2.2.2. Selection of Anchor Positions

It is assumed that for each rock type in the investigated section there are areas which are visually on the first visual inspection better and others which are worse suited as base material (Figure 2). Well suited or undisturbed areas were assumed to be (i) not disturbed in the close-up range (1.5 × hef) by visually recognizable joints (see Figure 2a). In contrast, worse suited or disturbed areas were defined as (ii) affected by at least one optically detectable joint. (Figure 2b). In order to consider the worst case in terms of fastening, anchors were directly positioned in a visually recognizable joint (Figure 2). Test quantities per rock type and fastening area (disturbed/undisturbed) are plotted in Table 1. This procedure is used for a visual assessment on site and is intended to represent two possible base material extremes and, derived from this, the fastening quality.

**Figure 2.** Anchor positions one to nine in (**a**) undisturbed area (not affected by visual detectable joints) and (**b**) disturbed area (affected by joints).

#### **3. Results**

#### *3.1. Influence of the Fastening Area (Disturbed/Undisturbed)*

Table 3 shows that existing joints in the fastening area next to the anchor strongly influence the load-bearing capacity. For example, granulite and granite show a deviation undisturbed to disturbed—of approximately 60% and dolomitic limestone shows approximately 50% (see Table 3). Undisturbed areas do not show any rock disturbances due to inhomogeneities and existing joints and are therefore more suitable ex ante as a base material for fastenings.

**Table 3.** Comparison of failure loads for the different rock types for disturbed and undisturbed areas.


#### *3.2. Influence of Joints on the Load-Bearing Capacity*

#### 3.2.1. Joint Quantity

As explained in Table 1, the number of critical joints was determined. The assessment was done visually after failure of the anchor occurred. It was assumed that high joint quantity results in low load-bearing capacities of the anchorages. For undisturbed areas generally a critical joint quantity of zero and high load-bearing capacities have been found. For disturbed areas, a joint quantity of at least one and low load-bearing capacities were recorded. In [9], more information about disturbed and undisturbed areas and also a comparison to classification models can be found. Thus, an influence of joint quantity on load-bearing capacity could be stated. However, further investigations of this relationship were not carried out, because critical joints can only be determined after failure occurs. Test No. 9 in granulite (epoxy resin mortar) in undisturbed base material serves as an example (Figure 3). While an optical assessment indicated an undisturbed area and no critical joints, retrospectively, the results indicated that many joints were found to be critical for failure.

**Figure 3.** Joint quantity next to the anchor (**a**) before pull-out test in undisturbed area–no critical joints visible and (**b**) after pull-out test–critical joints visible.

#### 3.2.2. Joint Weathering

The influence of joint weathering was considered in accordance to [23] and is mostly presented as discoloration of the surface (e.g., rust-brown coloration due to oxidation for granulite). Figure 4 demonstrates the failure load (Fu) unrelated to the anchor type per defined weathering class and rock type. According to Figure 4, the failure load and degree of weathering are strongly related. High weathering of joints leads to lower load-bearing capacities. The secondary y axis of Figure 4 shows the coefficients of variation (CV).

**Figure 4.** Failure load and CV as function of weathering class and rock type–weathering class determined after failure occurred (if *n* = 1 no CV is given and the beams are hatched as the data can contain an outlier).

Comparing the coefficients of variation, it was found out that with low degree of weathering failure loads are not only higher but are also less scattering. Like joint quantity, joint weathering was determined after failure occurred, too. Figure 5 indicates the reason for that, showing an installed chemical anchor where the degree of weathering of the joint

ȱ ȱ (**a**) (**b**)

is unclear before the pull-out test is carried out (Figure 5a), although high weathering of the joints could be observed after failure occurred (Figure 5b).

**Figure 5.** Joint weathering for (**a**) an installed anchor–weathering of joint unclear and (**b**) an anchor after failure–weathering of joint visible after failure occurred.

Figure 6 shows the relationship between the determined rebound value and joint weathering based on the different geologies. For high joint weathering, small rebound values were found. For low weathering, high rebound values could be determined. For different rock types, the above-mentioned correlation is varying. It should be mentioned the correlation can be determined only qualitatively, as classification of the weathering degree was also performed qualitatively. The secondary y axis of Figure 6 shows the coefficients of variation (CV). Table 4 presents the standard deviations for Figures 4 and 6.

**Figure 6.** Relation between joint weathering and R including CV (if *n* = 1 no CV is given and the beams are hatched as the data can contain an outlier).


**Table 4.** Standard deviations for Figures 4 and 6.

*3.3. Base Material Assessment by Rebound Hammer*

As explained in Section 2.2.2, the anchor positions in the experimental campaign were first visually divided into disturbed and undisturbed areas. After this visual assessment, eight rebound values were determined circularly around the anchor position at a distance of 1.5 × hef as shown in Figure 2. Initially, rebound values were taken to provide an indication of the rock strength. Secondly, rebound values also are used to validate the classification into disturbed and undisturbed areas. As shown in Figure 7, disturbed areas lead to smaller rebound values with visible joints in the investigated area, whereas undisturbed areas show higher rebound values with no visible joints.

**Figure 7.** Mean rebound values for disturbed and undisturbed areas for all rock types.

#### **4. Discussion**

#### *4.1. General*

The aspects discussed in the following are based on the experimental investigations described above, whereby no numerical insights are presented.

The given example in Section 3.2.1 (see Figure 3) demonstrates the difficulty of existing critical joints, which can be recognized only after failure has occurred. The fact that in some cases critical joints are not visible in advance implies that other methods in addition to a visual assessment should be carried out. A suggestion on a method how to verify the visual assessment can be found in Figure 8.

ØRdisturbed: mean value of all rebound values (disturbed) per rock type Ranchor: mean value of the eight rebound values per anchor

**Figure 8.** Flow chart for base material assessment by rebound hammer.

As for the joint quantity (see Section 3.2.1) the same is true for joint weathering (see Section 3.2.2). While the degree of weathering is unclear before the pull-out test is carried out, it can be easily determined retrospectively after the conduction of the test. From Section 3.2.2 it can be concluded that a low degree of weathering is well suited as an indicator for assessing the base material quality. Although a strong correlation was observed, an exact preliminary assessment of joint weathering is not possible. Hence, also the relation between the rebound value and joint weathering was investigated in Figure 6. Figure 6 indicates that joint weathering also correlates with rebound values taken around the anchor position (see Figure 2 and Section 3.2). In other words, rebound values determined next to the anchor position indicate joint weathering and thus also the base material quality. This causes a significant advantage, as rebound values can be determined easily using the base material surface, prior to failure and even before the installation of the anchor. Therefore, the relationship between rebound values and load-bearing capacities was investigated.

In order to compare rebound values with failure loads, a validation of the optical assessment was performed according to Figure 8. Firstly, the mean value of all rebound values of disturbed areas was calculated (ØRdisturbed). ØRdisturbed was then compared to Ranchor, which is the mean value of rebound values per anchor. This procedure, according to Figure 8, is used to validate the visual assessment. To be able to assume an undisturbed area, both the optical assessment and the comparison of Ranchor with ØRdisturbed must provide the result "undisturbed".

#### *4.2. Relation between Rebound Value and Load-Bearing Capacity*

As concluded in Section 3.1 it seems that rebound values next to the anchor position can be used as an indicator for rock quality as base material. Therefore, Figure 9 plots the relationship between failure load and rebound value (as the mean value of 8 values circularly around the anchor position) per rock type and fastening area (disturbed/undisturbed). According to Figure 9, the disturbed areas (grey color in Figure 9) are characterized by lower rebound values and failure loads, while the values are widely distributed around the line of closest fit. In contrast, undisturbed areas (black color in Figure 9) show high rebound values and high failure loads for all rock types. It can also be seen that disturbed and undisturbed areas cannot be clearly separated, but on the contrary are overlapping to some extent. Considering this in addition to the existing relationship between rebound values and failure loads, it can be concluded that the estimation of base material quality by determining rebound values is possible. However, it should be noted that a high correlation is evident for disturbed and not for undisturbed areas. For the undisturbed areas, the rebound values are capped at about 70 while the failure loads are not. The lack of correlation demonstrates that the rebound hammer is not indicative for the failure load above a certain rock strength but ensures a minimum value of load bearing capacity. The exponential correlation curve between rebound values and uniaxial compressive strength [19]

is considered reasonably low for the undisturbed areas. In addition, it is possible that microcracks in the undisturbed rock cannot be detected by means of rebound hammers, although they have a significant influence on the loading of the anchor pull-out, since here the rock experiences tensile stress. For dolomite, no undisturbed fastening areas could be observed, and therefore only one data set for disturbed areas is shown. Accordingly, estimating base material quality by rebound values varies in its suitability for different rock types.

**Figure 9.** Relationships between rebound values and failure loads for various rock types.

In Figure 10, all rock types are examined together. The rebound values (R) illustrated are equivalent to the mean rebound values from the anchor position. These are calculated out of eight values taken next to the anchor position (compare to Figure 2). Therefore, it is possible to indicate not only the mean rebound values, but also to plot the scattering per value (described by the coefficient of variation, CV). This form of presentation was chosen in Figure 10, where large data points indicate a high coefficient of variation. According to Figure 10, disturbed areas result in more scattering of rebound values than undisturbed areas. Inhomogeneities around the anchor position in disturbed areas thus lead to the varying rebound values. In undisturbed areas, intact rocks with more homogeneous

properties lead to a more uniform distribution of rebound values, whereas low CVs should therefore indicate good rock properties.

On the contrary, poor uniformly distributed rebound values can lead to a small scattering too. Small CVs therefore do not automatically indicate good fastening properties. Instead of that, they can originate from good or poor a priori rock properties. In Figure 11, the measured rebound values taken next to the anchor are shown using a radar chart. For both examples, the rebound values are evenly distributed. Although this results in similar CVs, the failure loads differ significantly. Therefore, using CVs to identify good rock properties is not sufficient. In order to prevent wrong conclusions being drawn from a low CV in regard to good rock properties, it is necessary to have a combined consideration of CV and mean R value.

**Figure 11.** Uniformly distributed rebound values R (CV, Rmean, Fu). (**a**) uniformly distributed with low R values; (**b**) uniformly distributed with high R values.

Thinking further, it is also possible to neglect the CV altogether. In fact, the rebound value scattering is not decisive if the mean rebound value succeeds a certain level. Figure 12 demonstrates an example for this conclusion. Although a high CV can be observed due to downward statistical outliers, it was still possible to achieve a good load-bearing capacity. Hence, in order to identify good rock properties in advance, it should be sufficient if the tested rebound values per anchor are not falling below a certain level. A further consideration of the coefficient of variation was therefore not carried out.

mainly high R values including two downward outliers - Rmean=62,9; CV=26,2%; Fu=63,2kN (granulite - chemical anchor - undisturbed)

**Figure 12.** High rebound values including two downward outliers (CV, Rmean, Fu).

In Figure 13, a lower threshold value for the rebound values was defined. In order to determine the threshold value, a log normal distribution was assumed for all undisturbed rebound values. Calculating the 5% fractile from this distribution, a mean rebound value of 53.2, a standard deviation of 1.3, and a k-value of 1.645 for an infinite sample size were used. Conclusively, a threshold of 36 resulted. When highlighting all anchors in undisturbed areas for which none of the eight rebound values is below this threshold, good rebound values and failure loads can be obtained.

Some data points for disturbed areas also show comparable failure loads and rebound values. In principle, the same procedure can be used for anchor positions in disturbed areas, if compared to the threshold of undisturbed rebound values. However, resulting failure loads are lower and show a larger scattering, which can be explained by the existing inhomogeneities in the base material. The rock quality for post-installed anchors for these areas could be described as average.

The approach should therefore always be used in combination with a visual assessment. Nevertheless, Figure 13 indicates that using a lower threshold allows to identify good rock properties when combined with a visual assessment. A classification of base material properties by means of a combination of visual assessment and the determined threshold can be obtained from Table 5.

**Figure 13.** Relationship between rebound values and failure loads–anchors where R values do not fall below threshold are highlighted.

**Table 5.** Base material classification.


As described above, good base material quality can be assumed when the threshold is met in undisturbed areas. Average base material can be expected if (1) the rebound values are above the threshold in disturbed areas or (2) the threshold is not fulfilled in undisturbed areas. Ultimately, poor base material should be considered when rebound values are below the limit value in disturbed areas.

#### **5. Conclusions**

Small scale investigations on rock were performed in order to identify influencing parameters on the load-bearing capacity of post-installed anchors. It was shown that, for disturbed areas, a high number of joints are usually critical for failure and lead to low failure loads. For undisturbed areas, higher load capacities could be found with fewer joints, whereby the joint quantity was determined retrospectively. Nevertheless, it was shown that it is not possible to determine critical joints before failure occurs.

Weathering degree also shows a correlation with failure loads. High degrees of weathering of joints lead to smaller failure loads. Once more, it is not possible to determine the weathering degree before failure. However, it was possible to show that rebound values around the anchor position correlate with the degree of weathering. A high degree of weathering leads to low rebound values and low joint weathering leads to high rebound values. Therefore, rebound values provide the possibility of making an estimation about base material quality in advance of failure. Accordingly, high rebound values indicate good base material quality. From the investigated rebound values, a threshold can be calculated based on a log-normal distribution. If rebound values around optically undisturbed anchor positions do not fall below this threshold, good base material properties can be assumed. If the criterion is met in areas of optically disturbed anchor positions, average base material quality can be assumed. This procedure should therefore always be combined with a visual assessment. Average base material can also be considered if the threshold is not met in undisturbed area. Finally, poor base material should be assumed when the criterion is not met in disturbed areas.

This technical paper was able to demonstrate the influence of joint quantity and weathering next to the anchor position on post-installed anchors in rock. Further, an approach for a preliminary assessment to classify the base material quality was proposed. An open question remains concerning the extent to which t a design concept for the base material classes can be derived from this and this will be the subject of future research. A detailed investigation of these questions helps engineers of post-installed anchors to become more familiar with the less known base material rock.

**Author Contributions:** Conceptualization, S.L., O.Z. and K.V.; methodology, S.L., O.Z. and K.V.; software, S.L.; validation, S.L., O.Z. and K.V.; formal analysis, S.L. and O.Z.; investigation, S.L. and K.V.; resources, O.Z. and K.V.; data curation, S.L.; writing—original draft preparation, S.L.; writing—review and editing, O.Z. and K.V.; visualization, S.L.; supervision, O.Z. and K.V.; project administration, O.Z. and K.V.; funding acquisition, O.Z. and K.V. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

