An Experimental Study on the Failure Mechanism of Load Distributive Compression Anchors in Residual Soil

doi:10.21203/rs.3.rs-4208609/v1

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An Experimental Study on the Failure Mechanism of Load Distributive Compression Anchors in Residual Soil

https://doi.org/10.21203/rs.3.rs-4208609/v1

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The use of Load Distribution Compression Anchors (LDCAs), known for their high bearing capacity and removable strands after construction, has grown recently. Unlike conventional anchors, LDCAs have multiple anchor bodies along their length, presenting unique pull-out behaviors that remain insufficiently understood. This study aimed to investigate the failure mechanisms of LDCAs through physical model tests conducted in residual soil with a 90% relative density, adjusting variables such as anchor length, the number of anchor bodies, and the spacing between these bodies. To assess the effect of the surrounding soil on these mechanisms, the results of the experiment were compared with those from experiments conducted at a 70% relative density. Findings revealed that anchor body-grout tensile failure occurred during the initial loading stage. The tensile failure was determined by the grout strength itself rather than the effect of the surrounding soil. After anchor body-grout tensile failure, each anchor body behaves independently. However, when the spacing between the anchor bodies was small, local grout-ground interface failure occurred at both 70% and 90% relative density conditions, resulting in the overlapping of grout axial loads. Lastly, it was confirmed that the ultimate bearing capacity of LDCAs (multiple anchor bodies) can be less than that of compression-type anchors (single anchor body). The shear field developed by each anchor body in LDCAs overlapped and reduced the grout-ground shear strength. The reduction in ultimate bearing capacity was more pronounced in the dense soil condition and narrow anchor body spacing condition.

Load distributive compression anchor

Failure mechanism

Pull-out behavior

Physical model test

Relative density of residual soil

Ground anchors are used to support a variety of geotechnical structures, such as retaining walls and slope stabilization systems. Different types of ground anchors have been developed based on the load transfer mechanism between the strands, grout, and ground [26, 36]. The recently developed Load Distributive Compression Anchor (LDCA) features plate-shaped anchor bodies distributed along the anchor's length, with the load transmitted to the grout and surrounding ground through the movement of each anchor body. Therefore, unlike conventional tension and compression-type anchors, where the load is concentrated, LDCAs offer higher resilience to grout failure and grout-ground interface failure due to the load distribution along the anchor's length. Furthermore, unlike tension-type anchors where the strand is bonded to the grout, LDCAs allow for strand removal after construction, facilitated by a sheath tube that protects the strand along the entire anchor length. Consequently, LDCAs are increasingly used in urban construction sites, where remaining strands can cause environmental issues or obstruct future excavation [7, 8, 27].

Despite the increasing use of Load Distributive Compression Anchors (LDCA) due to their high bearing capacity and removable strands, the failure mechanism of LDCAs remains unclear. Numerous full-scale field experiments have assessed the field applicability of LDCAs, confirming their higher bearing capacity compared to conventional ground anchors [2, 9, 16, 35]. However, most previous studies have evaluated LDCA’s bearing capacity based on load-displacement curves, conceptually attributing the increased capacity to the load distribution characteristics without fully elucidating the failure mechanism. Recent research investigating the load transfer mechanism in LDCAs has revealed that interference between multiple anchor bodies can produce additional grout axial loads or grout-ground shear stress [28–30]. This suggests that LDCAs may experience grout failure or grout-ground shear failure, which are not anticipated by conventional failure mechanisms. Therefore, evaluating the failure mechanism and pull-out behavior of LDCAs is essential for their efficient design.

In this study, the pull-out behavior of LDCAs was investigated through physical model tests. A scaled-down model of the prototype LDCA was designed, and pull-out tests were conducted on residual soil, commonly used as a supporting stratum for ground anchors in South Korea. These tests, carried out at 90% relative density with variations in the number and spacing of anchor bodies, were compared to those at 70% relative density. This comparison aimed to examine the load-displacement behavior, grout axial load distribution, and grout-soil shear stress distribution, with particular attention given to the effect of the soil’s relative density on the failure modes of LDCAs.

2.1. Failure modes of a compression-type anchor

The failure modes of ground anchors can be classified into three categories: (1) external failure mode, related to the overall stability of the entire system, including the structure and the ground where the anchor is installed; (2) internal failure mode, concerning the stability of the anchor's constituent materials; and (3) facing failure mode, associated with the stability of the supporting structure into which the anchor is installed [26]. This study focuses on the internal failure mode, particularly the pull-out behavior and the ultimate bearing capacity of the ground anchor.

Figure 1 illustrates the load transfer mechanism and internal failure modes of a compression-type anchor with a single anchor body. In such anchors, the strand is protected by a sheath tube along the anchor's entire length and connects to the anchor body at the tip. Thus, when the strand is loaded, the load is fully transferred to the anchor body, resulting in constant tensile stress in the strand along the anchor’s length [11]. The ultimate tensile load (${Q}_{ut}$) of the strand in a compression-type anchor can be calculated as follows:

$${Q}_{ut}=n{A}_{t}{f}_{ut}$$

Where, $n$: number of strands, ${A}_{t}$: Cross-sectional area of strand, and ${f}_{ut}$: Tensile strength of strand. Additionally, in compression-type anchors, the anchor body moves toward the anchor head due to the load from the strand, generating compressive stress in the grout. The axial load distribution in the grout equals the applied load (${P}_{apply}$) at the anchor tip, diminishing due to grout-ground shear stress towards the anchor head [11, 12]. Grout compression failure may occur if the applied load exceeds the grout’s compressive failure load (${Q}_{ug}$), calculated as:

$${Q}_{ug}={A}_{g}{f}_{ug}$$

Where, ${A}_{g}$: Cross-sectional area of grout, ${f}_{ug}$: Compressive strength of grout. Grout-ground interface failure, the last failure mode, is when failure occurs across the interface of the anchor, resulting in complete pull-out. The grout-ground interface shear stress is determined by the relative displacement between the grout and the ground. Therefore, the grout-ground shear stress distribution exhibits a similar distribution to the grout axial load during the initial loading step, resulting in a maximum at the anchor tip and decreasing with distance. However, as the applied load increases, localized grout-ground interface failure will develop, and when shear stresses equivalent to the grout-ground shear strength are developed along the entire length of the anchor, the anchor may pull out. Assuming the same grout-ground shear strength along the entire length of the anchor, the grout-ground interface failure load (${Q}_{uf}$) can be evaluated as shown in Eq. (3).

$${Q}_{uf}=\pi DL{\tau }_{max}$$

Where, $D$: diameter of anchor, $L$: length of anchor, and ${\tau }_{max}$: grout-ground interface shear strength. In designing compression-type anchors, the ultimate bearing capacity is determined by the smallest value among ${Q}_{ut}$, ${Q}_{ug}$, and ${Q}_{uf}$.

2.2. Failure modes of a LDCA

As mentioned in the introduction, the failure modes of LDCA have not yet been identified. An LDCA is designed based on the ultimate bearing capacity evaluation method for compression-type anchor. For example, when designing an LDCA with double anchor bodies, where two strands are connected to each body, the strand tensile failure load is calculated using n = 4 in Eq. (1). Since the applied load is distributed and transmitted to the double anchor bodies, the grout failure load is evaluated as twice the grout compressive failure load determined by Eq. (2), given that the load on each anchor body is half the total applied load. For grout-ground interface failure loads, the same Eq. (3) used for compression-type anchors is applied to assess the ultimate capacity of LDCAs, without accounting for the effect of multiple anchor bodies.

However, recent physical model tests aimed at evaluating the pull-out behavior of LDCAs have shown that LDCAs, comprising multiple anchor bodies, might exhibit different failure modes compared to single-anchor body compression-type anchors [10]. Initially, tensile cracks were observed to develop between the grout and the 2nd anchor body near the anchor head, as depicted in Fig. 2(a). Due to the high susceptibility of grout to tensile stress, the tensile crack occurred at a significantly lower load (6.85 kN per anchor body), after which the 1st and 2nd anchor bodies behaved independently. Furthermore, local failure at the grout-ground interface of the 1st anchor body, following the grout tensile crack, led to overlapping grout axial loads as shown in Fig. 2(b). This local failure resulted in excessive slip in the 1st anchor body, while the 2nd anchor body restricted its movement, causing an overlap in grout axial load. In this case the 2nd anchor body may experience a grout axial load greater than half of the applied load (${P}_{apply}$/2). Moreover, load-displacement curve analysis of single and double anchor bodies indicated that the ultimate load for double anchor bodies is reduced due to the interference effect between the anchor bodies. This finding contrasts previous studies, which suggested that a smaller ultimate load might occur during pull-out (i.e., grout-ground interface failure), even with load distribution along the anchor length.

However, the results of the previous study are limited by the fact that the tests were conducted under the same soil conditions (residual soil with a relative density of 70%). Given the dependency of group efficiency (i.e., pile-soil-pile interaction) in group piles on relative density [18, 19], the effect of multiple anchor bodies on the pull-out behavior of LDCA is also expected to depend on the relative density of the surrounding soil. Therefore, this study conducted physical model tests on residual soil with a relative density of 90% to investigate LDCA’s pull-out behavior under different soil conditions, comparing these findings with test results from 70% relative density soil. In particular, the grout-ground shear stress for each experimental condition was compared to analyze the interference effect of multiple anchor bodies.

3.1. Experimental condition

Granite constitutes about 35% of South Korea's geological layers, with weathered residual soils from granite widely distributed across the country [13]. In this study, residual soils were reconstituted using Completely Decomposed Granite (CDG) to simulate the field's ground conditions for physical model testing. Particle size analysis indicated that the CDG used in this experiment classified as SM according to the Unified Soil Classification System (USCS) and exhibited a particle size distribution similar to the typical residual soil of South Korea reported by Park [21]. Table 1 presents the basic properties of the CDG used in this study.

Table 1

Basic Properties of CDG.
USCS	Specific gravity	Optimum moisture content (%)	Dry density (g/cm³)
			Minimum dry density	Maximum dry density
SM	2.61	10.53	1.25	1.98

Physical model test results with relative densities of 70% and 90% were compared in this study. These densities represent medium-dense and dense soil conditions, corresponding to Standard Penetration Test (SPT) N-values of 35 and more than 50, respectively [32]. To assess the grout-soil interface behavior, a critical factor in the pull-out behavior of LDCA, direct shear tests were conducted on CDG at relative densities of 70% and 90%. Figure 3 illustrates specimens with only residual soil and specimens with a grout-residual soil interface, where direct shear tests were performed under confining pressures of 50, 100, and 200 kPa.

The results of the direct shear test depending on the relative density are shown in Fig. 4. The direct shear test results for specimens with only residual soil show that the cohesion and friction angle increase as the relative density increases from 70–90%. The cohesion showed a significant increase of about 3 times as the relative density increased. The direct shear tests on grout-residual soil interface specimens showed that both cohesion and friction angle increased more significantly with higher relative density compared to the specimens of only residual soil. Therefore, it is anticipated that LDCAs installed in soil with 70% and 90% relative densities will exhibit different behaviors. By comparing these two experimental conditions, the impact of soil conditions on the pull-out behavior of LDCA can be assessed. The detailed experimental methods and results of the direct shear tests are described in Shin et al. [31].

To analyze the pull-out behavior of LDCA under varying ground conditions, the physical model tests conducted under a total of eight conditions were compared, as detailed in Table 2. Additional experiments adjusted the relative density to 90%, maintaining the same number of anchor bodies, anchor length, and spacing between anchor bodies as in the previous physical model tests (T1-T4) conducted at 70% relative density. All experiments assessed the load-displacement curve, grout axial load distribution, and grout-soil shear stress distribution to analyze the influence of relative density on the pull-out behavior of LDCA.

Table 2

Experiment condition
Test No.	D_r (%)	Number of anchor bodies	Length of ground anchor (mm)
T1	70 Jo et al. [10]	Single	600	–
T2		Single	1200	–
T3		Double	1200	450
T4		Double	1200	234
T5	90	Single	600	–
T6		Single	1200	–
T7		Double	1200	450
T8		Double	1200	234

3.2. Physical modeling of LDCA

In this study, the SAMJ-U-TURN, manufactured by Samjin Steel Industry, was selected as a prototype for the LDCA to conduct physical model tests under field-like conditions, as illustrated in Fig. 5. The components of the prototype LDCA, including the anchor body, strand, and sheath tube, were scaled down by a ratio of 1:2 to create a model LDCA. The model anchor body was manufactured with the same shape and material as the prototype but was scaled down to half the length. To simulate the 12.7 mm diameter 7-wire steel strand, a 7.14 mm diameter wire rope was used as the model strand. Given that the wire rope is made from a different material than the steel strand, the tensile tests were conducted. The yield load and elastic modulus of the wire rope (i.e., model strand) were determined to be 38.5 kN and 150 GPa, respectively. The sheath tube, which prevents adhesion between the strand and grout, was scaled down from the commonly used 16 mm diameter in the field to an 8 mm diameter plastic tube for the model LDCA.

The model LDCA was assembled in the following order: (1) To prevent friction between the wire rope and the plastic tube, a sufficient amount of grease was applied to the outside of the wire rope, and the wire rope was inserted into the plastic tube. (2) The previously assembled wire rope and plastic tube were installed on the model anchor body. The model anchor body used in this study is a U-turn type anchor body, which connect the wire rope and plastic tube through a U-shaped groove. (3) For the double anchor body condition, the process of (1) and (2) was repeated to assemble the 2nd anchor body, and the gap between the 1st anchor body and the 2nd anchor body was adjusted according to the experimental conditions. "In this study, the 'anchor body spacing' is defined as the distance between the upper part of the first anchor body and the lower part of the second anchor body, with the two anchor bodies installed at a 60° rotation angle to each other (see Fig. 5). (4) An embedded strain gauge was installed between the plastic tubes. In this study, the grout strain was measured using an electrical resistance mold strain gauge from Tokyo Measuring Instruments Laboratory, and the spacer was installed so that the strain gauge could be located in the center of the grout.

3.3. Pull-out test method

In this study, the pull-out test was conducted following the proposed procedure from Jo et al.[10]. This test method is based on the field pull-out test procedure proposed by FHWA and BS [5, 26]. Figure 6 shows experimental set-up for physical model tests. A series of pull-out tests were conducted using the following sequence: (1) A guide wall with an outer diameter of 50 mm was installed in the center of the soil tank to form a borehole, and the model ground was prepared around the guide wall. The model ground was created using tamping methods, and compaction was performed every 20 cm to ensure a homogeneous ground condition. After completing the pull-out experiment, the moisture content and relative density were examined by utilizing a sampling can that had been pre-inserted during the model ground's preparation. It was confirmed that both measurements matched the predetermined values. (2) Following the guide wall's removal to create the borehole, the assembled model LDCA was inserted into the borehole. After that, the grout, with a water-to-cement ratio of 0.45, was injected into the borehole. To ensure that the void between model LDCA and borehole was fully occupied, the grout was pumped from the bottom of model LDCA. (3) After allowing 14 days for the grout curing, the pressurizing chamber simulating the confining pressure of the surrounding soil was installed on the model ground. Given that the typical unit weight of residual soil is 20 kN/m³, a pressure of 200 kPa was applied, simulating a LDCA installed at a depth of 10 m from the ground surface. (4) A loading system capable of applying an identical load to each anchor body was installed. According to Barley and Windsor[2], it is necessary to apply the same load to each anchor body when implementing the LDCA. Therefore, this study developed a loading system that could distribute an equal load to the cylinders installed in each strand through a hydraulic synchronized system and it was utilized to conduct the pull-out test. (5) Linear Variable Differential Transformers (LVDTs) were installed on each strand, and a wire type LVDT was installed on the grout surface. During the pull-out test, the LVDTs measured the displacement of each strand and the grout surface, while a load cell positioned between the pressurizing chamber and the loading system measured the total applied load. Additionally, the grout strain was measured through the embedded strain gauges attached during the assembly of the model LVDTs. (6) The pull-out test was conducted. The maximum load for the experimental conditions was determined by the failure load of a single strand (36.0 kN) multiplied by the number of strands. An initial alignment load, equivalent to 5% of the maximum load, was applied to align the model LDCA with the loading system. The load was incrementally increased by 5% of the maximum at each step, holding each for five minutes, employing a load control approach akin to the field pull-out tests [5, 26].

4.1. Single anchor body

To assess the overall pull-out behavior according to the experimental conditions, the load-displacement curves of the anchor bodies were evaluated. The slip displacement of the anchor body, excluding the elastic displacement of the strand, was calculated by Eq. (4):

$${d}_{a}={d}_{m}-\frac{{P}_{s}{L}_{s}}{{E}_{s}{A}_{s}}$$

where ${d}_{a}$is the displacement of the anchor body, ${d}_{m}$ is the measured displacement of the model strand, ${P}_{s}$ is the applied load on the model strand, ${L}_{s}$ is the length of the model strand, ${E}_{s}$ is Young’s modulus of the model strand, and ${A}_{s}$ is the cross-sectional area of the model strand.

Figure 7 presents the load-displacement curves for a single anchor body condition, where solid symbols represent the anchor body’s curve and open symbols denote the grout surface’s curve. In the 600 mm anchor length condition, as depicted in Fig. 7(a), peak loads were noted at both 70 and 90% relative densities, with significant displacement increases in both the anchor body and grout following the peak load. This suggests that at shorter anchor lengths, grout-ground interface failure occurs at peak load, leading to excessive slip displacement and anchor pull-out. The peak load rose by approximately 26%, from 20.4 kN to 25.9 kN, as the relative density increased from 70–90%, while the slope of the load-displacement curve remained consistent across densities. This behavior mirrors the direct shear test findings (Fig. 4(a)), where shear strength rose with relative density, but the shear stress-displacement curve’s gradient stayed similar. The grout surface experienced displacement at a load of around 15 kN, irrespective of the relative density, indicating that grout-soil interface shear stresses were fully dissipated before reaching 600 mm (anchor length) under loads of 15 kN or lower, with displacement triggered by load transfer to the grout surface from 15 kN.

Figure 7(b) presents the load-displacement curve as a function of relative density for an anchor length of 1200 mm. Under the 70% relative density condition, a peak load of 39.6 kN was observed, followed by a significant increase in displacement. In contrast, at 90% relative density, strand tensile failure occurred at 49.5 kN. Although the tensile failure load for a single anchor body was determined to be 77 kN from tensile test results, the failure occurred at the strand's bend point, where the load was concentrated, as depicted in Fig. 6. Notably, the ultimate load increased by 26% for a 600 mm anchor length with increasing relative density, leading to an estimated ultimate load of 49.9 kN for a 1200 mm anchor length at 90% relative density, aligning closely with the observed strand failure load. This suggests that, at 90% relative density and an anchor length of 1200 mm, grout-ground interface failure is likely to follow in the subsequent loading step. Therefore, it can be said that the grout-ground interface failure load increased with the relative density, even for an anchor length of 1200 mm. Displacement on the grout surface occurred consistently from a load of approximately 22 kN across all relative densities. This indicates that, as the anchor length increases, a larger load is dissipated before reaching the grout surface, and the load is transferred to the grout surface at the applied load of 22 kN.

4.2. Double anchor bodies

Figure 8 illustrates the load-displacement curves for the double anchor bodies condition. In this condition, the displacements of the first and second anchor bodies were different; therefore, the average displacement of each anchor body was calculated to assess the overall pull-out behavior. The results for the double anchor bodies consistently showed a peak load, followed by a significant increase in displacement, indicating that grout-ground interface failure occurred under all experimental conditions. However, the influence of relative density on the peak load varied with the spacing between anchor bodies. With a 450 mm spacing, the peak load increased from 37.6 kN to 42.2 kN as the relative density rose from 70–90% (Fig. 8(a)). Conversely, in the 234 mm spacing condition, the peak load decreased from 35.8 kN to 34.7 kN with an increase in relative density (Fig. 8(b)). This suggests that, unlike the single anchor body condition where the ultimate load capacity typically increases with higher relative density, the double anchor body condition may exhibit a reduction in ultimate load capacity despite an increase in relative density.

Table 3 presents the ultimate bearing capacities (i.e., peak load) under each experimental condition and the reduction ratios for double anchor bodies. The reduction ratio reflects the percentage decrease in ultimate capacity for the double anchor bodies compared to the single anchor body, under identical relative density and anchor length conditions. The analysis revealed that, consistent with previous results at 70% relative density, the double anchor bodies at 90% relative density exhibited a lower ultimate capacity. Specifically, at 450 mm anchor spacing, the ultimate capacity decreased by approximately 14.1% relative to the single anchor, and this reduction increased to 29.3% with a reduced anchor spacing of 234 mm. The comparison of the reduction ratio of the double anchor bodies according to the relative density shows that the reduction ratio increases as the relative density increases. Particularly, for narrow anchor body spacing, a substantial decrease in ultimate load capacity was observed at 90% relative density compared to 70%, resulting in lower ultimate load capacity despite the increase in relative density. The effect of multiple anchor bodies on ultimate bearing capacity, as shown in Fig. 2(c), increases with dense soil conditions. Thus, it seems necessary to propose a new evaluation method for the grout-ground interface failure load of LDCAs, taking into account the influence of multiple anchor body systems and ground conditions.

Table 3

Ultimate bearing capacity of all experimental conditions
No.	Dr (%)	No. of anchor bodies	Length (mm)	Spacing (mm)	Ultimate bearing capacity (kN)	Reduction ratio (%)
T1	70	Single	600	–	20.4	–
T2		Single	1200	–	39.6	–
T3		Double	1200	450	37.6	-5.4
T4		Double	1200	234	35.7	-9.8
T5	90	Single	600	–	25.9	–
T6		Single	1200	–	49.5	–
T7		Double	1200	450	42.2	-14.1
T8		Double	1200	234	34.7	-29.3

5.1. Tensile failure at anchor body-grout interface

In this study, the grout axial load distribution under double anchor bodies condition was analyzed to evaluate the effect of relative density on the failure modes of LDCA. The grout strain (${\epsilon }_{g}$) measured by the embedded strain gauge and the elastic modulus (${E}_{g}$) of the grout evaluated by the unconfined compression test were utilized to evaluate the grout axial load ($P$) at the point where the strain gauge was installed as Eq. (5).

$$P={E}_{g}{A}_{g}{\epsilon }_{g}$$

Where, ${A}_{g}$: the cross-sectional area of the grout. In this study, a loading system that can apply the same load to each anchor body was applied, so the load applied to the 1st and 2nd anchor bodies is half of the total applied load measured from the load cell. Therefore, the axial load of the 1st anchor body was applied as half of the total applied load, and the axial load of the 2nd anchor body was applied so that the load increment generated on the 2nd anchor body has the same value as half of the total applied load. Figure 9 shows the grout axial load distribution of the double anchor bodies at the initial loading stage. During the initial loading phase, the grout axial load distribution of the double anchor bodies showed very similar behavior regardless of the relative density and anchor body spacing. In the first three load increments (below about 10.5 kN), tensile loads were applied to the grout in the 1st anchor body and compressive loads were applied to the grout in the 2nd anchor body. However, at a load of approximately 13.7 kN, redistribution of grout axial loads occurred in all experimental conditions. The tensile load of the 1st anchor body decreased slightly, and the compressive load of the 2nd anchor body increased significantly. Therefore, it seems that a tensile crack occurred between the 2nd anchor body and the underlying grout at the initial loading stage. In the experiment, a fracture sound occurred inside the LDCA at 13.7 kN loading, and after checking the appearance of the LDCA after the pull-out test, it was confirmed that a tensile crack occurred between the 2nd anchor body and the bottom grout as shown in Fig. 10.

A key observation from the grout axial load analysis during the initial loading phase is that the anchor body-grout tensile failure occurred consistently at the same load, independent of relative density and anchor body spacing. This indicates that the tensile failure of the anchor body-grout interface is determined by the grout's properties used in LDCA construction, rather than the surrounding ground conditions or the configuration of multiple anchor bodies. The grout axial loads recorded under the 2nd anchor body at loadings of 10.5 kN (in tests T3, T4, T7, and T8) were − 2.24, -1.86, -2.69, and − 2.41 kN, respectively, reflecting tensile stresses of 0.9–1.3 MPa in the grout. Given that direct tensile tests on grout reported tensile strengths between 0.45 and 3.2 MPa, it is inferred that the grout under the 2nd anchor body was subjected to tensile loads nearing its tensile strength at 13.7 kN under double anchor bodies conditions. In particular, the tensile crack was observed at the anchor body-grout interface, which is expected to have a bond strength smaller than the tensile strength of the grout itself.

Tensile cracking at the anchor body-grout interface, as observed in the physical model test, is also anticipated to occur in field applications. With a scaling factor of 2 applied to the model LDCA, considering the scaling law, anchor body-grout interface failure is expected in the prototype LDCA under a total applied load of 54.8 kN. This suggests that the second anchor body might undergo tensile failure when 27.4 kN is applied to it. This load represents approximately 8.8% of the maximum load capacity (312 kN) for a single prototype anchor body, using a 12.7 mm diameter 7-wire steel strand. Given that the alignment load is set at 5% of the maximum load in the FHWA performance test [26], anchor body-grout failure could likely occur in field-applied LDCA during the initial load increments, or even while applying the alignment load.

5.2. Overlapping of grout axial load

Figure 11 depicts the distribution of grout axial load with increasing load after anchor body-grout tensile failure. When calculating the axial load of the 2nd anchor body, the tensile load of the grout beneath this anchor body was excluded due to tensile failure, and instead, the compressive load in the lower grout was considered for the calculation of the 2nd anchor body's axial load. The axial load distribution in the grout after the tensile failure exhibited similar patterns across different relative densities but varied with the anchor body spacing. In the 450 mm anchor body spacing condition (Figs. 11(a) and (c)), the axial load in the grout under the 2nd anchor body remained constant despite the increasing load. At a 90% relative density, a sudden increase in tensile load in the grout under the 2nd anchor body occurred at a load of 40.2 kN. However, load-displacement curve analysis indicated that the pull-out behavior started first with the 2nd anchor body, transferring unexpected tensile load to the end of the 1st anchor body. Below a load of 36.8 kN, the axial load in the grout under the 2nd anchor body remained constant, while the compressive stress in the remaining part of the grout increased. In the case of LDCA applied in the field, unlike the physical model test, the length of the 2nd anchor body is designed to be very long, so it is expected that the additional tensile load generated at 90% relative density will not be expressed, and the axial load of the grout under the 2nd anchor body will remain constant after the anchor body-grout tensile failure, as shown in the result at 70% relative density. The direct tensile tests on the grout conducted by Li and Li [15] demonstrated that the grout behaves very brittlely under tensile stress. Therefore, it can be concluded that at the moment of anchor body-grout tensile failure, the 2nd anchor body and the lower grout would have completely separated, leading to the independent behavior of the 1st and 2nd anchor bodies thereafter.

Under the 234 mm anchor spacing condition, residual grout axial load was induced in the grout under the 2nd anchor body at both 70 and 90% relative density (Fig. 11(b) and (d)). The axial load in the grout under the 2nd anchor body increased continuously with the increase of applied load, reaching a compressive load of 1.6 kN at 70% relative density and 1.3 kN at 90% relative density at the ultimate loading step. Therefore, it appears that under the 90% relative density condition, the grout-ground interface failure extended from the 1st anchor body to the grout beneath the 2nd anchor body, similarly to the 70% relative density condition, and grout axial load superposition occurred as shown in Fig. 2(b). In the case of the anchor body spacing condition of 234 mm, the length from the 1st anchor body to the grout under the 2nd anchor body is 384 mm, which is a rather short length, and it is estimated that the difference in the grout-ground interface failure load according to the relative density was not significant.

The pull-out test results for narrow anchor body spacing demonstrate that the grout axial load on the 2nd anchor body can exceed the applied load due to residual axial load in the grout. This suggests that relying solely on the comparison of Eq. (2) with the applied load for evaluating grout compressive stability, as in the current LDCA design method, may lead to unexpected grout failure. To avoid such failures, the spacing between anchor bodies (or the length of each anchor body) should be designed to prevent overlapping axial loads in the grout. Both physical model tests in this study and numerical simulations by Shin et al. [29] have shown the necessity of designing anchor body lengths to avert localized grout-ground interface failures. Table 4 shows the ultimate transfer loads (grout-ground interface failure loads per unit length) provided by the FHWA for designing soil anchor lengths [26], along with the calculated minimum anchor body spacings for various soil conditions. These spacings were determined based on an applied load of 187.2 kN, which is 60% of the prototype strand’s tensile failure load as per the FHWA’s design method, to ensure the full dissipation of the applied load. Current design practices typically involve a 2 m anchor spacing; our findings suggest that a spacing of 2 m or less is adequate to prevent local failures in most soil conditions. However, in very soft soils such as loose silty sand and silty clay, larger anchor body spacings are required to avert local failures, and the conventional 2 m spacing may result in grout failure. Consequently, further research on silt and clay conditions, which exhibit shearing behavior distinct from weathered soil, is essential for a more accurate LDCA design.

Table 4

Minimum anchor body spacing in various soil conditions.
Soil type	Relative density (SPT N value)	Ultimate transfer load (kN/m)	Min. spacing between anchor body (m)
Sand and gravel	Loose (4–10)	145	1.3
	Medium dense (11–30)	220	0.9
	Dense (31–50)	290	0.6
Sand	Loose (4–10)	100	1.9
	Medium dense (11–30)	145	1.3
	Dense (31–50)	190	1.0
Sand and silt	Loose (4–10)	70	2.7
	Medium dense (11–30)	100	1.9
	Dense (31–50)	130	1.4
Silt-clay mixture	Stiff (10–20)	30	6.2
Silt-clay mixture	Hard (21–40)	60	3.1

5.3. Interference effect of multiple anchor bodies

In this study, grout-ground shear stress was evaluated in each experimental condition to explain the cause of reduction in bearing capacity with relative density and anchor body spacing. Figure 12 shows the grout axial load (${P}_{x}$) and grout-ground shear stress (${\tau }_{x}$) acting on a compression-type anchor.

As shown in the force equilibrium of the grout element, in a compression-type anchor, the grout axial load decreases as it progresses to the opposite side of the anchor body due to the shear stress generated at the grout-ground interface. Therefore, the grout-ground shear stress of a compression-type anchor with LDCA can be evaluated as shown in Eq. (5) [4, 20, 34]. Since this study evaluated the grout axial load at the points where the embedded strain gauges were installed, the gradient of the grout axial load was used to estimate the average grout-ground shear stress between the points where each gauge was installed.

$${{\tau }}_{x}=-\frac{1}{D\pi }\frac{d{P}_{x}}{dx}$$

Figure 13 shows the grout-ground shear stress distribution at the ultimate loading step for the single anchor body condition. The dashed line shows the average grout-ground shear stress over the entire length of the anchor. In the single anchor body condition, the grout-ground shear stress was high at the anchor body regardless of relative density and decreased as it approached the anchor head. Unlike tension-type anchors, in compression-type anchors, compressive stress in the grout is generated, and the normal stress at the grout-ground interface increases due to the Poisson effect [34]. Therefore, the grout-ground shear stress (i.e., grout-ground interface shear strength) is large in the part of the anchor body where the compressive force is large, and the grout-ground shear stress is likely to decrease as the compressive force becomes smaller as it is further away from the anchor body. The average grout-ground shear stress at 70 and 90% relative density is 178.6 kPa and 232.8 kPa, respectively, confirming the high grout-ground shear strength at 90% relative density as expected from the direct shear test.

In this study, the grout-ground shear stress distribution for double anchor bodies was compared with that for a single anchor body to assess the effects of relative density and anchor body spacing on the ultimate bearing capacity. For the shear stress distribution of 2nd anchor body, the position of the 2nd anchor body was set at the bottom (x = 0) for comparison purposes. Figure 14 and Table 5 present the grout-ground shear stress variations depending on relative density and anchor body spacing. the reduction ratio for double anchor bodies was calculated by dividing the average shear stress of the 1st or 2nd anchor body by the average shear stress of the single anchor body. The grout-ground shear stress of the double anchor bodies condition revealed that the 2nd anchor body exhibited lower shear stress than the 1st anchor body across all relative densities and anchor body spacings. In all experimental conditions, the grout-ground shear stress of the 1st anchor body had similar values to the single anchor body, and the 2nd anchor body had a lower grout-ground shear stress than the single anchor body. Consequently, the shear stress reduction in the 2nd anchor body was more pronounced at narrower anchor body spacings, with the 90% relative density condition exhibiting a greater reduction than the 70% relative density condition.

Table 5

Average grout-ground shear strength of double anchor bodies conditions
No.	Dr (%)	No. of anchor bodies	Spacing (mm)	Average grout-ground shear stress (kPa)	Reduction ratio of grout-ground shear stress
T1	70	Single	–	178.6	–
T3		Double	450	193.4 (1st anchor body) 143.2 (2nd anchor body)	1.08 0.80
T4		Double	234	221.8 (1st anchor body) 125.4 (2nd anchor body)	1.24 0.70
T5	90	Single	–	232.8
T7		Double	450	225.7 (1st anchor body) 160.2 (2nd anchor body)	0.97 0.69
T8		Double	234	239.1 (1st anchor body) 114.3 (2nd anchor body)	1.03 0.49

Since grout-ground interface failure occurred in all experimental conditions, the average grout-ground shear stress at the ultimate loading step can be considered as the grout-ground shear strength generated by each anchor body. Therefore, similar to the group effects on later resistance of the pile foundation, in the double anchor bodies condition, the grout-ground shear strength was reduced by the superposition of the shear fields generated by each anchor body (Fig. 15). In the case of group piles, it is known that the bearing capacity of the pile located in the trailing row is reduced by the interference (shadowing) with the shear field generated by the front row pile [3, 22, 24]. Similarly, in the double anchor body condition, each anchor body behaves independently, so it seems that the shear field generated by the 1st anchor body moved the ground around the 2nd anchor body and reduced the grout-ground shear strength. Furthermore, similar to the group pile effect, where a greater reduction in bearing capacity occurs as the spacing between piles decreases [3, 17, 25, 37], the overlap of the shear field increases as the spacing between anchor bodies decreases, and it is believed that a smaller grout-ground shear strength was generated at the 2nd anchor body. The stress field generated by each anchor body is expected to increase with increasing relative density. Davidson et al. [6] found that the magnitude of the shear field generated during cone penetration tests increased with increasing relative density. Therefore, similar to group piles where group efficiency decreases with increasing relative density [18, 19], double anchor bodies appear to experience greater shear field overlap and lower grout-ground shear strength with increasing relative density. The results of the above studies suggest that applying the same grout-ground interface shear strength along the anchor length, as in the current LDCA design criteria, may overestimate the grout-ground failure load of LDCAs. Therefore, it is necessary to propose a reduction factor based on the spacing of the anchor bodies, similar to that used for group piles, to evaluate the accurate ultimate bearing capacity of LDCAs.

In this study, a physical model test using a scaled-down LDCA was conducted to assess the failure modes and pull-out behavior of LDCA under different ground conditions. The tests were performed at 90% relative density with various numbers of anchor bodies and spacings, comparing these results with those at 70% relative density. The following conclusions were drawn from the model experiments.

The load-displacement curves indicated an increase in ultimate bearing capacity with higher relative density in the single anchor body condition. At 600 mm and 1200 mm total lengths, the capacity increased by approximately 26% and 25%, respectively, when relative density rose to 90%. However, in the double anchor body condition, the ultimate bearing capacity was lower than in the single anchor body setup, with a greater decrease in capacity as relative density increased.

Axial grout load analysis under different conditions revealed that tensile failure between the second anchor body and the underlying grout occurred at a very low load in the double anchor body setup, regardless of relative density and spacing. This failure, due to the grout's susceptibility to tensile stress, could happen at loads as low as 9% of the maximum applied load, even in field-applied prototype LDCAs.

The grout axial load distribution after anchor body-grout tensile failure showed a similar tendency regardless of the relative density. For the wide anchor body spacing condition, the tensile load of the grout beneath 2nd anchor body remained constant, indicating that the 1st and 2nd anchor bodies behaved independently. However, for the narrow anchor body spacing condition, local grout-ground interface failure occurred at the 1st anchor body, and the overlapping of grout axial load was generated.

Based on the grout-ground interface failure load presented in FHWA, the anchor body spacing to prevent grout axial load superposition was evaluated. It was confirmed that an anchor body spacing of 2 m or less is sufficient to prevent superposition of grout axial loads in most soil conditions when 60% of the strand tensile failure load is applied to the prototype LDCA. However, in the case of loose silty sand, silty clay, it was found that anchor body spacing of 2 m or more was required to prevent superposition of grout axial loads. Considering that the anchor body spacing of 2 m is currently used as a conventional practice, further research is needed for silt and clay, which have very different shear behavior from weathered soil.

The analysis of grout-ground shear stress distributions showed that the shear strength of the 1st anchor body in double anchor body setups was comparable to that of a single anchor body, whereas the 2nd anchor body exhibited lower shear strength. This reduction is attributed to the overlapping stress fields from each anchor body, diminishing the grout-ground shear strength of the 2nd anchor body. With decreased anchor body spacing and increased relative density, this overlapping intensified, leading to a notable decrease in ultimate bearing capacity. To facilitate a more accurate evaluation of the grout-ground interface failure load (i.e., ultimate bearing capacity) of LDCA, it is imperative to develop a reduction factor for interface shear strength that accounts for anchor body spacing and ground conditions.

Competing Interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Author Contribution

B.-H, Jo: Conceptualization, Experimental investigation, Writing—review & editing.C.-K Chung: Conceptualization, Resources, Writing—review & editing, Supervision.G.-B Shin: Conceptualization, Experimental investigation, Writing—original draft.

Acknowledgement

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1A2C2010771) and the Institute of Engineering Research and Entrepreneurship at Seoul National University.

Data Availability Statement

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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An Experimental Study on the Failure Mechanism of Load Distributive Compression Anchors in Residual Soil

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Abstract

Figures

1. Introduction

2. Background

2.1. Failure modes of a compression-type anchor

2.2. Failure modes of a LDCA

3. Physical model tests

3.1. Experimental condition

3.2. Physical modeling of LDCA

3.3. Pull-out test method

4. Load-displacement relationship

4.1. Single anchor body

4.2. Double anchor bodies

5. Effect of relative density on LDCA Failure Modes

5.1. Tensile failure at anchor body-grout interface

5.2. Overlapping of grout axial load

5.3. Interference effect of multiple anchor bodies

6. Conclusions

Declarations

Author Contribution

Acknowledgement

Data Availability Statement

References

Additional Declarations

Status:

Version 1