPER PLATEN 

θ

Figure 5. Simulating rigid arching in the NIOSH Mine 

Roof Simulator. 

P 

Moment Equilibrium HF w × ρ × L2 

= HF × L / 2 8 

2 × HF 

ρ .8 x t - δ ρ = h L/2 w × (L / 2) 

ρ = transverse load, 

w = width of the wall, 

L = height of the wall, 

P = thrust force, and 

HF = horizontal force. 

P t 

Figure 6. Moment equilibrium equations for half-wall 

section of stopping subjected to transverse loading. 

A relationship between horizontal displacement and 

transverse pressure can be developed from figure 6. In 

figure 6, the equivalent horizontal force is shown acting on 

ends of the wall while the resultant arching thrust is acting 

perpendicular to the horizontal force. As the wall rotation 

increases the lateral displacement will increase (see 

figure 7), decreasing the horizontal force as shown in 

equations 1 and 2. 

P × (0.8 × t − δ h ) = HF × L/2 (1) 

2 × P ×( 0.8× t − δh )

ρ = 2 (2) w×(L/ 2 ) 

Where P = thrust load, 

t = thickness of the wall, 

δh	 = lateral displacement of the wall at the mid 

span, 

HF = horizontal force, 

 L/2 = half-wall height, 

ρ	 = transverse load, and 

w = width of wall. 

Thrust moment arm, Pm 

Lateral Displacement, δh 

Figure 7. Diagram showing that increased lateral 

displacement of the stopping reduces the arch thrust which 

reduces the transverse load capacity of the stopping. 

3	 Half-wall Testing of Stoppings with Deformable 

Materials 

A test program was designed to conduct a series of halfwall transverse load tests, using the protocol established to 

simulate arch loading, with a variety materials that provide 

a range of capability to prevent premature failure of the 

stopping due to convergence. The deformable material was 

placed at the top of a 1.2-m (48-in) high half-wall as shown 

in figure 8 to evaluate conditions that do not provide rigid 

arching behavior. This can be caused by either non-rigid 

roof or floor boundaries or by deformable material added 

to the wall construction for the purpose of absorbing 

ground deformation. A representative cellular concrete 

block with strength of about 3,450 kPa (500 psi) was used 

for the study. This is lightweight block with a material 

density of 618 kg/m3

 (38.6 lbs/ft3) and a unit weight of 

23.4 kg (51.5 lbs) for a 20x30x60-cm (8x12x24-inch) 

block. 

Deformation material 

Block wall 

Deformation material 

Upper 

wall 

section 

Lower 

wall 

section 

δh 

Half-wall test set-up Side-view after horizontal displacement 

Figure 8. Deformable material placed at the roof interface 

in the MRS testing program. 
 

 

 

 

 

 

 

Table 1. Material properties of the deformable materials. 

Material Thickness, mm (in) Strain, % Modulus, MPa (psi) System Modulus, MPa (psi) 

Low preload tests 

Plywood 12.0 (0.472) 14 34 (5,000) 287 (41,631) 

Hard Rubber 9 3 (0.367) 14 18 (2,666) 276 (40,084) 

Soft Rubber 9.8 (0.386) 12 4. (600) 195 (28,260) 

Drywall 13.0 (0.513) 8 7 (1,000) 198 (28,752) 

Homasote 13 1 (0.515) 17 15 (2,222) 241 (34,911) 

Thick Foam 20.7 (0.815) 77 1 (130) 45 (6,475) 

High preload tests 

Plywood 12.0 (0.472) 29 74 (10,800) 310 (45,000) 

Hard Rubber 9 3 (0.367) 32 19 (2,750) 302 (43,781) 

Soft Rubber 9.8 (0.386) 28 7 (1,000) 277 (40,224) 

Drywall 13.0 (0.513) 24 8 (1,125) 229 (33,261) 

Homasote 13 1 (0.515) 40 45 (6,500) 221 (30,647) 

Thick Foam 20.7 (0.815) 99 14 (2,000) 276 (40,049) 

The deformable materials were selected based on their 

modulus of elasticity to create a range of boundary 

conditions to study. These are not materials that are 

currently used in mine constructions. Table 1 documents 

the relevant properties of the test materials used in the 

study. The stress-strain response of some of these materials 

is nonlinear, many with strain-hardening behavior as they 

deform. For those materials, the modulus was 

approximated by taking the slope of the stress-strain 

response at the level of deformation which was consistent 

with the preload applied to the stopping prior to the 

application of transverse loading. The effective system 

modulus (Esys) of the block wall and deformable material 

was computed using the series stiffness relationship 

described in equation 3 with the block wall modulus (Ew) 

of 310 MPa (45,000 psi) computed from testing of a unit 

block column. The preload is necessary to simulate the 

condition where convergence causes deformation of the 

deformable material prior to the application of transverse 

pressure. Two levels of preloading were evaluated: (1) a 

nominally small preload of about 345 kPa (50 psi) and (2) 

high preload of about 1,896 kPa (275 psi) equating to 

about 60 pct of the block strength.

A × E k × k

ksys = = (3) 

sys w dm 

sys sys w dm 

l k + k 

Where ksy = system stiffness, 

Asys = surface area, 

Esys = system modulus of elasticity, 

lsys = system height,

 kw = wall stiffness, and

 kdm = deformation material stiffness. 

4 Discussion of Test Results 

Under arch loading conditions, the transverse load capacity 

of a stopping is determined by the force-couple formed by 

the thrust force at the hinge points generated by the 

deflection of the wall from the application of the transverse 

pressure against the face of the stopping. As the diagram in 

figure 7 illustrates, the thrust moment is reduced as the 

lateral displacement of the wall increases. Hence, all other 

things being equal, the transverse capacity of a stopping 

will decrease as the deflection of the wall increases. 

The deflection is governed by the deformational 

properties of the wall and the surrounding roof and floor 

boundaries. Equation 2 provides a theoretical relationship 

between the wall deflection and transverse load developed 

by Barczak (2005). This is verified in the test data as 

shown in figure 9. Two conclusions are drawn from these 

results. First, the amount of lateral displacement decreases 

with increasing preload, thereby increasing the transverse 

pressure capacity of the stopping. Second, the slope of the 

curve increased for the high preload tests with the same 

deformable material applications that were used for the low 

preload tests. 

LATERAL DISPLACEMENT, in 

0 0.5 1 1.5 2 2.5 3 3.5 

0 

5 

10 

15 

20 

25 

30 

35 

40 

45 

50 

TRANSVERSE PRESSURE, kPa 

TRANSVERSE PRESSURE, psf 

Low Preload 

High Preload 

0 13 25 38 51 64 76 89 

LATERAL DISPLACEMENT, mm 

1000 

900 

800 

700 

600 

500 

400 

300 

200 

100 

0 

Figure 9. Transverse pressure capacity is reduced as the 

lateral displacement of the wall increases. 
 

 

10 

70 

80 

90 

Low Preload 

High Preload 

18 

16 

LATERAL DISPLACEMENT (High

Preload), mm 

LATERAL DISPLACEMENT (Low

Preload), mm 

14 

60 12 

50 10 

40 8 

30 6 

20 4 

2 

0 0 

0 500 1000 1500 2000 2500 

SYSTEM MODULUS, kPa 

Figure 10. Lateral displacement decreases as the 

modulus of elasticity of the deformable material of the 

wall increases, causing an increase in system modulus. 

Barczak’s analysis also indicated that the deflection would 

be governed by the effective material modulus or stiffness 

of the system (in this case, the block wall and surrounding 

roof and floor boundaries). Test data shown in figure 10 

confirms this relationship. The modulus of the deformable 

material incorporated in the stopping ranged from a low of 

1 MPa (130 psi) for a foam material to as high as 75 MPa 

(10,800 psi) for plywood. To put this in perspective, the 

block wall had an effective modulus of 310 MPa (45,000 

psi). The lateral displacements increased from a low 12.5 

mm (0.5 inches) to approximately 76.2 mm (3 inches) for 

the low preload tests and from 10.2 to 15 2 mm (0.4 to 0.6 

inches) for the high preload tests. The slope of trendline for 

the high preload tests was about six times greater than the 

low preload test trendline. The reason for this is due in part 

to the strain-hardening of the material resulting in a higher 

system modulus at the higher preload. 

Figure 11 shows the transverse pressure as a function 

of the system stiffness. The stiffness is related to the 

modulus by the relationship expressed in equation 3 and 4.

E w dm w ss × E × (L + L ) (4) E = sys L w dm dm w × E +L × E

Where Esys = system modulus of elasticity, 

Ew = wall modulus of elasticity, psi, 

Edm = deformable modulus of elasticity, 

Lsys = wall height, and 

Ldm = deformable height. 

The chart shows that the transverse load capacity of a 

stopping (low preload situation) can be reduced by a factor 

of 2.5 (22 kPa or 450 psf in this case) by reducing the 

system stiffness by an order of magnitude through the 

addition of deformable materials to the wall construction. 

This reduction in transverse capacity could also be created 

by softening the roof or floor boundary condition 

compared to a rigid abutment situation. The impact of the 

deformable material can be mitigated by convergence that 

would induce a (vertical) preload on the wall. The slope of 

the low preload trendline is about twice that of the high 

preload tests shown in figure 11. The high preload tests 

conducted in this study found that the transverse load 

decreased by about 4.8 kPa (100 psf) for a 30 pct reduction 

in system stiffness. 

SPRING STIFFNESS OF SYSTEM, lbs/in 

0 50 100 150 200 

48 1000 

43 High Preload 

Low Preload 

TRANSVERSE PRESSURE, kPa

TRANSVERSE PRESSURE, psf 

38

34 

29 

24 

19 

14 

10 

5 100 

0 0 

0 4 7 11 14 18 21 25 28 32 35 

SPRING STIFFNESS OF SYSTEM, kN/m 

200 

300 

400 

500 

600 

700 

800 

900 

Figure 11. Transverse pressure capacity is increased as 

the system stiffness of the material of the wall increases 

due to the use of a higher modulus strain-softening 

material. 

5 Conventional Portland Cement Block Studies 

There has been increased interest in using cellular concrete 

materials for stopping construction due to their lower 

density material allowing lighter weight block fabrication 

or larger block sizes. Cellular block were used as the 

baseline for the study. However, stoppings have 

traditionally been constructed from solid concrete masonry 

style blocks (CMU’s) made from conventional Portland 

cement and aggregate materials with a material density of 

1,922 kg/m3

 (120 lbs/ft3). These were also evaluated in this 

study using the same deformable materials that were used 

for the cellular block tests. Figure 12 compares the 

transverse load as a function of the system stiffness for the 

two block types. The results of the CMU blocks were 

different than expected and less consistent than the cellular 

concrete block: 

•	 Lower system stiffness – The half-walls constructed 

from CMU block, which has a compressive strength 

of slightly more than twice that of the cellular block, 

had a lower stiffness and effective modulus. 

Normally, it would be expected that the stiffness 

would tend to increase with increasing compressive 

strength, but that did not happen in this case. It is 

believed that the reason for this apparent discrepancy 

is due to the poorer block dimensional quality control 

with the CMU block. These blocks did not stack 

together well since their thicknesses were not well 

controlled. This created stress concentrations over the 

contact loading surfaces that effectively degraded 

their loading capacity and resulting stiffness of the 

half-wall block column. 
 

•	 Lateral displacement inconsistent with expected 

trend – As was shown in figure 9, an increase in 

lateral displacement should cause a decrease in 

transverse loading. There was little change in lateral 

displacement among the softer materials with the 

CMU tests, and the data indicate a weak trend 

showing increased displacement resulted in higher 

transverse load capacity. For this to happen, the arch 

thrust resultant locations must have been moved 

outward toward the block edges (see figure 6). While 

this is possible, additional testing will need to be 

conducted to confirm this hypothesis. 

 

Cellular Block Wall with Low Preload Conventional CMU Block Wall with Low Preload 

SYSTEM STIFFNESS (WALL AND STRAIN SOFTENING 

MATERIAL), kips/in 

0 20 40 60 80 100 120 140 160 180 200 

TRANSVERSE PRESSURE, psf 

800 

700 

600 

500 

400 

300 

200 

100 

0.0 0 

4.8 

9.5 

14.3 

19.0 

23.8 

28.5 

33.3 

38.0 

TRANSVERSE PRESSURE, kPa 

Conventional 

CMU Block Wall 

Cellular Block Wa l 

0 4 7 11 14 18 21 25 28 32 35 SYSTEM STIFFNESS (WALL AND STRAIN SOFTENING 

MATERIAL), kN/m 

Figure 12. Performance comparison showing the 

transverse load capacity as a function of the system 

modulus between stopping walls constructed from cellular 

concrete blocks and Portland concrete blocks (CMU’s). 

6 Conclusions 

Although ventilation stoppings have considerable load 

resistance, they often cannot fully control the ground 

movement and are still subject to the closure of the mine 

entry. Introducing a deformable material into the stopping 

construction reduces the stiffness of the ventilation 

stopping wall by lowering the effective system modulus. 

This helps to prevent premature failure due to the 

convergence, but will also degrade the transverse load 

capacity of the stopping under arch loading conditions. 

Using a weak foam material as is commonly done now, 

essentially removes the arch loading behavior of the 

stopping, and reduces the transverse load capacity back to 

a freestanding condition of 2 kPa (39 psf). This study 

shows that the transverse load capacity can be preserved by 

using a higher modulus material that is closer to that of the 

block. However, the compromise is that the higher 

modulus material reduces the capability of the stopping 

wall to absorb convergence without failing. 

References 

Barczak, TM and Batchler, TJ, 2006. Development of new 

protocols to evaluate the transverse loading of mine 

ventilation stoppings. Proceedings of the 11th 

U.S/North American Mine Ventilation Symposium, pp. 

569-577 

Barczak TM, 2005. Evaluation of the transverse load 

capacity of block stoppings for mine ventilation 

control (Ph.D. Dissertation, West Virginia University).