### Ultimate load

As shown in Fig. 6, the average ultimate pull-out loads of the TC-anchorage system and T-anchorage system are 26.30 kN/m and 18.85 kN/m, respectively. Ignoring the difference of bolts structure and assuming that the shear stress distributes uniformly along the embedment length, the average shear strength of the bolt–slurry interface of TC-anchorage system and T-anchorage system are 0.26 MPa and 0.19 MPa, respectively. Obviously, the average interfacial shear stress of TC-anchorage system increases by about 40% compared with that of T-anchorage system. This benefits from the positive role played by TC-bolt structure in improving anchorage capacity, which is also supported by the research of different research fields, different materials anchors and different bolt structures, as well as similar research on changing the stress mode between bolt and slurry by changing bolt diameter [28,29,30]. When comparing with the practical design value (3 kN/m) [31] from the perspective of stabilisation, the anchorage capacity provided by TC-anchorage system can better meet the protection requirements of earthen heritage sites.

According to the results of laboratory tests and field tests, the following parameters can be obtained: \(\tau_{f}\) is equal to the average shear strength of bolt–slurry interface of T-anchorage system, i.e., \(\tau_{f}\) = 0.19 MPa, \(\mu\) = 1, \(L_{\text{c}}\) = 100 mm and \(f_{cu}\) = 1.92 MPa. The value of \(P_{TC}\) calculated from Eq. (1) is 25.07 kN. From Fig. 6, it can be seen that \(P_{TC}\) is less than the actual ultimate load mean of TC-anchorage system. This may be mainly due to the uniaxial unconfined compressive strength of \(f_{cu}\) used in calculating \(P_{c}\), while the slurry in pressure-bearing section is in a three-dimensional stress state during the actual stress process, so \(f_{cu}\) is less than the actual compressive strength of slurry, resulting in a slightly smaller calculation result \(P_{TC}\) than the mean test value. For practical engineering, the calculation of ultimate load of the TC-anchoring system using \(f_{cu}\) is biased towards safety.

### Load–displacement

As shown in Fig. 7, there are three inflection points and four stages in load–displacement curve of TC-anchorage system during cyclic loading process. The load–displacement curve is in the elastic stage before the first inflection points (yield point), which is basically linear. The curve between yield point and the second inflection point (reinforcement point) is in the plastic stage, which shows a non-linear and non-uniform increasing relationship. In this stage, the bolt–slurry interface enters the stage of full plasticity, and the pressure-bearing body and slurry are compressed tightly into rigid body, which can be proved from each cyclic path of the load–displacement curve. No response is observed for displacement of each cyclic path regardless of load rise or fall. Only when the load exceeds the maximum cyclic load of the previous stage and increases into the next stage of larger cyclic load, the displacement can continue to increase. The curve between the reinforcement point and the third inflection point (peak point) is reinforcement service stage, and the load–displacement curve shows an obvious non-linear non-uniform increase relationship. When the load reaches peak point, load–displacement curve enters the stable stage. In the stable stage, the load value decreases slightly (1–2 kN) compared with the peak value, and then remains stable in the process of about 40 mm displacement after the peak value.

During the cyclic loading process of T-anchorage system, there are two inflection points and three stages in the load–displacement curve. Similar to TC-anchorage system, the load–displacement curve is elastic before the first inflection point (yield point), which is basically linear. The curve between yield point and the second inflection point (peak point) is the plastic stage, which shows a non-linear and non-uniform increase relationship. In this stage, the bolt–slurry interface enters a stage of plastic deformation with a certain amount of elastic deformation. This phenomenon can be evidenced by the elastic and plastic strains in the load–displacement curves of the two cyclic loading processes. When the load reaches peak point, load–displacement curve enters the failure stage, which includes three processes. First, during the displacement of about 5 mm after the peak point, the load shows a sharp decline (8–10 kN). Then, the load increases slightly (2–3 kN) during the next 4 mm; Thereafter, during the next 70 mm displacement, the load (residual load) remained basically stable.

Moreover, according to the characteristics of load–displacement curves of two kinds of anchorage systems, TC-anchorage system shows greater ultimate load and ductility than T-anchorage system. This is manifested in: (1) although the load at the yield point of TC-anchorage system and T system are both 8 kN, the displacement at the yield point of TC-anchorage system is about 7.5 mm larger than that of T-anchorage system. (2) The load–displacement curve of TC-anchorage system has more reinforcement point and reinforcement service stage than that of T-anchorage system, and this reinforcement service stage has the characteristics of small increase of load and large increase of displacement. (3) The displacement of the peak point of TC-anchorage system is 7–14 times of that of T-anchorage system. (4) The post-peak load of T-anchorage system decreases sharply and the residual load is about 60–70% of the peak load. However, the residual load of TC-anchorage system anchorage system decreases only slightly, which is about 92–97% of the peak load and remains stable during the process of large displacement. Therefore, from the results and analysis of load–displacement curves of two kinds of anchorage systems, it can be concluded that T-anchorage system is a typical burst failure mode, while TC-anchorage system is an ideal progressive reinforced failure mode. The TC-anchorage system exhibits the expected characteristics of “high anchorage force, large deformation resistance”. The TC-anchorage system still provides considerable anchorage force when large deformation (e.g., over 80 mm) occurs.

### Strain distribution along the embedment length

Figure 8a, b shows the distribution of interfacial strain along the embedment length of each anchorage system under different levels of load. For TC1-anchorage system: (1) Elastic stage (0 → 8 kN). In 0 → 4 kN stage, the curve shows a positive skewness curve (a short curve on the left side and a long curve on the right side) with a peak value at L = 20 cm, in other words, the strain increases sharply from L = 0 to L = 20 cm, and decreases from L = 20 to L = 100 cm. In 4 → 8 kN stage, the strain of each monitoring point increases with the increase of load in varying degrees and the curve is still positive skewness distribution, but the peak value appears at L = 40 cm. This phenomenon shows that in 0 → 8 kN stage, the pull-out effect mainly occurs in the front of the embedment length. With the increase of load, the peak strain shifts back, that is, the pull-out stress of the interface transfers to the end of the embedment length. (2) Plastic stage (8 → 24 kN). In 8 → 12 kN stage, the curve still shows a positive skewed single peak distribution. Although the peak value is still at L = 40 cm, the strain increment at L = 40–100 cm is much larger than that at L = 0–20 cm. In 12 → 16 kN stage, the curve has a double peak shape, the higher peak value is L = 40 cm, the lower peak value is slightly prominent at L = 80 cm, and the strain increment at L = 60–100 cm is much larger than that at L = 0–40 cm. During the period of 16 → 20 kN, the double peak position of the curve remained unchanged, except that the strain at the peak value of L = 80 cm increased significantly. In 20 → 24 kN stage, the strain increment at L = 60–100 cm is much larger than that at L = 0–40 cm, and the peak value at L = 80 cm has exceeded that at L = 40 cm. During the 8 → 24 kN period, the curve experienced the typical stages of positive skewness, double peaks of front-high and back-low, and double peaks of front-low and back-high. The above phenomena show that: In this process, the interface strain at the back of the embedment length increases gradually, and the uplift resistance provided by the back of the embedment length increases gradually. The bolt–slurry interface at the front of the embedment length is gradually decoupled and the main pull-out action section is gradually transited from the front tension anchorage section to the back end of the tension anchorage section and the pressure-bearing body to bear together. (3) Reinforcement service stage (24 → 28kN): In this stage, the curve shows a single peak distribution with negative skewness, and the peak value is at L = 80 cm. The closer the measuring point is to L = 80 cm, the greater the strain increase is. This indicates that the main pull-out part has transited to L = 80–100 cm, in other words, the pressure-bearing body plays the main pull-out role.

The distribution of interfacial strain along embedment length in TC2-anchorage system is similar to that in TC1-anchorage system: (1) Elastic stage (0 → 8kN). The curve path has a positive skewed single peak distribution, and the peak value shifts from L = 20 to L = 40 cm. (2) Plastic stage (8 → 16kN): The curves show double peaks at L = 40 cm and L = 80 cm respectively, and the strain increment in L = 60–100 cm is much larger than that in L = 0–40 cm. The curve also shows a transition from the double peaks of front-high and back-low to the double peaks of front-low and back-high. (3) Reinforcement service stage (16 → 20 kN): the curve shows a negative skewness single peak shape and the peak value is at L = 80 cm. The above phenomena show that: with the continuous increase of pull-out load, the strain in front of embedment length increases slightly, while the strain in back of embedment length increases substantially. The position where the bolt–slurry interface provides the main pull-out resistance is transferred to the end of embedment length. The larger the load is, the stronger the pull-out resistance of the back part of the embedment length of TC-anchorage system can be.

As shown in Fig. 8c, d, the strain distribution curve of the bolt–slurry interface in T-anchorage system shows a negative exponential decay along the embedment length, and the peak strain is always at L = 0 cm. With the increase of load, the strain of each measuring point increases. The closer the measuring point is to L = 0 cm, the greater the strain increase is, and the more significant the curve attenuation is. The strain mainly distributes in L = 0–40 cm. This phenomenon is similar to the results of previous studies [17, 18], that is, the strain distribution at the bolt–slurry interface is not uniform, and the stress mainly concentrates on the front end of the embedment length.

The strain distribution along embedment length of T-anchorage system decreases negatively exponentially from low load to high load, and the strain increment is always large in the range of L = 0–40 cm, which fully shows that only the front end of embedment length plays a major role in uplift resistance. However, the strain distribution along embedment length of bolt–slurry interface in TC-anchorage system is unimodal positive skewness distribution under low load; It is in the process of bimodal dynamic transition from high front peak-low back peak to low front peak-high back peak under the load from low to high; It presents a unimodal negative skewness distribution under ultimate load. Distribution of strain at bolt–slurry interface along embedment length of TC-anchorage system shows that the whole embedment length plays a full role in pull-out, especially in the pressure-bearing section. Obviously, TC-anchorage system has more reasonable spatio-temporal continuity than T-anchorage system. However, it is noteworthy that TC-anchorage system still has defects. Under different levels of loads, the whole bolt–slurry interface of TC-anchorage system is not an ideal uniform force, but a local force mode which transfers from the front end of embedment length to the back end of embedment length in stages. Although this force mode can ensure the continuity of the force on the interface, it is not conducive to greatly improving the ultimate load of TC-anchorage system.

### Failure law

During the pull-out test, there were no cracks in the heritage sites soil, and the bolts were not broken. All tests were forced to stop when the displacement of anchor head cannot converge or the pull-out load cannot increase. Observing the external phenomena of field parallel test (Fig. 9a), the bolts of the two anchorage systems were pulled out in slurry and a few radial cracks appeared in slurry near the orifice (the front end of embedment length). After pulling out the bolts of the two kinds of anchorage systems, the failure modes of the two kinds of anchorage systems show obvious differences: (1) there is a certain amount of slurry bonding on the whole bolt surface of T-anchorage system. The slurry-soil interface did not exhibit debonding and slippage. There is no excessive damage to the slurry in the hole, and slurry powder residues at the bottom of the hole (Fig. 9b). The local slurry in the hole presents threads mosaic with the shape of the bolt, and there are rough scratches in the local slurry. (2) There is a certain amount of slurry bond on the surface of TC-anchorage system bolt with the whole embedment length. The slurry forms a conical slurry based on the pressure-bearing body at the end of the bolt (Fig. 9c). The surface of the conical slurry has friction marks and is smooth. The slurry in the anchor hole is broken, and the hole wall is partly scratched and relatively complete. Observing the residual slurry in the anchor hole, it has become small fragments or powders. There is a thin-bedded slurry bonding somewhere in the inner wall of the hole, and some of the thin layer of soil on the surface of the hole wall appears fresh friction fracture marks.

The measured heights of conical slurry of TC1-anchorage system and TC2-anchorage system are 55 mm and 50 mm respectively, and the calculated angles between the conical surface and the bottom are 66.43° and 64.36° degree, respectively (Fig. 9d). According to Mohr–Coulomb criterion, the internal friction angle of conical slurry can be obtained by Eq. (4). The formula is as follows:

$$\alpha = 4 5^\circ + \varphi / 2$$

(4)

where α is the angle between the direction of conical surface and the direction of the hollow truncated cone plane; φ is the internal friction angle of the conical slurry. The units of α and φ are the degree (°).

The calculated values of TC1-anchorage system and TC2-anchorage system are 42.86° and 38.73° respectively, which are not much different from the internal friction angle (φ = 41.92°) measured in laboratory. This shows that the conical surface is a shear fracture surface formed by the combined action of the maximum principal stress provided by the hollow truncated cone and the small principal stress provided by the hole wall of heritage site soil.

From the analysis of the above phenomena and results, it can be concluded that slurry shearing and dilational slip lead to the debonding and decoupling of the bolt–slurry interface in T-anchorage system. The failure mode of tension section of TC-anchorage system is consistent with that of T-anchorage system, but the failure mode of pressure-bearing section is completely different. The difference between the failure modes of the two anchorage systems is mainly related to the stress mode of the confined structure in the pressure-bearing section of TC-anchorage system. The failure mode of pressure-bearing section of TC-anchorage system is that slurry is cut into the conical slurry. According to Mohr strength theory, the shear strength of failure surface is related to the properties of slurry and the normal stress of failure surface. Under the confining pressure produced by pressure-bearing body, anchor hole wall and slurry in the tension section, normal stress of slurry failure surface in the pressure-bearing section is effectively increased, which effectively improves shear strength of slurry. After the formation of conical slurry, under the continuous pull-out load, conical slurry moves forward to compact its peripheral slurry. The confining pressure of the hole wall and the compressive performance of slurry in the compaction zone will be fully utilized, which once again forms an effective pull-out effect on the conical slurry of TC-anchorage system. It is also revealed that the pull-out performance of TC-anchorage system depends on the shear and compressive properties of slurry in the pressure-bearing section.