The paper presents the design of a calibration chamber, developed for the testing of a novel self-burrowing probe for in situ soil investigation. The self-burrowing probe is currently under development at ETH Zurich, and its key components will be proof-tested in the controlled environment of the developed chamber. The design of the latter incorporates specific solutions for the testing of the probe: the chamber is equipped with a central opening at the top and base plates, enabling the probe to vertically protrude from the chamber. This aspect is useful for eliminating the tip resistance of the probe and isolating its response, which is relevant when assessing the resistance of the probe’s anchoring system or, in general, for the evaluation of interface properties. The chamber allows for testing under two boundary conditions: (i) zero lateral strain or (ii) constant lateral stress. In the latter case, the radial stress is applied by water pressure inside a membrane, while a pneumatic, doughnut-shaped cushion at the base is used to impose the vertical stress. The paper outlines the key components of the chamber, the sample preparation, and the testing procedures, along with the results of the proof tests conducted in dry Perth sand.
1. Introduction
Geotechnical calibration chambers have proven to be an effective tool for the development and verification of in situ testing instrumentation, such as cone penetrometers and pressuremeters (Ajalloeian and Yu, 1998; Jamiolkowski et al., 2003; Salgado et al., 1998; Schnaid and Houlsby, 1992). The onset of calibration chambers can be traced back to the one designed for the Australian Country Road Board in 1969 (Holden, 1971) and the one developed at the University of Florida in 1970 (Reese, 1975). The proceedings of the first symposium on calibration chamber testing in 1991 contain valuable insights into early-stage calibration chamber testing. In the following years, similar chambers were developed with varying complexity, dimensions, stiffness, boundary conditions, and sample preparation methods, as well as the capability to handle saturated and partially saturated samples (Salgado et al., 1998). Mechanically detailed descriptions of calibration chamber design can be found in the work of Bellotti et al. (1982) and Sweeney and Clough (1990). The majority of early calibration chambers were used to derive deeper insights into the interpretation of cone penetration test (CPT) results in cohesionless soil. In that context, most of the relevant studies focused on assessing the effect of chamber size on CPT results (Been et al., 1986; Houlsby and Hitchman, 1988; Salgado et al., 1998; Schnaid and Houlsby, 1991; Wesley, 2002).
Recent developments of calibration chambers have proposed novel design concepts and advanced measuring techniques, focusing on testing of a wider variety of soils. Fleischer et al. (2012) describe the development of a small-volume calibration chamber at the University of Bremen for mini-CPT testing, using circumferential laser triangulation sensors and glass windows. Characteristic is also the example described by Galvis-Castro et al. (2019), who outline the testing of model piles using digital image correlation, along with an observation window in the half-cylindrical calibration chamber of Purdue University. Moreover, Pournaghiazar et al. (2011) describe the development of a chamber at the University of New South Wales, capable of testing variably saturated sand samples by applying controlled suction. Finally, Ayala et al. (2020) and Wiklund (2024) describe the development of calibration chambers for testing of mine tailings materials at the University of Western Australia and at Luleå University of Technology, respectively.
These examples are indicative of the capabilities of calibration chambers for an effective and systematic investigation of the response of soil under controlled loading conditions. Within the scope of designing and testing a novel self-burrowing probe for in situ soil investigation at ETH Zurich (ETHZ), a new calibration chamber has been developed. It aims at evaluating the performance of the probe in the controlled environment of a calibration chamber. Similar to previous research on the subject (Borela et al., 2021; Chen et al., 2021; Martinez et al., 2020; Tao et al., 2020; Winter et al., 2014), the self-burrowing probe targets autonomous subsurface movement: an anchoring unit is designed to generate the necessary reaction of the surrounding soil mass, allowing for self-penetration of the probe. With a diameter of 100 mm, the anchoring unit consists of four rigid steel blocks, equally spaced at 90°, that extend radially in the surrounding soil (Alber and Anastasopoulos, 2020). In the newly developed calibration chamber, soil samples of controllable relative density and repeatable fabric are prepared and subjected to strictly controlled boundary conditions and applied stress paths. This allows testing of the anchoring unit at 1:1 scale, which forms an essential step for the development of the self-burrowing probe. This paper presents the design and development of the calibration chamber, targeting this specific application, describing in detail its key components and all the procedures required for testing, as well as the corresponding setup for sample preparation. Preliminary tests of the anchoring unit in dry, dense Perth sand are presented, serving as proof-of-concept of the developed calibration chamber.
2. Calibration chamber design
As depicted in Figure 1, the design of the calibration chamber is based on well-established chamber concepts found in literature, while incorporating the necessary features for testing of the self-burrowing probe. Similar to the concept described by DeJong (2001) and Martinez and Frost (2017, 2018), the chamber includes a central, circular perforation at the top and bottom of the device. However, the chamber developed herein also allows for application of vertical stress at the base, which, in combination with the double-perforation and the chamber size, results in a challenging design, as most components need to be ‘doughnut-shaped’. This includes, for instance, the rigid base plate, which is supported by a special pedestal construction, and the pneumatic cushion, which is used to generate the vertical stress at the base of the chamber. On the contrary, this double perforation allows for crucial testing advantages: the self-burrowing probe can protrude vertically from the top and bottom of the chamber, thus avoiding the mobilisation of any tip resistance when the probe is vertically pushed for the testing of the resistance of the anchoring system. In the presence of tip resistance (as would be the case with existing calibration chamber designs), isolating the resistance of the anchoring unit would be challenging, complicating the interpretation of the results of vertical push tests of the self-burrowing probe. Avoiding the generation of tip resistance, the double-perforation design is of equal importance for interface tests. Using the loading frame and the electric actuator positioned on the rigid cap, the self-burrowing probe can be vertically pushed. With a soil sample of 670 mm dia. and 730 mm height, the entire experimental setup (including the loading unit) weighs ∼900 kg in its empty state, accommodating a soil volume of 0.26 m3 (corresponding to about 450 kg in the case of dense Perth sand).
The image depicts a vertical experimental apparatus designed for material testing, featuring a cylindrical tank with a broad base and a narrower upper section. At the top, an electric actuator is mounted on a loading frame, positioned above the tank. The cylindrical unit includes several labelled components, such as a Rigid cap, Sample former, Anchoring unit, and Loading plate. Inside the tank, a Membrane and a Pneumatic cushion are shown, with Cell pressure indicated as a function of the system. The tank dimensions include measurements of 670 millimetres and 730 millimetres. The background illustrates equipment settings such as monitors and wiring, indicating a laboratory environment for conducting experiments.Outline of the developed calibration chamber: photo (left) and schematic cross-section (right)
The image depicts a vertical experimental apparatus designed for material testing, featuring a cylindrical tank with a broad base and a narrower upper section. At the top, an electric actuator is mounted on a loading frame, positioned above the tank. The cylindrical unit includes several labelled components, such as a Rigid cap, Sample former, Anchoring unit, and Loading plate. Inside the tank, a Membrane and a Pneumatic cushion are shown, with Cell pressure indicated as a function of the system. The tank dimensions include measurements of 670 millimetres and 730 millimetres. The background illustrates equipment settings such as monitors and wiring, indicating a laboratory environment for conducting experiments.Outline of the developed calibration chamber: photo (left) and schematic cross-section (right)
2.1 Boundary conditions and stress application
It is well known that the response of a device tested in a calibration chamber is strongly affected by the circumferential boundary conditions of the soil specimen (Salgado et al., 1998). Even though boundary effects are more significant for dense sand, Schnaid and Houlsby (1991) have concluded that such effects are present for any sand density. The literature includes recommendations for a minimum chamber diameter in function of the diameter of the device to be tested (Ajalloeian and Yu, 1998; Ayala et al., 2020; Mayne and Kulhawy, 1991; Sweeney and Clough, 1990). Given the 100 mm dia. of the self-burrowing probe (which is significantly larger than typical devices tested in calibration chambers), following such recommendations would result in a very large calibration chamber. The latter would be excessively costly and operationally challenging and would also require a larger capacity (floor strength) and lab space height, which was not readily available at ETHZ. Therefore, a compromise was made with respect to the size of the chamber, accepting that the chamber tests will not be immune to boundary effects. The latter will be alleviated by combining experimental and numerical modelling: the calibration chamber test results will be used to validate advanced numerical models, which will be subsequently employed to analyse the real problem with the boundaries extended to (numerical) infinity, thus indirectly alleviating boundary effects.
The chamber allows for two different types of lateral boundary conditions: (i) zero lateral strain (rigid wall chamber) or (ii) constant lateral stress (flexible wall chamber), using a rubber membrane to impose lateral confinement. In the latter case, water pressure is applied through the membrane package, controlling in this way the radial stresses imposed on the sample. Thanks to the modular design of the membrane package, it can be removed, allowing for the chamber to be used in the rigid wall configuration. The advantage of the latter is the simpler setup, which allows faster preparation of the test. The key disadvantage is the absence of control of lateral stresses. In both cases, the vertical stress in the soil specimen is generated through a pneumatic cushion installed at the bottom of the chamber. The cushion pushes vertically a rigid loading plate in the direction of the soil, which is confined by the rigid cap at the top. The pneumatic cushion was chosen instead of a hydraulic cylinder, as it has a much smaller installation height, and it can also accommodate the doughnut-shaped geometry of the base plate while offering a more distributed load transfer to the loading plate. With the pneumatic cushion and the water pressure, the chamber offers an independent control of lateral and vertical confining pressures acting on the specimen.
3. Calibration chamber components
3.1 Chamber tank
The tank of the calibration chamber is a rigid steel cylinder with flanges on the top and bottom. To achieve water-tightness, rubber O-rings are installed in specially machined grooves on these flanges, complemented by bolted connections between the cap and the base plate to the corresponding flanges. The tank is a repurposed strong box, coming from the former centrifuge centre at RUHR University Bochum. After polishing and galvanising (to remove and prevent rust in the future), it is of 746 mm inner diameter, with a wall thickness of 12 mm, and 750 mm height. Four stiffening plates are positioned at an angle of 90° around the central axis to increase its radial rigidity.
3.2 Chamber top and bottom
The top cap consists of a ‘sandwich’ structure, composed of two circular stainless-steel plates, connected to each other by means of three load cells. In this way, the lower plate that is in contact with the specimen transfers the stresses developing in the soil through the load cells to the upper plate (and therefore facilitates their measurement), which is tightly screwed via bolt sleeves to the tank. Both plates encompass a central perforation of 120 mm dia. and are equipped with stiffening beams, welded to their upper surface to limit deformations. At the bottom of the chamber, the tank is mounted on a stainless-steel base plate, founded on a pedestal construction. The latter allows for distribution of the weight of the entire assembly to a larger floor area (at its maximum weight the chamber together with the raining system and the soil reaches 1.8 t), facilitating access to the bolts and the pressure supply below the main body of the chamber. Besides the central 120 mm dia. perforation, the base plate also encompasses several core holes, necessary for the installation of various mechanical components (such as the membrane package and the linear variable differential transformers) on the inside of the chamber. Due to all these holes in the base plate, an assembly of stiffening beams was designed and welded underneath the plate to limit its flexural deformation during sample loading. Guide brackets that are mounted at the top and bottom perforation serve the purpose of closing the gap between the probe (or any device to be tested) and the perforated plates, helping to keep the probe in position during the test.
3.3 Membrane package
A custom-vulcanised membrane made out of natural rubber (Super Para) is employed to apply the water cell pressure inside the chamber. As shown in Figure 2, the membrane is cylinder-shaped, having a diameter of 690 and a 1 mm thickness. The cylindrical shape is achieved by vulcanising a rubber sheet, which unavoidably requires an overlap area. To avoid irregularity, the thickness of the resulting double-thickness rubber sheet in this area is locally reduced to maintain the 1 mm thickness. A total of 72 holes were manually punched along the perimeter at the upper and lower ends of the rubber membrane, necessary to clamp the membrane between a pair of stainless-steel rings, making a ‘ring-sandwich’ structure composed of a flat steel ring, an NBR sealing ring, the rubber membrane, and an additional flat steel ring. This ‘ring-sandwich’ structure is then bolted to the base plate on the inside of the chamber, while the opposite end of the rubber membrane is fixed in the same manner to an L-shaped steel ring, which is placed directly on top of the upper flange. Such modular design of the membrane package allows for easy replacement or removal of the membrane in the case of the rigid wall configuration. If the membrane package is used for multiple chamber tests, its functionality is checked between consecutive tests, using a ‘dummy’ specimen. The latter is composed of a hollow wooden cylinder, capable of offering the necessary reaction force to the water pressure exerted by the membrane.
The image depicts an interior view of a cylindrical structure, illustrating several components. The Upper flange is located at the top, while a Rubber membrane is positioned below it. The Base plate is at the bottom and shows a circular shape with a central hole. An L-shaped steel ring is visible along the inner walls, and a ring-sandwich component is located along the lower edge. The components are clearly marked with labels to indicate their specific functions within the structure. The layout allows clear observation of how these parts fit together.Photo of the membrane package under vacuum pressure
The image depicts an interior view of a cylindrical structure, illustrating several components. The Upper flange is located at the top, while a Rubber membrane is positioned below it. The Base plate is at the bottom and shows a circular shape with a central hole. An L-shaped steel ring is visible along the inner walls, and a ring-sandwich component is located along the lower edge. The components are clearly marked with labels to indicate their specific functions within the structure. The layout allows clear observation of how these parts fit together.Photo of the membrane package under vacuum pressure
3.4 Pneumatic cushion
The vertical loading is achieved through a custom-vulcanised, doughnut-shaped pneumatic cushion (Figure 3). With an inner diameter of 190 mm and an outer diameter of 580 mm, the cushion is made out of coated, fibre-reinforced nitrile-PVC. In order to be stable when inflated, it is fixed by several threads to the base plate of the chamber, through which the air pressure is also supplied. A key advantage of the pneumatic cushion is its very small height, which does not exceed 15 mm in the uninflated state. The price to pay is the dependence of the imposed vertical force, not only on the supplied air pressure but also on the inflation height. The increase of air pressure leads to an axial extension of the cushion, which is unavoidably accompanied by a certain bulging, leading to a decrease of its contact area with the loading plate on top. This requires a calibration procedure to give a correlation of the force imposed on the soil specimen at the bottom of the chamber as a function of inflation pressure and stroke (i.e. inflation height). The cushion has a maximum operating air pressure of 10 bar, resulting in a maximum theoretical force of 200 kN, while the maximum applicable stroke reaches 50 mm.
The image depicts a large metallic base structure designed for industrial use, situated in a workshop environment. At the centre of the design is a circular base plate, which is covered by a black pneumatic cushion. The base plate is surrounded by a pedestal construction consisting of steel panels forming a circular shape with gaps cut out, allowing visibility to the floor beneath. Various tools and items surround the component, providing context for the workshop setting. The structure edges show wear from previous use, indicating its application in a practical context. The overall focus is on the mechanical and structural aspects of the component.Photo of the pneumatic cushion installed on the base plate
The image depicts a large metallic base structure designed for industrial use, situated in a workshop environment. At the centre of the design is a circular base plate, which is covered by a black pneumatic cushion. The base plate is surrounded by a pedestal construction consisting of steel panels forming a circular shape with gaps cut out, allowing visibility to the floor beneath. Various tools and items surround the component, providing context for the workshop setting. The structure edges show wear from previous use, indicating its application in a practical context. The overall focus is on the mechanical and structural aspects of the component.Photo of the pneumatic cushion installed on the base plate
3.5 Loading plate
Made out of stainless steel, the doughnut-shaped loading plate (of 670 and 125 mm, inner and outer diameter, respectively) is placed between the pneumatic cushion and the soil specimen, facilitating homogenised transmission of the imposed load. To prevent loading of the cushion at its uninflated state, protective spacers are installed to support the loading plate. A cylindrical bracket is fixed on the central perforation of the base plate, serving as a guide that maintains horizontality of the loading plate while the latter is moving in the vertical direction by the force exerted by the pneumatic cushion. The upper and lower surfaces of the loading plate experience evenly distributed pressures, thanks to the contact with the cushion on the lower side and the soil specimen on the upper side, thus allowing for a relatively small thickness of 15 mm of the plate without the need for stiffeners. The upper surface of the plate incorporates porous stones and an inner channel system, which can be used for sample saturation (not discussed herein).
3.6 Sample former
The design described by Pournaghiazar et al. (2011) is adopted for the sample former. It comprises four curved, stainless-steel shell elements of 3 mm thickness and 690 mm height, with a width of one quarter of the membrane perimeter. As illustrated in Figure 4, the shell elements are installed between the tank and the membrane package (not shown herein), functioning as a jacket support for the membrane and the specimen during the filling process. Once this is completed, an adequate cell pressure is applied, undertaking the lateral support of the soil specimen, and the sample former is retracted towards the chamber wall. To facilitate such lateral movement, the shell elements of the sample former are connected to a crank system outside the chamber, which allows their manual movement towards or away from the centre of the chamber. The shell elements of the sample former have a perforated surface and rubber covers on the edges, thus facilitating its movement within the pressurised water without damaging the membrane.
The image depicts a top view of a cylindrical tank designed for industrial use. Several parts are labelled, including a Rubber cover at the top, Shell elements arranged around the interior, and the Tank structure. The tank shows numerous holes along the outer edge, indicating points for securing or connecting other components. The structure appears metallic with a smooth interior surface, while the background includes various tools and items, suggesting an engineering or workshop environment. The labels are positioned to clearly indicate the location of each component within the tank.Photo of the sheet elements of the sample former inside the calibration chamber
The image depicts a top view of a cylindrical tank designed for industrial use. Several parts are labelled, including a Rubber cover at the top, Shell elements arranged around the interior, and the Tank structure. The tank shows numerous holes along the outer edge, indicating points for securing or connecting other components. The structure appears metallic with a smooth interior surface, while the background includes various tools and items, suggesting an engineering or workshop environment. The labels are positioned to clearly indicate the location of each component within the tank.Photo of the sheet elements of the sample former inside the calibration chamber
3.7 Loading frame
The loading frame offers the necessary support system for the electric actuator, which is deployed to push the probe (or any device to be tested) vertically into the specimen. The frame is bolted to the tank through the same connections that are used for mounting the top cap to the tank. In this way, the tank provides the reaction to the loading frame, keeping the forces internal and minimising the load that is transferred to the floor. The actuator has a maximum stroke of 200 mm and a maximum axial traction/thrust force of 55 kN. At the front of the piston rod, a load cell of 56 kN maximum capacity is attached. A laser sensor is installed in the loading frame, targeting a thin aluminium plate for measuring the vertical displacement of the actuator.
3.8 Control and data acquisition
LabView of National Instruments is used for the control and data acquisition during calibration chamber tests (Figure 5). The cell pressure in the membrane, as well as the air pressure in the cushion, is controlled and measured by digital pressure regulators and gauges. For the membrane pressure, an air–water reservoir is used to convert the air pressure into water pressure. The top cap incorporates three load cells of 100 kN maximum nominal capacity, which are used to record the vertical stresses that reach the top of the chamber. The 120° spacing between the load cells allows monitoring of the uniformity of the loading of the sample. Three linear variable differential transformers (LVDTs) are placed underneath the loading plate to track its vertical movement, which is equal to the inflation height of the pneumatic cushion and the vertical deformation of the soil specimen. Their 120° spacing around the central axis of the chamber allows for monitoring of any tilting of the loading plate. Three additional ‘bending’ LVDTs are placed underneath the base plate, measuring its flexural deformation. On the inside of the bottom plate of the chamber, a pressure mapping sensor is installed for direct measurement of the developing vertical stresses at the bottom of the soil specimen.
The diagram depicts a detailed experimental setup for measuring pressures and forces. It includes an air-water reservoir on the left connected to a laboratory air pressure line with pressure regulators and gauges. Central to the setup is a tank or container that houses load cells, a laser transducer, and a pressure mapping sensor. Below, the structure features bending L V D T s and standard L V D T s for measuring displacements. Data is transmitted to a Data acquisition system, D A Q, shown on the far right. The layout is systematic, guiding from the air reservoir to the measuring instruments in a top-down flow, with connections illustrated by lines showing the pathways of pressure and data transmission.Schematic illustration of the control and data acquisition system of the calibration chamber
The diagram depicts a detailed experimental setup for measuring pressures and forces. It includes an air-water reservoir on the left connected to a laboratory air pressure line with pressure regulators and gauges. Central to the setup is a tank or container that houses load cells, a laser transducer, and a pressure mapping sensor. Below, the structure features bending L V D T s and standard L V D T s for measuring displacements. Data is transmitted to a Data acquisition system, D A Q, shown on the far right. The layout is systematic, guiding from the air reservoir to the measuring instruments in a top-down flow, with connections illustrated by lines showing the pathways of pressure and data transmission.Schematic illustration of the control and data acquisition system of the calibration chamber
4. Sand pluviator
Stationary air pluviation is adopted for the preparation of the dry sand specimens, as it has been widely and successfully used in calibration chamber testing (Bellotti et al., 1982; Jacobsen, 1976; Sweeney and Clough, 1990). Similar to the concept described by Richards (2019), the developed raining system consists of an additional tank, identical to that of the main body of the calibration chamber, along with a hopper (containing the sand i.e. to be filled) fixed on top of the additional upper tank (Figure 6). The hopper encompasses a perforated base plate with an equilateral triangular grid of holes (20 mm hole diameter and 60 mm centre-to-centre pitch). It is connected through roller supports to a perforated shutter plate, which is fixed on top of the additional upper tank. The two perforated plates have matching hole patterns, which are initially not aligned (preventing any flow of sand) and are aligned by lateral movement of the hopper when raining is performed. To allow adjustment of the mass flow rate, interchangeable, perforated Plexiglas sheets with holes of smaller diameter (10, 5 and 2.5 mm), but of the same centre-to-centre pitch, are installed inside the hopper. Furthermore, a thin diffuser mesh with 5 mm wide squared openings and an 8 mm centre-to-centre pitch is inserted in the upper tank, at a distance of 420 mm from the shutter plate. The additional upper tank allows for sufficient falling height in order to reach terminal velocity and therefore uniformity of the sand specimen with height, while also preventing dust dispersion in the surrounding environment. Since the pluviator is in a fixed position, the drop height of the sand varies during the raining process, resulting in a minimum clearance of 750 mm when the calibration chamber is almost fully filled. For complete pluviation of the chamber, the hopper has to be refilled multiple times, due to its limited size and the big residual of sand in the hopper after each pluviation cycle.
The image depicts a piece of equipment with multiple labelled components. A large central section labelled Hopper features openings for material input and a Shutter plate for flow control. Below, the Calibration chamber is visible, providing a space for adjustments. The Additional tank is mounted beside the main structure, and a Diffuser mesh is shown above the lower section, designed to regulate air or material flow. Surrounding the main structure are detailed close-ups that highlight the Diffuser mesh, showing its intricate pattern and texture. The image captures a clear view of the various components and their arrangement, which is essential for understanding the machine functionality.Photo of the air pluviator (left), along with detailed views of the hopper and the diffuser mesh (right)
The image depicts a piece of equipment with multiple labelled components. A large central section labelled Hopper features openings for material input and a Shutter plate for flow control. Below, the Calibration chamber is visible, providing a space for adjustments. The Additional tank is mounted beside the main structure, and a Diffuser mesh is shown above the lower section, designed to regulate air or material flow. Surrounding the main structure are detailed close-ups that highlight the Diffuser mesh, showing its intricate pattern and texture. The image captures a clear view of the various components and their arrangement, which is essential for understanding the machine functionality.Photo of the air pluviator (left), along with detailed views of the hopper and the diffuser mesh (right)
A study was conducted, exploring the sensitivity of the achieved relative density to the aforementioned pluviation parameters. The relative density is measured by direct sampling, using pots at various locations inside the chamber. A wide range of relative densities (DR) is achieved, mainly influenced by the size of the holes in the hopper: the loosest state (DR = 22%; e = 0.74) is achieved with 20 mm holes in the hopper and no diffuser mesh, while the densest state (DR = 79% and e = 0.54) is reached with the 2.5 mm holes and the diffuser mesh. Several identical tests were repeated at the dense state, achieving very good repeatability, with the differences in DR not exceeding 1%. Considering the variation of relative density in the horizontal direction, the maximum difference of DR is on average 5% (corresponding to a difference of 0.02 in voids ratio).
By placing the pots at different heights in the calibration tank, it was observed that there is a slight tendency of lower relative densities at the bottom of the chamber. However, the maximum difference of DR with depth does not exceed 2% (corresponding to a difference of around 0.01 in voids ratio) and is therefore within the scatter of the results in the horizontal direction. Furthermore, it is noted that by adding the diffuser mesh or varying the mesh position, the relative density is not significantly altered. However, without the mesh or by having the mesh at a higher position, concentrated sand jets tend to form, resulting in a less uniform sand surface after pluviation. If the mesh is placed farther away from the shutter plate, it helps to disperse the sand and to create uniform sand raining (Figure 7). More information about the calibration process of the air pluviator using Perth sand can be found in Alber (2025). The performed process allows an estimate of the average relative density that is obtained using the air pluviator; nonetheless, it should be pointed out that in this way, the boundary effects due to the additional upper tank and the probe to be tested, or the membrane of the calibration chamber, are not accounted for.
The image depicts three sequential frames illustrating a process in which a hand operates a spray device suspended from above, releasing thin strands of material. The first frame shows the device positioned over a surface with a ring and a container placed below. The second frame captures the moment when the strands begin to form a curtain-like appearance. The focus remains on the interaction between the hand, the spray device, and the material falling towards the surface, where a mixture of powder and a circular ring is located, suggesting a controlled environment for layering or coating. The surroundings include various objects, indicating a workspace setting.The effect of the diffuser mesh position on the rain uniformity: no mesh (left), high mesh (centre), and low mesh (right)
The image depicts three sequential frames illustrating a process in which a hand operates a spray device suspended from above, releasing thin strands of material. The first frame shows the device positioned over a surface with a ring and a container placed below. The second frame captures the moment when the strands begin to form a curtain-like appearance. The focus remains on the interaction between the hand, the spray device, and the material falling towards the surface, where a mixture of powder and a circular ring is located, suggesting a controlled environment for layering or coating. The surroundings include various objects, indicating a workspace setting.The effect of the diffuser mesh position on the rain uniformity: no mesh (left), high mesh (centre), and low mesh (right)
5. Test procedure
The test procedure is described using as an example the calibration chamber tests of the anchoring unit of the self-burrowing probe in dry, dense Perth sand (which is a poorly graded quartz sand). As depicted in Figure 8, the test procedure can be divided into three main steps: (i) specimen preparation; (ii) consolidation; and (iii) anchoring unit test with a radial expansion and an axial locomotion.
The image illustrates a labelled diagram showing four distinct processes related to a mechanical system. On the left, Specimen preparation depicts a vertical apparatus with a funnel top and a cylindrical section. The second section, titled Consolidation, depicts horizontal arrows indicating movement within a similar cylindrical setup. The next segment, labelled Anchoring unit radial expansion, depicts a wider cylindrical unit with arrows showing radial movement. The final section, Anchoring unit axial locomotion, depicts another cylindrical apparatus with vertical arrows indicating axial movement. Each section shows a distinct machinery configuration corresponding to each process.Schematic illustration of the test procedure
The image illustrates a labelled diagram showing four distinct processes related to a mechanical system. On the left, Specimen preparation depicts a vertical apparatus with a funnel top and a cylindrical section. The second section, titled Consolidation, depicts horizontal arrows indicating movement within a similar cylindrical setup. The next segment, labelled Anchoring unit radial expansion, depicts a wider cylindrical unit with arrows showing radial movement. The final section, Anchoring unit axial locomotion, depicts another cylindrical apparatus with vertical arrows indicating axial movement. Each section shows a distinct machinery configuration corresponding to each process.Schematic illustration of the test procedure
5.1 Sample preparation
The tests are performed on a wished-in-place anchoring unit. The probe is centrally installed into the chamber before raining, and an aluminium tube of the same diameter as the anchoring unit is stacked on top until the hopper height, aiming to minimise shadow effects. In order to test the anchoring unit in the most challenging conditions, the discussed test is conducted in dense sand. Additionally, the preparation and handling of a dense sand specimen is less sensitive to disturbances and also less conservative in terms of boundary effects. The target average relative density of DR = 79% (e = 0.54) is achieved using the previously discussed air pluviator, with a 2.5 mm hole diameter and diffuser mesh. Before raining is initiated, the membrane is stretched towards the sample former using a vacuum pressure of 4–5 kPa, thus achieving a perfectly cylindrical shape of the specimen. Once the cap of the chamber is placed on the levelled sand surface, a small confining pressure of 20–30 kPa is applied to the membrane at mid-height of the chamber so that the sample former elements can be retracted.
5.2 Consolidation
The sample is consolidated to two target stress levels: (i) vertical stress σv = 200 kPa and horizontal stress σh = 100 kPa, corresponding to a field-testing depth of about 12 m; and (ii) σv = 100 kPa and σh = 50 kPa, corresponding to a depth of 6 m. The loading of the chamber is performed stepwise, targeting a ratio of horizontal over vertical stress of K = 0.5 at the end of consolidation. Note that the vertical and horizontal stresses (σv and σh) are referring to the mid-height of the chamber, where the testing of the anchoring unit is conducted. Since the vertical stress σv is applied to the base of the sample, a lower σv is obtained at the top of the sample due to frictional losses and the self-weight of the specimen. Hence, the vertical stress σv is assumed to vary linearly with the chamber depth and is calculated as follows for the position at mid-height of the chamber:
where the stress σv,top at the top of the sample is monitored by the three load cells installed at the top cap; σv,bottom at the bottom of the sample is calculated considering the area of the loading plate A, the force of the cushion Fcushion given by the previously discussed calibration of the pneumatic cushion in function of air pressure and inflation height, and the force due to the self-weight of the loading plate Fplate:
In every test, the consolidation is completed with a vertical push of the cushion. This aims to minimise any arching effects in the horizontal direction of the sample, improving the readability of the load cells at the top and of the pressure mapping sensor at the bottom of the chamber.
5.3 Anchoring unit test
In order to analyse the response of the anchoring unit independently from the other units of the self-burrowing probe, the section of the anchors is isolated and incorporated at mid-length of an elongated cylindrical ‘dummy’ tube of the same diameter as the anchoring unit. The tube is long enough to protrude from the tank at the top and the bottom. The test of the anchoring unit, which has been calibrated beforehand outside the chamber, consists of a radial expansion of the four anchoring boxes in the consolidated soil. The response of the anchors in terms of radial pressure–displacement is recorded by measuring the displacement of each anchor box via an internal magnetic sensor and by correlating the soil pressure to the anchor force derived from the oil pressure gauge. In a next step, the anchoring unit is pushed downwards by means of the electric actuator, moving vertically along the consolidated sand. With this step, the axial force-displacement response of the vertical anchor locomotion is recorded.
6. First results
In the consolidation phase, the two target stress levels of σv = 200 kPa and σh = 100 kPa (high stress level) and σv = 100 kPa and σh = 50 kPa (low stress level) are reached at mid-height of the specimen by means of the pneumatic cushion at the base of the chamber and the cell pressure in the membrane. Pushed by the pneumatic cushion and guided through the central cylinder, the loading plate moves uniformly upwards. Its vertical displacement, which is measured by the three LVDTs, reaches on average 2.4 and 1.3 mm for the high and the low stress levels, respectively. No significant tilting of the loading plate is observed, with the maximum measured difference between the LVDTs being less than 0.5 mm, resulting in an inclination of the loading plate of no more than 0.06°. In terms of bending of the base plate, which is tracked by the additional LVDTs, a maximum deformation of 0.1 mm is detected without any plastic deformation. Based on the calibration of the pneumatic cushion, a final vertical stress of 220 and 114 kPa is applied at the bottom of the chamber in the case of the high and low stress levels, respectively. At the top of the chamber, a stress of 175 and 87 kPa is measured by the load cells for the two stress levels at the end of the consolidation phase. Hence, the difference in vertical stress from top to bottom is higher than the one caused by the self-weight of the sample (around 13.4 kPa), which can also be observed in Figure 9, which shows the stress paths at the top and bottom of the chamber for the high and low stress levels. It can be seen that, omitting the vertical stress due to the self-weight of the sample, the paths do not follow the line of equal increase (dashed line), but there is a stress loss from bottom to top of about 20% of the average vertical stress. This stress gradient is the result of internal losses, mostly due to friction on the interface between the probe and the sand. Testing in the rigid wall chamber showed that the stress gradient is even more pronounced in that case, which can be clearly attributed to the large interface between the internal rigid chamber wall and the sand. This highlights the importance of friction reduction measures with respect to the interfaces inside the chamber. Comparing the vertical stress, calculated from the calibration of the pneumatic cushion, with the recordings of the pressure mapping sensor at the bottom of the chamber, it can be observed that these compare well qualitatively. However, further investigations are needed, given the difference of around 20% between the measured and estimated stress values, which can most likely be explained by the sensor being too sensitive to granular structures, for example, arching effects.
The image depicts a graph with the X-axis labelled as vertical stress at the top in kilopascals, ranging from 0 to 180 kilopascals. The Y-axis illustrates vertical stress at the bottom in kilopascals, ranging from 0 to 250 kilopascals. Two lines represent different stress levels, a grey line for the High stress level and a black line for the Low stress level, each showing a general increasing trend. A dashed reference line at a one-to-one ratio is also shown, indicating equivalence between the two axes. The graph illustrates the relationship between vertical stress at the top and bottom under varying conditions.Indicative test results of the consolidation phase in the calibration chamber
The image depicts a graph with the X-axis labelled as vertical stress at the top in kilopascals, ranging from 0 to 180 kilopascals. The Y-axis illustrates vertical stress at the bottom in kilopascals, ranging from 0 to 250 kilopascals. Two lines represent different stress levels, a grey line for the High stress level and a black line for the Low stress level, each showing a general increasing trend. A dashed reference line at a one-to-one ratio is also shown, indicating equivalence between the two axes. The graph illustrates the relationship between vertical stress at the top and bottom under varying conditions.Indicative test results of the consolidation phase in the calibration chamber
In terms of testing the anchor expansion, the pressure-displacement response of the anchoring unit is depicted in Figure 10 (top) for the high and the low stress level, with the thin lines being the individual responses of the four anchors and the bold line being the average response. It can be observed that the anchors start expanding at a stress of about 50 and 110 kPa for the low and high stress levels, respectively. This ‘lift off’ stress gives an indication of the initial horizontal stress, which needs to be overcome for the anchor to start moving. These values are in good agreement with the applied cell pressures, even though they are slightly higher, which most likely stems from sand ingress on the sides of the anchor boxes. Furthermore, it can be seen that by the end of the force-controlled expansion phase, the anchors achieved a displacement of 0.3 and 1.2 mm for the low and high stress levels, respectively, reaching an anchoring stress of 800 kPa. This verifies the capability of the anchoring system to fully mobilise its maximum available capacity in terms of force, at least for the analysed stress fields.
The image depicts two line graphs. The upper graph illustrates the relationship between pressure, measured in kilopascals, and displacement, measured in millimetres, with higher stress levels represented by lighter lines and lower stress levels by darker lines. The Y-axis shows Pressure and the X-axis shows Displacement. An inset on the right illustrates a technical diagram of the apparatus, detailing measurement points for pressure. The lower graph illustrates force, measured in kilonewtons, versus displacement, measured in millimetres. The Y-axis displays Force, and the X-axis displays Displacement. The graph is labelled for low stress levels, with an inset diagram illustrating measurement parameters for the applied force. Both graphs include clear axes and labels showing the functional relationship between the measured variables.Indicative test results of the testing of the anchoring unit expansion (top) and axial locomotion (bottom) in the calibration chamber
The image depicts two line graphs. The upper graph illustrates the relationship between pressure, measured in kilopascals, and displacement, measured in millimetres, with higher stress levels represented by lighter lines and lower stress levels by darker lines. The Y-axis shows Pressure and the X-axis shows Displacement. An inset on the right illustrates a technical diagram of the apparatus, detailing measurement points for pressure. The lower graph illustrates force, measured in kilonewtons, versus displacement, measured in millimetres. The Y-axis displays Force, and the X-axis displays Displacement. The graph is labelled for low stress levels, with an inset diagram illustrating measurement parameters for the applied force. Both graphs include clear axes and labels showing the functional relationship between the measured variables.Indicative test results of the testing of the anchoring unit expansion (top) and axial locomotion (bottom) in the calibration chamber
As a next step in the case of the low stress level, the anchor is pushed down axially, resulting in the force-displacement response of Figure 10 (bottom). It can be observed that the mobilised ultimate capacity is about 11 kN, which is mostly mobilised by the shearing along the frictional interfaces and the normal stress at the bottom of the expanded anchor boxes. Although a good performance of this axial locomotion test is achieved through the bottom perforation of the chamber, an optimisation of the test procedure is still required. One problematic aspect is that the probe is already subjected to some pre-shearing during the consolidation phase, due to the moving soil mass and the anchors being fixed in the central position. Therefore, the force-displacement response in Figure 10 (bottom) does not start from zero. In addition, the locomotion test comes with parasitic, frictional resistance of parts of the anchor unit’s dummy elongation. This extra resistance needs to be quantified by performing a test with the anchors not expanded in order to deduct it from the axial locomotion capacity.
In all performed anchor tests, boundary effects due to the limited chamber size cannot be excluded and have to be analysed numerically in the literature. For example, for the case of the anchor radial expansion, which offers some similarities to pressuremeter loading, Ajalloeian and Yu (1998) suggest that for the early stages of pressuremeter loading (cavity strain <10%), the chamber boundary does not affect the results significantly, provided that the ratio of the chamber to pressuremeter radius is greater than 15. In the case of the chamber presented herein, the ratio of chamber to probe radius is 6.7 – significantly lower than 15. However, the final, maximum displacement in the anchor expansion is relatively small, as shown in Figure 10 (top). When expressed in terms of cavity strain, it does not exceed 2.3%. Considering these aspects, no clear conclusion can be drawn in terms of boundary effects without assessing it numerically. These aspects will be explored in a forthcoming publication.
7. Conclusions
This paper has presented the development of a calibration chamber for the testing of a novel self-burrowing probe. The design of the chamber includes a bespoke pluviation system and a number of novel chamber attributes, such as the circular perforation at the bottom and the vertical stress application through the resulting doughnut-shaped section at the base of the chamber. The design enables testing of devices that extend vertically through the top and bottom of the chamber, allowing them to be pushed along the consolidated soil without mobilising any tip resistance. This feature is necessary for testing of the self-burrowing probe at the component level, as well as for the more general case of interface testing of components of penetration devices. The stress inside the chamber is generated by the doughnut-shaped pneumatic cushion at the base, along with regulated water pressure inside a radial membrane. Some first test results of the anchoring unit of the self-burrowing probe in dry, dense Perth sand were presented. When interpreting the chamber test results, a significant vertical stress gradient from the bottom to the top of the chamber is noticed due to the presence of the wished-in-place probe. This highlights the importance of minimising the friction of the components inside the chamber and also demonstrates the significance of a reliable stress monitoring system. The results of this study show that the developed calibration chamber provides a well-controlled testing environment, which, in combination with an adequate numerical environment for the quantification of chamber size and boundary effects, will be instrumental for the testing and calibration of the novel self-burrowing probe.

