This paper describes the results of an experimental investigation on the coefficient of friction at the interface of a PVC–sand–PVC layer that is utilised as part of a low-cost geotechnical seismic isolation devised to be used in low-income countries. The PVC–sand–PVC configuration consists of two smooth PVC surfaces enclosing a single layer of sand grains, with surface densities between 0.5 kg/m2 and 3 kg/m2, which aim to facilitate relative sliding at friction resistance between 0.15 and 0.30 depending on the design acceleration, by acting like “non-perfectly rounded ball bearings”. The latter isolation method has been extensively studied both numerically and experimentally by means of large-scale testing at the shaking table of the EQUALS Earthquake Laboratory of the University of Bristol. However, in the light of the construction of the first building worldwide to be designed and constructed in Nepal with the particular low-cost PVC–sand–PVC sliding interface, it was deemed necessary to reliably assess the mean and dispersion of the coefficient of friction as a function of vertical pressure, sand density and degree of saturation. The results of the tests performed using an improved direct shear apparatus are presented herein using sand samples and PVC sheets that were locally resourced in Nepal to be used in construction. The results indicate that the variation of friction is reasonably low and in any case within the desirable range, irrespectively of the parameters examined, thus establishing confidence to the forthcoming design of the novel isolated building.
Hinweise
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1 Introduction
The vulnerability of buildings to strong ground motion continues to cause significant losses in earthquake-prone countries, especially in low- and moderate-income economies as has been demonstrated after the devastating Mw7.8 earthquake in Nepal in 2015 [1, 2] and the sequence with magnitudes Mw7.8 and Mw7.5 of 6 February 2023 in Turkey–Syria [3]. Apart from the inherent uncertainties associated with seismic performance of structures, this is also a major social and financial issue as it relates to seismic code implementation and quality control enforcement, which are often lacking in these regions. The recent earthquake in Marrakech, Morocco Mw6.8 (8/9/2023) has further stressed the fact that major earthquakes can also occur in regions of moderate assessed seismicity, in which case, the lack of hazard awareness can significantly increase the earthquake loss, particularly if the building stock is dominated by earth/stone masonry and heritage structures.
During the past decades, several efficient methods have been introduced for the pre-earthquake strengthening of existing buildings along with the well-established capacity design approach prescribed in the new generation of seismic codes. However, the problem is still that existing structures (i.e. designed to old versions of the seismic codes or without seismic provisions) form most of the building stock in most seismic-prone regions, whereas the financial burden of seismic upgrade cannot be easily undertaken by the owners. Similarly, new built structures often suffer from poor workmanship and quality control, while more advanced technologies such as seismic isolation are still too expensive and require high expertise to be used for residential buildings at a large scale, even in developed countries.
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Along these lines, research efforts have been made to devise base isolation solutions for enhancing, at a reasonable cost and labour, the seismic performance of buildings in low- and middle-income countries [4‐6] mainly involving recycled rubber fibre-reinforced elastomeric isolators (RR-FREIs), scrap tire rubber bearings [7] and recycled tire isolators and rubber–soil mixtures [8] (see Galano and Calabrese [9] for a detailed review). A separate class of methods, often called geotechnical seismic isolation (GSI) [10, 11], introduces softer, soil-based materials at the foundation level, as a means to initiate sliding during strong shaking and hence limit the amount of seismic energy that is transferred to the superstructure.
In this context, Tsiavos et al. introduced a “sandwich” type of seismic isolation, by encapsulating a thin sand layer [12, 13] between two PVC surfaces right below the foundation of a structure. The sand grains act as “non-perfectly rounded ball bearings”, enabling to decrease and control of the resistance to relative sliding between the two PVC surfaces. The benefit of this approach is that, by controlling the friction coefficient, which can typically vary in the range of 0.15–0.30 for sand plastic interfaces, the threshold of initiation of sliding can match the design acceleration. Note that, even though glass/roller balls are not, strictly speaking, a form of geotechnical seismic isolation, their encapsulation within the PVC surfaces also belongs in the category of a low-cost seismic isolation scheme and can reduce the coefficient of friction to 0.08–0.15 [14].
The above sliding system is essentially a “hybrid” design, where the superstructure, designed as per the provisions of modern codes, is expected to be resisting the design seismic forces (i.e. with probability of exceedance of 10% in 50 years) “as normal” by ductile behavior, while it is allowed to slide on the foundation “fuse”, in case of ground motions acceleration that exceeds the design one. The above series of large-scale tests were complemented (Fig. 1a) by the probabilistic assessment of the structural performance of the system for a large sample of near-field and far-field earthquake motions (Fig. 1b) leading to reliable estimates of maximum and residual foundation displacements [15]. The degree of expected damage with and without the implementation of the PVC–sand–PVC interface was also evaluated. Next, the seismic design of a two-storey “hybrid” (i.e. ductile-sliding) R/C building was undertaken with the aim to proceed with construction in Kathmandu, Nepal, in spring 2023 (Fig. 1c).
Fig. 1
a Large-scale tests of the PVC–sand–PVC system at the University of Bristol; b sample results of the predicted seismic response of a two-storey building resting on the low-cost isolation system [15] and c overview of the construction stage of a school in Nepal using the above system
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The objective of this paper is to present the small-scale experimental campaign that was organised using the direct shear apparatus of the University of Bristol and samples of sand and PVC that were locally resourced from the area of construction in Nepal, with the wider aim to inform the design process with accurate estimates of the friction coefficient. More specific objectives are also to:
(a)
determine the mean and dispersion of the friction coefficient at the sliding interface as a function of its contact stress levels, different surface densities and alternative dry/partially saturated/saturated conditions,
(b)
explore the comparative behaviour at a particle level (i.e. rocking, rolling or sliding) of sands that are different in terms of grain angularity but have similar grading curves [16].
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Both the above side objectives are critical for design of a real structure as the interface friction defines the threshold of system sliding and the upper bound of the acceleration that is transferred to the superstructure. The description of the testing protocol as well as the results obtained are described and discussed in the following.
2 Experimental equipment, materials and procedure
2.1 Testing apparatus
The winged direct shear apparatus (WDSA) has been employed to determine the frictional resistance of the PVC–sand–PVC sandwich system. The WDSA is a modification of the conventional direct shear apparatus (DSA), typically used for soil–soil and soil–interface shear characterisation, developed by Lings and Dietz [17].
A schematic illustration and a picture of the WDSA are provided in Fig. 2, detailing its salient features and the positions of instrumentation. A pair of wings is attached to the sides of the upper frame through which shear load is applied by ball races. The point of application of the load from the shear box to the load cell is near the centre of the sample. Parasitic forces and moments are prevented, and vertical movements can occur unimpeded. This provides an improved articulation of the force transmission and its application in line with the shear plane, such that loads acting on the sheared specimen are more reliably quantified. The above feature has a particular benefit for the determination of friction properties at low to very low stresses [18, 19].
Fig. 2
a Schematic view of the WDSA and b photo of the WDSA
×
For this experimental investigation, the apparatus has been used in a slightly modified configuration if compared to conventional soil–surface shear testing, as shown in Fig. 3. PVC plates have been attached to the top and bottom frames through a series of countersunk screws, such that no protrusion of the screws was allowed. The thin layer of soil to create the PVC–soil–PVC sandwich configuration was placed between the PVC plates.
Fig. 3
Cross-section of the PVC–sand–PVC system shear testing configuration
×
The WDSA accommodates 120 mm × 120 mm frames, although the shearing takes place over an area of 100 mm × 100 mm to avoid any influence of the fixing screws. The WDSA was instrumented with two linear variable differential transformers (LVDTs) to measure horizontal and vertical displacement and an S-type load cell to measure the required shearing force. The vertical load is applied through calibrated dead weights, placed on a weight holder and applied to the specimen through a lever arm.
The sample preparation procedure included the following stages:
1.
Securing using countersunk screw the PVC plates to the bottom and top frames of the WDSA and placement of the bottom frame of the WDSA within the shear carriage of the equipment (Fig. 4a).
2.
Watering the shear carriage gently at ambient laboratory temperature, i.e. between 20 and 22 °C, in cases where tests needed to be carried out under submerged conditions in order to simulate full saturation of the sandwich system.
3.
Pouring, using the dry pluviation method, the required amount of sand on the top of the lower PVC plate. The sand was poured through a stack of sieves (100 mm × 100 mm planar dimensions) of different apertures to ensure its uniform distribution over the area (Fig. 4b). The number and type of sieves were selected upon visual inspection of uniform distribution across the PVC area (Fig. 4c), and the same amount of sieves and height was used in all performed tests.
The sand content is measured through the sand surface density (ρs), which is defined as the mass of the sand (Ms) over a surface area (A):
A visualisation of the amount of sand spread over the surface for the surface densities explored in this research (\(\rho_{{\text{s}}}\) from 0.5 kg/m2 to 3 kg/m2) is shown in Fig. 5.
4.
Lowering gently the upper frame on the top of the soil. Particular care was taken for tests under submerged conditions to avoid that water and soil particles being displaced during this operation (Fig. 4d).
Fig. 4
Overview of the PVC–sand–PVC sample preparation and testing procedure
Fig. 5
Visualisation of LB sand grains for the surface density distributions
×
×
The vertical load was then applied through calibrated dead weights, placed on a weight holder and applied to the specimen through a lever arm, as per conventional direct shear testing. Shearing was applied by moving the bottom frame at a speed of 0.8 mm/min. The reaction force of the top frame, attached to the load through the winged system, was measured during the process.
2.2 Materials
2.2.1 Sand
Four different sets of geomaterials were used in this investigation. A standard UK-sourced material, Leighton Buzzard sand (LB), has been selected for its uniformity and subrounded particle shape. The other three materials were sourced in Nepal and selected for the vicinity of the building site in order to increase sustainability and decrease construction costs. These materials, named NS1, NS2 and NS3, have different particle size distribution curves as well as particle shapes, which were all more angular if compared to Leighton Buzzard sand except NS3. The properties of the four grains of sand are summarised in Table 1, while their particle size distribution is reported in Fig. 6. A visual inspection of the grain shape is also provided in Table 1.
Table 1
Properties of the tested sands
Sand type
Source
D50 (mm)
Coefficient of uniformity
Cu = D60/D10
Coefficient of curvature
Cc = (D30)2/D60 × D10
Grain shape
Photographs
Leighton Buzzard sand (LB)
UK
0.889
1.445
0.960
Subrounded
Nepal sand type 1 (NS1)
Nepal
0.740
4.924
0.665
Angular–subangular
Nepal sand type 2 (NS2)
Nepal
0.767
3.104
1.504
Subangular–subrounded
Nepal sand type 3 (NS3)
Nepal
0.846
1.687
1.028
Subrounded
DX refers to the sand particle size (diameter) at which x% of the material is finer
Fig. 6
Grain size distributions of Nepalese sand (NS1, NS2 and NS3) and Leighton Buzzard (LB) sand
×
2.2.2 PVC plates
Two sets of PVC plates were sourced for the experimental investigations. Commercially available PVC plates available in the UK and widely available PVC from Nepal, respectively, indicated as uPVC and nPVC for the sake of this study (where “u” and “n” stand for the country of material sourcing, i.e. u = United Kingdom and n = Nepal). The properties of the two sets of PVC materials are provided in Table 2. The two PVCs have the same hardness of 85 on the shore D scale [20]. The roughness of the PVC surface was measured using the conventional method of contact profilometry using a Taylor Hobson Form 50 Talysurf [21]. The average roughness Ra for a cut-off length λc of 0.8 mm (corresponding to about the D50 of the four tested soils) suggests that both PVCs are smooth, although the PVC sourced in Nepal has a slightly higher value of roughness. A new set of virgin PVC plates was employed for each individual test described in the following section to eliminate any effect of progressive shearing induced surface damage on experimental results.
Table 2
PVC properties
Material
Thickness (mm)
Density (gr/cm3)
Shore D hardness (%)
Surface roughness
Cut-off λc (mm)
Ra (µm)
uPVC
4.87
1.42
85
0.8
0.223
nPVC
2.47
1.74
85
0.8
0.472
3 Experimental programme
The experimental programme has been divided into three stages.
Stage 1 employed the uPVC and sand sourced in the UK, respectively, uPVC and LB sand, to investigate the repeatability of the results and the potential for low friction sandwich composites. The experimental programme included a suite of 35 tests to investigate the repeatability and influence of several testing conditions, including the sand density ρs between the plates, the applied vertical force or stress level and the saturation degree (fully saturated or dry conditions) on the overall sandwich composite performance. The sand surface density varied between 0.5 kg/m2 and 3.0 kg/m2. The three levels of actual applied vertical loads (98 N, 314 N and 510 N) were selected to result in the nominal vertical stress level of about 10 kPa, 30 kPa and 50 kPa, respectively, which are the expected stress at the foundation level in the Nepal construction. The differences between actual and nominal values occurred as a result of the shear box upper cap mass (1.976 kg) being considered. A list of the performed initial tests is also provided in Table 3. Please note that the name of the test is representative of the material used and the imposed loading conditions: The first four letters refer to the PVC material used (uPVC or nPVC), followed by the sand type (LB, NS1, NS2 and NS3), sand area density (0.5,0.75, 1, 2 and 3 expressed in kg/m2), nominal vertical stress (10, 20 and 30 expressed in kPa) and finally the saturation conditions (D = Dry and S = Saturated). Table 3 further reports the cardinal results for each test, including the applied vertical load (V), the average shear force (Favg) determined over the horizontal displacement range of 2–10 mm for which the shear force will show a stable average and the average coefficient of friction (μavg = Favg/V).
Stage 2 aimed at selecting the best combination of PVC and sand material locally sourced in Nepal. Due to the limited number of PVC samples which could be shipped from Nepal to the UK, the experimental programme first aimed at investigating the friction coefficient of uPVC (PVC from the UK) and the three sourced grains of sand in Nepal in order to select the most suitable geomaterials for field use. This set of tests was carried out at the sand area density of 1 kg/m2. Beyond the design selection process, the use of different soil types enables the investigation of the effect of soil type and particle shape on the overall sandwich performance and provides some insight into the PVC–soil interaction process. A summary of tests is provided in Table 4.
Stage 3 Finally, the best-performing geomaterial Nepalese sand 3 (NS3) was tested in combination with the nPVC (PVC from Nepal) to investigate the variability friction coefficient for a range of stress levels and surface densities in order to support the design and select the optimal configuration. The performed tests are summarised in Table 5. The slight difference in vertical stress between nPVCs and uPVCs is due to the weight difference of the PVC materials.
Table 3
Stage 1: list of tests for uPVC-LB-uPVC and main results
Test no.
Test name
Sand surface density ρs (kg/m2)
Applied vertical load V (N)
Average friction force Favg (N)
Average friction coefficient μavg
Standard deviation of friction coefficient
1R
uPVC_LB_1_21.5_D
1
215.23
29.786
0.138
0.017
2R
uPVC_LB_1_21.5_D
1
215.23
31.996
0.149
0.007
3R
uPVC_LB_1_21.5_D
1
215.23
36.646
0.170
0.020
4R
uPVC_LB_1_21.5_D
1
215.23
31.444
0.146
0.018
5R
uPVC_LB_1_21.5_D
1
215.23
32.173
0.149
0.023
1
uPVC_LB_0.5_10_D
0.50
97.83
13.986
0.143
0.038
2
uPVC_LB_0.5_30_D
0.50
313.57
50.282
0.160
0.029
3
uPVC_LB_0.5_50_D
0.50
509.71
83.428
0.164
0.058
4
uPVC_LB_0.75_10_D
0.75
97.83
14.726
0.151
0.037
5
uPVC_LB_0.75_30_D
0.75
313.57
53.164
0.170
0.031
6
uPVC_LB_0.75_50_D
0.75
509.71
104.135
0.204
0.024
7
uPVC_LB_1_10_D
1
97.83
18.329
0.187
0.058
8
uPVC_LB_1_30_D
1
313.57
49.544
0.158
0.024
9
uPVC_LB_1_50_D
1
509.71
95.283
0.187
0.014
10
uPVC_LB_2_10_D
2
97.83
12.294
0.126
0.023
11
uPVC_LB_2_30_D
2
313.57
44.334
0.141
0.011
12
uPVC_LB_2_50_D
2
509.71
76.627
0.150
0.011
13
uPVC_LB_3_10_D
3
97.83
15.311
0.157
0.020
14
uPVC_LB_3_30_D
3
313.57
53.558
0.171
0.008
15
uPVC_LB_3_50_D
3
509.71
88.263
0.173
0.006
16
uPVC_LB_0.5_10_S
0.50
97.83
15.039
0.154
0.031
17
uPVC_LB_0.5_30_S
0.50
313.57
54.307
0.173
0.023
18
uPVC_LB_0.5_50_S
0.50
509.71
96.082
0.189
0.024
19
uPVC_LB_0.75_10_S
0.75
97.83
17.984
0.184
0.057
20
uPVC_LB_0.75_30_S
0.75
313.57
57.307
0.183
0.028
21
uPVC_LB_0.75_50_S
0.75
509.71
92.055
0.181
0.028
22
uPVC_LB_1_10_S
1
97.83
19.197
0.196
0.023
23
uPVC_LB_1_30_S
1
313.57
58.966
0.188
0.025
24
uPVC_LB_1_50_S
1
509.71
98.386
0.193
0.031
25
uPVC_LB_2_10_S
2
97.83
13.696
0.140
0.032
26
uPVC_LB_2_30_S
2
313.57
47.547
0.152
0.022
27
uPVC_LB_2_50_S
2
509.71
93.658
0.184
0.011
28
uPVC_LB_3_10_S
3
97.83
14.092
0.144
0.012
29
uPVC_LB_3_30_S
3
313.57
56.585
0.180
0.009
30
uPVC_LB_3_50_S
3
509.71
98.861
0.194
0.005
Table 4
Stage 2: list of tests for uPVC-NSs-uPVC and main results
Test no.
Test name
Sand surface density ρs (kg/m2)
Applied vertical load V (N)
Average friction force Favg (N)
Average friction coefficient μavg
Standard deviation
1
uPVC_NS1_1_10_D
1
97.83
27.637
0.283
0.109
2
uPVC_NS1_1_30_D
1
313.57
106.017
0.338
0.054
3
uPVC_NS1_1_50_D
1
509.71
238.519
0.468
0.077
4
uPVC_NS2_1_10_D
1
97.83
22.636
0.231
0.061
5
uPVC_NS2_1_30_D
1
313.57
98.099
0.313
0.117
6
uPVC_NS2_1_50_D
1
509.71
136.466
0.268
0.030
7
uPVC_NS3_1_10_D
1
97.83
13.199
0.135
0.011
8
uPVC_NS3_1_30_D
1
313.57
56.232
0.179
0.010
9
uPVC_NS3_1_50_D
1
509.71
103.428
0.203
0.012
Table 5
Stage 3: list of tests for nPVC-NS3-nPVC and main results
Test no.
Test name
Sand surface density ρs (kg/m2)
Applied vertical load V (N)
Average friction force Favg (N)
Average friction coefficient μavg
Standard deviation
1
nPVC_NS3_1_10_D
1
97.08
17.28
0.178
0.026
2
nPVC_NS3_1_30_D
1
312.83
66.95
0.214
0.031
3
nPVC_NS3_1_50_D
1
508.97
112.99
0.222
0.036
4
nPVC_NS3_1.5_10_D
1.5
97.08
14.76
0.152
0.024
5
nPVC_NS3_1.5_30_D
1.5
312.83
64.13
0.205
0.019
6
nPVC_NS3_1.5_50_D
1.5
508.97
122.66
0.241
0.025
7
nPVC_NS3_2_10_D
2
97.08
14.56
0.150
0.014
8
nPVC_NS3_2_30_D
2
312.83
68.20
0.218
0.013
9
nPVC_NS3_2_50_D
2
508.97
121.13
0.238
0.01
10
nPVC_NS3_2_30_Dry
2
312.8
71.94
0.230
0.011
11
nPVC_NS3_2_30_25%W
2
312.8
73.20
0.234
0.025
12
nPVC_NS3_2_30_50%W
2
312.8
71.01
0.227
0.015
13
nPVC_NS3_2_30_75%W
2
312.8
82.58
0.264
0.016
14
nPVC_NS3_2_30_S
2
312.8
76.95
0.246
0.02
4 Experimental results
4.1 Stage 1: uPVC-LB sandwich system
4.1.1 Repeatability and typical results under shearing
The repeatability of the experimental procedure was investigated for five uPVC-LB sandwich samples tested under the same conditions, by applying a vertical load level of 215.3 N (corresponding to about 21.5 kPa stress level) and using a sand surface density of 1 kg/m2, as reported in Fig. 7. The results are reported in terms of mobilised shear force F versus horizontal displacement d (Fig. 7a); mobilised friction coefficient μ versus horizontal displacement d (Fig. 7b) and the average friction coefficient μavg (with standard deviation reported as error bar) versus the test repeat number (Fig. 7c).
Fig. 7
Repeatability of a shear force and horizontal displacement behaviour; b mobilised friction coefficient and horizontal displacement and c average friction coefficient for uPVC-LB sandwich system at a vertical load level of 215 N and surface density of 1 kg/m2
×
The trends of mobilised shear friction and friction coefficient (Fig. 7a and b) show a steep initial increase followed by a stabilisation around a mean value but still characterised by a pronounced sequence of peaks and troughs. This latter stage of shearing represents the occurrence of shear failure in the system. It is believed that, for an individual test, the fluctuation of the mobilised shear force and friction coefficient with horizontal displacement is due to complex PVC–sand interaction and re-arrangement of particles within the PVC sandwich layer. Nevertheless, the five tests yield to the similar average coefficient of friction μavg between 0.138 and 0.170 (determined over the displacement range 2 mm–10 mm), with standard deviations for individual friction coefficient (i.e. due to the sequence of peak and throughs) ranging between 0.005 and 0.058, as reported in Table 3. The overall average friction coefficient among the five tests is 0.15 with a standard deviation among the five average coefficients of friction of 0.013. This suggests that, while the determination of the friction properties is indeed repeatable, it can be characterised by a scatter which can be quantified in a variation between about 0.01 and 0.02 (roughly corresponding to about 10% of the determined friction coefficient).
4.1.2 Effect of submerged condition
The effect of saturation conditions (fully submerged in water and dry) was carefully investigated for all the tested conditions explored in the experimental Stage 1. A typical comparison between the two conditions in terms of mobilised shear force versus horizontal displacement and mobilised friction coefficient versus horizontal displacement is reported in Fig. 8a and b for the uPVC-LB configuration with a surface density of 3 kg/m2. The overall force–displacement and friction–displacement behaviour do not show considerable differences, although it appears that the submerged samples typically exhibit slightly higher resistance to shearing. Figure 8c reports a direct comparison of all the average friction coefficients for the dry and water-submerged samples, and it suggests a systematic increase in the friction coefficient by about 10% for the fully submerged conditions. This may imply that the water slightly acts as an anti-lubricant within the tested system.
Fig. 8
Effect of saturation conditions (dry versus water-submerged samples) for a mobilised shear force versus horizontal displacement behaviour; b mobilised friction coefficient versus horizontal displacement behaviour and c comparison of average friction coefficient for uPVC-LB sandwich system, dry versus submerged conditions
×
4.1.3 Effect of stress level
The typical effect of the stress level on the overall response of the uPVC-LB sandwich system is reported in Fig. 9 for the surface density of 2 kg/m2 and nominal stress levels ranging between 10 and 50 kPa, which corresponds to the expected vertical pressure of the building under design at the level of the foundation. As anticipated, for friction-dominated phenomena, the mobilised shear force increases with the applied vertical load (Fig. 9a). However, the overall values of the mobilised friction coefficient seem also to increase with the stress level, as shown in Fig. 9b and c. As discussed by Fang et al. [16], the movement pattern between the soil particles is affected by the stress level of the PVC–sand particles, as larger contact stresses may increase the penetration (or indentation) of the sand grains within the PVC, thus opposing the particle rolling or sliding during shearing. For the value of mobilised friction recorded here, typically at or below 0.15, it is believed that particle sliding is the main movement pattern. The occurrence of particle sliding was also visually observed through some analogous testing using a transparent plexiglass plate, while other occasional phenomena such as particle rolling, rotation and interaction (including the release of built-up stress) were also observed. Figure 9a and b also shows a decrease in the fluctuations of the mobilised shear force and friction coefficient with the stress level, which can be related to the relative variability of the shear force with respect to normalisation for its main value. These fluctuations can be quantified through the standard deviation of the mobilised friction coefficient, over the displacement range of 2 mm–10 mm, which decreases with increasing stress level as shown by the error bars in Fig. 9c.
Fig. 9
a General mobilised shear force and horizontal displacement behaviour of the uPVC-LB sandwich system; b relationship between mobilised friction coefficient and horizontal displacement of uPVC-LB sandwich system and c variations of average friction coefficient versus vertical stress levels of uPVC-LB sandwich system
×
Figure 10 reports the trends of variation of average friction coefficient and its standard deviation with stress level for all the tests performed on the uPVC-LB configuration under dry conditions and submerged conditions. Despite some minor deviations that are attributed to the variability of experimental results, the trends of (i) slight increase in friction coefficient with increasing stress level and (ii) decrease in standard deviation (i.e. fluctuation) of friction coefficient with increasing stress level are confirmed throughout the investigated testing conditions.
Fig. 10
Variations of average friction coefficient versus vertical stress for dry (a) and submerged (b) testing conditions. Standard deviation of friction coefficient versus vertical stress for dry (c) and submerged (d) testing conditions
×
4.1.4 Effect of surface density
Figure 11 provides a comprehensive overview of the experimental results by comparing mobilised friction coefficient trends versus horizontal displacement for the five values of sand surface densities adopted at different stress levels tested under dry conditions. The result suggests that there is no clear trend of average friction coefficient with the surface density, while it appears that the variability of the friction coefficient decreases when a larger number of soil particles (large surface density values) is involved in the shearing. This may indeed not be surprising as a larger number of soil–plastic contacts may hide local or occasional build-up and release of stresses. The trends provide a visual confirmation that the fluctuation of mobilised friction decreases with the stress level.
Fig. 11
Trends of mobilised friction coefficient versus horizontal displacement for uPVC-LB sandwich system for different surface density and three stress levels of a 10 kPa; b 30 kPa and c 50 kPa
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Figure 12 provides trends of average and standard deviation of friction coefficient with the surface density for all tests of experimental Stage 1 under both submerged and dry testing conditions. It can be observed that there is no clear trend of average friction coefficient with sand surface density (ρs) but its variability decreases with larger sand amounts. For low stress levels, standard deviation of the friction coefficient up to 0.06 can be observed, while this variability considerably decreases for density in excess of 1 kg/m2, especially for the higher stress levels (i.e. 30 and 50 kPa). The occurrence of large peaks for the friction resistance may be an issue for the field application of the technique, although it is unsure whether peaks may disappear when full-scale conditions (shearing over much larger areas than the 100 mm × 100 mm element tested in this research) are considered, such that performance of further tests on much larger specimens is currently under planning. Nevertheless, on the side of caution, it was deemed more appropriate to consider surface densities in excess of 1 kg/m2 to minimise the variability of the friction properties for the PVC–sand–PVC sandwich system.
Fig. 12
Variations of average friction coefficient versus surface density for dry (a) and submerged (b) testing conditions. Standard deviation of friction coefficient versus surface density for dry (c) and submerged (d) testing conditions
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4.2 Stage 2: comparison of different sand types
Stage 2 aimed at selecting the most suitable sand type for use in the case study in Nepal. Due to the limited availability of PVC and difficulty in shipping, the initial sand selection procedure has been carried out by analysing the friction properties of sandwich systems composed of the PVC sourced in the UK (uPVC) and the three-sand bulk sourced in Nepal. Following the findings of Stage 1, for this selection exercise, the tests have been carried out using a sole sand surface density and dry conditions.
Figure 13 compares the friction results of the sandwich system with the three sands from Nepal as well as the Leighton Buzzard sand, included for benchmarking purposes. Visual inspection of the force–displacement curve immediately suggests that the use of NS1 and NS2 would result in much higher mobilised friction coefficient values if compared to the previously tested LB, while NS3 provides values in the similar order of magnitude. A summary and direct comparison of the average friction coefficient for all four sand types are provided in Fig. 14. Figure 14a presents the evolution of the average coefficient with the stress level for all types of sand. For all the soil, there is a typical trend of coefficient friction increase with the stress level, with values of NS1 and NS2 much higher than those for NS3 and LB which are approximately similar. It should be noted that while NS3 and LB are rather similar in terms of both particle size distribution (Fig. 6) and grain shape (rounded/subrounded) (Table 1), NS2 and NS1 sands are characterised by much more inhomogeneous and angular particles (subrounded/subangular and subangular/angular, respectively). Figure 14b provides trends of the average friction coefficient versus the particle shape, clearly suggesting that particle shape may have a primary role in the friction properties of the sandwich system.
Fig. 13
Trends of mobilised friction coefficient versus horizontal displacement for the uPVC-NS-LB sandwich system for 1 kg/m2 surface density and three stress levels of a NS1; b NS2; c NS3 and d LB sands
Fig. 14
Trends of a average friction coefficient versus stress level for different sand types and b average friction coefficient versus particle shape
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It is believed that particle angularity can increase local indentation upon the application of the vertical load to trigger larger ploughing of the PVC surface upon the application of relative shear displacement between the two PVC plates. Graphs like those in Fig. 14b could be further used for a preliminary assessment of the expected friction coefficient and initial selection of the sand material, given PVC plates of similar properties.
4.3 Stage 3: nPVC and NS3 sandwich system
Following the results of Stage 2, Nepal sand NS3 was selected for the field application, and the properties of the nPVC-NS3 sandwich system are studied here, and the experimental results are reported in Fig. 15. The use of the PVC sourced from Nepal (nPVC) results in a slightly higher friction coefficient than the uPVC, with the same type of sand. For example, the average friction coefficient for the uPVC-NS3 configuration was 0.173 for 1 kg/m2 surface density rising to about 0.205 for the nPVC-NS3 configuration. This difference is expected to be linked to the higher waviness of the nPVC if compared to the flatter uPVC. The results also show that adopting larger surface densities do not change the friction coefficient but minimise its variability. It could be conjectured that the use of more particles decreases any local effect of waviness due to the presence of a thicker sand layer. Therefore, the sand surface density of 2 kg/m2 was selected for the field application to decrease the expected scatter and possibility of occurrence of high friction peaks.
Fig. 15
Trends of mobilised friction coefficient versus horizontal displacement for nPVC-NS3 sandwich system for different stress levels and surface densities of a 1 kg/m2; b 1.5 kg/m2; c 2 kg/m2 and d overall results of average friction versus surface density
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Finally, the effect of the presence of moisture within the system was investigated by mixing with different amounts of water. Amount of water is defined though the water content w:
where Mw is the mass of water, and Ms is the mass of sand. Water contents of 0%, 25%, 50%, 75% and fully submerged samples have been imposed, and the results are reported in Fig. 16. The results show that low amounts of water have negligible influence on the friction resistance but high water content and submerged conditions lead to increase of about 10–15% in line with the findings for the uPVC-LB sand in the previous Sect. 4.1.2. High values of friction coefficient of 0.264 are recorded for w = 75%, rising from a friction coefficient of 0.230 for dry conditions.
Fig. 16
Trends of a mobilised friction coefficient versus horizontal displacement for nPVC-NS3 sandwich system for water content and b average friction coefficient versus water content
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5 Conclusions
An experimental programme has been carried to investigate the performance and select the appropriate material for a novel low-cost seismic isolation, made up of a PVC–sand–PVC sandwich configuration, to be used in a real building application in Nepal. The PVC–sand–PVC configuration consists in two smooth PVC surfaces enclosing a small amount of sand (surface densities between 0.5 kg/m2 and 3 kg/m2) which, through an effect analogous to “non-perfectly rounded ball bearings”, should facilitate relative sliding at low friction resistance.
The experimental investigation carried out using an improved direct shear apparatus (WDSA), has focussed on the investigation of the achievable friction coefficients for the sandwich system and the factors affecting its value. In view of field applications, the experimental programme has considered a range of materials available in the UK and Nepal. The following conclusions could be drawn:
The experimental procedure for preparation and testing of the PVC sandwich system is deemed adequately rigorous, given that it led to repeatable experimental outcomes.
By selecting appropriate smooth PVC and sand materials, low friction coefficients between about 0.15 and 0.20 could be achieved in this research. This is key for practical applications.
The value of the friction was found to be dependent on the applied stress level, with higher frictions induced by higher stress level, as anticipated due to the partial indentation of sand grains within the PVC layers.
The friction resistance showed fluctuation and a degree of variability during sliding, possibly related to local phenomena of particles sliding, rolling and build-up/release of stresses. The use of a larger amount of sand (surface densities between 1 kg/m2 and 3 kg/m2) was found beneficial for reducing these fluctuations.
The presence of water within the system was found to act as an anti-lubricant with the coefficient of friction typically being 10% higher than the respective dry conditions. High values of moisture content were also found to increase the friction resistance, by about 10% for the investigated conditions.
The properties of the constituent materials for the sandwich systems govern the overall friction resistance. Among others, the shape of particles was found particularly important: the use of sands when sub-angular/angular particles were found to double the value of friction coefficient if compared to rounded/subrounded particles.
Overall, this study helped in selecting the appropriate PVC and sand materials to be used for low-cost seismic isolation of a building to be constructed in Nepal. Locally available PVC and rounded sand, dispersed at a surface density of 2 kg/m2, were selected, yielding to friction coefficient between 0.22 and 0.26 for the expected stress levels and moisture conditions at the site. Note that the above friction values are close to the design seismic coefficient at the site of interest.
The reasonably stable estimate of the coefficient of friction further shows that careful selection and testing of the sand to be used in practical design applications can establish confidence on the process. Furthermore, given that the “hybrid” (i.e. ductile-sliding) system discussed herein uses the sliding foundation as an additional “fuse” rather than as an explicit force reduction mechanism, the coefficient of friction does not need to be defined with absolute accuracy, and as such, the experimentally observed dispersion around its mean value is deemed tolerable. Besides, the desired isolation effect has been achieved owing to a single layer of sand thickness using as low as possible materials, which is environmentally sustainable, while creating a low-cost flat slider that efficiently executes in the field. It should be noted that the sand layer does not exhibit typical behaviour but behaves as a bearing surface. While the pilot application into a building is ongoing, further studies at the fundamental level will aim at unravelling the micro-mechanism of PVC–sand interaction and expand the experimental work presented in this paper, including testing larger PVC–sand–PVC specimens.
Acknowledgements
The authors would like to acknowledge the contribution of the National Society for Earthquake Technology in Nepal, particularly Dr. N. Marashini, Dr. S.N. Shrestha, Dr. H. Shrestha, Dr. Manandhar and Dr. R. Guragain, as well as the Global Challenges Research Framework for supporting the research project Seismic Safety and Resilience of Schools in Nepal (SAFER, EP/P028926/1).
Declarations
Conflict of interest
The authors have no relevant financial or non-financial interests to disclose.
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