1 Introduction

The Yungang Grottoes are located in southern Wuzhou Mountain, about 16 km west of Datong, Shanxi Province, P. R. China. It has more than 1500 years of history detailing its magnificent structure and rich historical content. It is known as the treasure house of ancient Chinese sculpture art. The Yungang Grottoes were inscribed into the World Cultural Heritage List by the United Nations Educational, Scientific and Cultural Organization (UNESCO) in December 2001 (Wang et al. 2014; Guo and Jiang 2015). For many years, due to natural weathering by sun and rain, frost and erosion, and other of man-made impacts, the caves and statues have suffered different degrees of damage (Li et al. 2012a; Qin et al. 2016). The former columns of the grottoes have been bearing the weight of the above rock masses for about 1500 years. The columns have begun to creep under the long-term load, which reduces the carrying capacity. Therefore, the long-term strength of the columns is the key issue whether the Yungang Grottoes can be preserved well into the future (Yang et al. 2009). Studies show that water is one of the main cause of weathering to the grottoes, and phenomena such as swelling, disintegration and softening occur after the water penetrates and interacts with the rock, reducing the stability of the geotechnical engineering (Lu and Wang 2017; Li et al. 2010).

Due to the high historical and cultural value of the Yungang Grottoes, many experts and scholars have performed a great deal of scientific research on water seepage, weathering mechanisms and protection measures. However, the previous research did not take into account the attenuation of rock strength under long-term loading (Huang 2008; Yan et al. 2015). The long-term strength of the rock load-bearing elements is related to the bearing capacity and stability when protecting stone cultural relics. Therefore, it is necessary to study the effects of rock-water interaction on the long-term strength of the former columns of the grottoes.

The effect of time and rheological characteristics are the most important basic properties of rock, and also the basis for long-term stability evaluation of rock engineering (Bobyleva and Shamaev 2017; Zhang et al. 2016a; Scotti et al. 2017). Currently, there are many studies on the creep principle of rock in either a dried or natural state, but few studies on the similarities and differences of creep principle between water-saturated rock and its dried counterpart (Zhao and Wan 2014; Cui and Fu 2006; Xu et al. 2012; Li et al. 2012b; Li and Shao 2016; Fahimifar et al. 2015; Zhu and Yu 2015; Rahimi and Hosseini 2015; Wang et al. 2017; Li et al. 2012c; Liu et al. 2013; Kang et al. 2016; Moore et al. 2016). Wu used uniaxial and biaxial creep tests to study the rheological behavior of hard rock in a dried state (Wu et al. 2016). Mishra made a series of uniaxial creep tests on dried shale, and studied the deformation and failure principles of rocks with time under complex stress conditions (Mishra and Verrna 2015). Therefore, we independently developed an experimental device called “the Gaseous Water Adsorption Intelligent Test System of Rock” to simulate the water absorption process of rocks in a warm and humid rainfall environment. We then performed creep experiments on samples from the former columns of Yungang Grottoes in either dried or water-saturated states respectively, and combined axial and transverse deformation analysis to comprehensively determine the effect of rock-water interaction on the long-term strength of rocks.

Cave No. 9 and Cave No. 10 of the Yungang Grottoes have the same shape and scale, as shown in Fig. 1. An extensive period of wind and rain erosion has made the former columns of the grottoes severely weathered (Yan et al. 2013). The original cylindrical columns are now visible deteriorating into rock piles surrounding cone-shaped pillars, threatening the stability of the grottoes, as shown in Fig. 2. In this paper, the rock rheological perturbation experiment system was used to analyze the long-term strength of the rock samples from columns of Cave No. 9 and Cave No. 10 in Yungang Grottoes in both dried and water-saturated states. The axial and transverse creep characteristics of the rock samples in the different states were evaluated and the bearing capacities of the columns were determined. The experimental results provide a reference for the long-term strength evaluation of column rock masses, and provide a theoretical basis for the waterproof protection of the World Cultural Heritage, Yungang Grottoes.

Fig. 1
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Columns of Cave No. 9, 10 in the Yungang Grottoes

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Fig. 2
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A conical column of No. 9 at the Yungang Grottoes

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2 Materials and Experiment

2.1 Sample Selection

This long-term strength experiment was based on medium-coarse sandstone rock groups typically found with the Yungang Grottoes. The lithology in the Yungang grottoes area is relatively simple, and the rocks are mainly middle Jurassic (J) sedimentary sandstones. The rock samples were cut by a rock cutting machine and processed into cylinders with a height of 100 mm and a diameter of 50 mm. The rock samples with similar wave velocity were screened using the acoustic wave velocity test to guarantee rock samples with similar properties and reduce experimental errors. The experimental rock samples were divided into two groups to test the long-term strength of the rocks in either a dried or water-saturated state (Toralv 2011; Liu et al. 2017; Zhang et al. 2016b). In order to avoid the effect of a high drying temperature on the mineral composition and structure, the dry rock samples were simply dried at room temperature until their masses were constant. The water-saturated rock samples used the “adsorption method of gaseous water” by using our independently developed experimental device “the Gaseous Water Adsorption Intelligent Test System of Rock” to fully saturate each sample with water, as shown in Fig. 3.

Fig. 3
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Intelligent testing system for gaseous water absorption of rock

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2.2 Water Absorption Experiments

The gaseous water adsorption intelligent test system creates a specified temperature and humidity environment in order to force the rock samples in the container to absorb water vapor. An electronic balance was used to measure the water absorption of rock samples within the container, which was then transmitted directly to a computer. The relevant application plots the characteristic curve of water vapor adsorption of a sample in real-time. During the test, the temperature was set to 20 °C and the relative humidity was set to 100%. The rock’s adsorption of gaseous water is very similar to the water environment faced by rock during the rainy season in practical engineering. Finally, the water-saturated rock samples were wrapped with waterlogged cotton paper and sealed with a layer of plastic wrap to maintain moisture content after removing from the apparatus.

2.3 Experimental Methods

Considering that the former columns of Cave No. 9 and No. 10 are only bearing the uniaxial long-term static load and column structure surfaces are not developed, the long-term strength of the rock masses were only tested by the uniaxial compressive creep experiment. Experimental instrument used a “Microcomputer control electro-hydraulic servo rock triaxial testing machine”, which has a stable load, clear grading, simple to operate, and accurately records strain data. The conventional compression test to measure the uniaxial compressive strength and ultimate strain of the rock samples were first performed. The loading device is shown in Fig. 4. Each rock sample was loaded step by step to ensure that the rock stably deformed after each stage load. Then the next stage load was imposed until the rock fails. The mean value of the load stress was regarded as the inherent long-term strength of the rock group.

Fig. 4
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Loading device

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The specific steps are as follows:

  1. 1.

    A rock sample was placed on the instrument and aligned with the center of the bearing plate, and the extensometers were installed to measure the axial strain and radial strain. The position of the rock during the first phase of loading was adjusted to ensure it was evenly loaded throughout all loading phases.

  2. 2.

    A sandstone sample was loaded at multiple levels according to measured uniaxial compressive strength in the previous loading period.

  3. 3.

    The instrument automatically recorded the load values and strain values during the experiment. After creep stability of rock, the next level load was imposed, and each stage of the load action time was maintained for at least 24 h.

  4. 4.

    The final load was when the rock sample was finally damaged, and the final load stress value was chosen as the long-term strength of the rock group.

2.4 Determination of Loading Basis

The uniaxial compressive strength of the medium-coarse sandstone samples in both dried and water-saturated conditions were measured before the long-term strength experiment. As a basis for the long-term strength experiment, the specific parameters are shown in Table 1.

Table 1 Experimental parameters of instantaneous strength of medium-coarse sandstone in dry and wet conditions
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The sandstones’ intensity attenuated after they were in contact with water, and decreased an average of 38.58%. The moisture content of water-saturated rocks was as high as 2.5%, indicating that the sandstones from the Yungang Grottoes easily absorbed water.

3 Experimental Results and Analysis

3.1 Analysis of Mineral Composition

In order to determine the mineral composition, the mineral content and content of the expansive clay minerals of representative samples from the Yungang Grottoes columns were analyzed qualitatively and quantitatively with X-ray diffraction (XRD). The analysis results of the mineral composition and clay mineral content of S-1, S-2 are shown in Table 2.

Table 2 XRD results of representative sandstone samples from columns of the Yungang Grottoes
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Clay minerals in the medium-coarse S-1 comprise up to 38.2%, along with large amounts of quartz and kalium feldspar. S-2 is mainly composed of quartz and clay minerals, of which clay mineral content is 40.5%, and also contains a small amount of calcite. Overall, clay mineral content is high and weathering is serious in the medium-coarse sandstone in the Yungang Grottoes. Kaolinite is the main clay mineral, comprising up to 70% of the clay content, followed by smectite, illite, and mixed layer illite/smectite. Mixed layer illite/smectite has strong water absorption capacities, lowering the rock strength after coming in contact with water.

3.2 Long-Term Strength of Rock Samples in Dried State

Taking the instantaneous strength of the rock uniaxial compression experiment in the dried state as a reference, the strain–time curves of each stage load were plotted (Fig. 5). When S-1 was in a stable creep stage under the current stage load, then the next stage load was imposed until the rock was damaged. The loading duration and creep deformation monitoring curves of each load during the experiment are shown in Fig. 5.

Fig. 5
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Relationship curve between strain and time of rock in dried state

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From relationship curve between strain and time of the dried rock S-1, throughout the first eight loads, both the transverse and axial creep strain of the S-1 were basically creep stable after about 24 h. There were no development trends nor did it continuously change. The variation range of axial creep deformation was essentially maintained at about 5%, and the variation of horizontal creep deformation was slightly larger. During this process, the pores of the rock were compacted. Under the last load, the S-1 had obvious accelerated creep and was rapidly destroyed after 4.5 h of loading at this stage, which was manifested as accelerated lateral creep expansion and destruction.

3.3 Long-Term Strength Test of Rock Samples in Water-Saturated State

Taking the instantaneous strength of the rock uniaxial compression experiment in the water-saturated state as a reference, the strain–time curves of each stage load are plotted (Fig. 6). When the S-2 was creep stable under current stage load, then the next stage load was imposed until the rock was damaged under the last load. The loading duration and creep deformation monitoring curves of each load during the experiment are shown in Fig. 6.

Fig. 6
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Relationship curve between strain and time of rock in water-saturated state

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From the relationship curve between strain and time of the water-saturated rock S-2, during the first two loads, both the transverse and axial creep strain of the S-2 was basically creep stable within 24 h, and the creep deformations were not obvious and quickly no longer continued to develop. Also, similar to the dry samples, the specimen pores were compressed during loading. From the third load, the transverse monitoring curve of S-2 had obvious creep expansion. The transverse deformation of the rock became uneven and the creep rate increased, which may be related to the water absorption expansion of the clay minerals. Small cracks appeared on the rock surface without macroscopic damage, and the sample was still in a stable creep state. Eventually, under the fifth load, the S-2 was damaged after 12 min, which was manifested as accelerated lateral creep expansion and destruction.

4 Comparative Analysis of Long-Term Strength Experiments in Dried and Water-Saturated State

4.1 Comparison of Uniaxial Compressive Strength

The results of long-term strength experiments under two types of water content conditions in medium-coarse sandstones are in Table 3.

Table 3 Comparison of long-term strength of medium-coarse sandstones in dry and wet conditions
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It can be seen from Table 3 that the uniaxial compressive strength and long-term strength of the medium-coarse sandstones in the water-saturated state were lower than those in the dried state, and both the instantaneous strength and long-term strength decreased by about 40%. The softening coefficient of long-term strength was close to the softening coefficient of uniaxial compressive strength, which was about 60%. The results show that the columns of the Yungang Grottoes are greatly impacted by weathering, and the engineering properties are poor. The content of swelling clays such as smectite in the rock mass is not too high as determined by the XRD results. The ratio of long-term strength and instantaneous strength of sandstones was only 82.8%, and the reduction of long-term strength was larger. Therefore, the strength reduction effect should be considered when implementing a protection plan for the Yungang Grottoes.

4.2 Analysis of Damage Degree

The degree of destruction of the dried rocks was much more severe than those in a water-saturated state. That is maybe due to the dried rock able to overcome the binding forces between the solid particles in the process of generating creep strain. As the creep strain continues to increase, the cohesion between particles is not sufficient to withstand sustained stress, then instantaneous axial splitting damage will occur. While the solid particles of water-saturated rocks are surrounded by water to form a lubricating effect, the binding forces between the particles are weakened. Cohesion decreases on a macroscopic level and the failure intensity is reduced (i.e., failure is a gradual process under saturated conditions rather than instantaneous as with the dry sample).

4.3 Analysis of Creep Characteristics

Through the uniaxial compression creep experiments of dried and water-saturated rocks both S-1 and S-2 have instantaneous elastic deformation immediately after the instantaneous load. When stress is small and constant, strain increases with time and tends to a stable value. Creep is not obvious and the rock is compacted. When the stress is large, rock deformation develops unsteadily over time, and the time needed to achieve stability are lengthened until the rock is damaged. In addition, transverse creep is more sensitive than the axial creep at the same stress levels. The transverse expansion of the water-saturated S-2 was more obvious at the later loading stage, which may be related to the interaction between clay minerals and water. The instantaneous strain, creep strain, and creep rate of S-2 were all larger than that of dried sandstone S-1. The difference indicates the influence of water–rock interaction on the creep characteristics of rocks, which increases the time for steady creep and the average creep strain rate.

4.4 Analysis of Stress–Strain Curve Characteristics

The stress–strain curves of the rock truly reflect the rock’s failure process, as shown in Fig. 7. The creep curves of the water-saturated rock sample were located on the outside of the dried rock, indicating that the deformation of the water-saturated rock was greater at the same stress level. In a sense, it can be said that the existence of water accelerates the rate of deformation. In the course of loading deformation to failure, S-1 shows the process of transition creep, stable creep, and accelerated creep. The compressive deformation is mainly characterized as a linear deformation behavior of elastic brittle medium-strength rock, and the stress–strain curves are approximate to a straight line or broken line. The instantaneous strains of water-saturated S-2 were greater than that of S-1, which may be due to the chemical interaction between water and rock. It dissolves some soluble substance in the sandstone, and the pores between particles increases, providing a certain space for stress change. The creep strain of the water-saturated rock was larger, and the time of deformation stability was longer under the same stress. In the continuous compression process, the pores of the dried rock were constantly compacted, and the instantaneous strains produced by extrusion were also less than the water-saturated rock.

Fig. 7
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Stress–strain curve of rocks

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According to the above analysis, the rock-water interaction leads to obvious creep characteristics and serious long-term strength reduction of rock masses. Therefore, to protect the Yungang Grottoes, waterproofing would greatly aid in preservation by preventing rain from coming in direct contact with the columns and walls. Also, reducing humidity inside the caves would aid in preservation. We infer that if no effective measures are taken to protect the columns, and they are allowed to continue to suffer weathering by sun and rain, instantaneous damage will occur with no precursory warnings of deformation. We should perform research on the long-term strength of rock masses and waterproof protection of grottoes based on the water source and seepage mechanisms, which have become the key to the long-term preservation of the world cultural heritage of the Yungang Grottoes.

5 Stability Analysis of the Columns

Hoek and Brown proposed the relationship between the ultimate stress and failure of rock masses, based on a large number of field experimental results and combined with rock properties, namely, the strength empirical equation of Hoek–Brown (Hoek 1990; Hoek and Brown 1997).

$$\sigma_{1} = \sigma_{3} + \sqrt {m\sigma_{c} \sigma_{3} + s\sigma_{c}^{2} }$$
(1)

where σ1, σ3—the maximum and minimum principal stresses of rock mass failure in units of MPa; σc—the uniaxial compressive strength of rock mass in units of MPa; m, s—the empirical parameters that reflect the degree of hardness and breakage of rock mass obtained from the relationship between rock mass quality and an empirical constant.

It is assumed that σ3 = 0, we can obtain the ultimate uniaxial compressive strength of rock σmc by:

$$\sigma_{mc} = \sqrt s \sigma_{c}$$
(2)

For intact rock, s = 1, then σmc = σc, the uniaxial compressive strength is equal to the compressive strength of the rock mass. However, for a weathered rock mass with fractures, s < 1. The rock mass quality, fissure development, and degree of weathering of the sandstone are comprehensively considered, determining the value of “s” is 0.1. Considering the effect of long-term loading, the long-term bearing capacities of the column rocks in both dried and water-saturated states respectively are 36.31 and 22.04 MPa. The long-term ultimate bearing capacities of the column rocks of Yungang Grottoes are 11.48 and 6.97 MPa, respectively. According to three-dimensional finite element numerical simulation of the compressive stress distributions on the top of Cave No. 9 and 10 columns (Yan and Fang 2004), we can easily calculate the experimental safety factor K of the columns, as shown in Table 4.

$$K = \frac{{\sigma_{mc} }}{{S_{p} }}$$

where K—the experimental safety factor of column; σmc—the ultimate uniaxial compressive strength of rock; Sp—the compressive stress on the column.

Table 4 Statistics of the top compressive stress and experimental safety factor for Cave No. 9 and No. 10
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When the value of safety factor K is equal to 1, the rock mass is in a limited equilibrium state. According to the “Building Foundation Design Code”, the safety factor of the bearing capacity of an independent column should be above 3. The safety factors of the former columns of Cave No. 9 and No. 10 are near 3, although not high enough. With the continuous development of weathering cracks, the safety factors will be further reduced, which may lead to instability of the columns. Therefore, it is necessary to take timely measures to strengthen the columns, construct protective cave eaves, and repair the severely damaged sides of the columns. We should waterproof and dehumidify within the caves according to water sources and seepage mechanism in order to reasonably protect and develop the world cultural heritage, the Yungang Grottoes.

6 Conclusion

The former columns of the Yungang Grottoes have been bearing for over 1500 years, and the strengths of the rocks have been reduced due to creep of a long-term load. Due to the important cultural value of the Yungang grottoes, we performed creep experiments on rock samples of former columns in both dried and water-saturated states, and obtained the following conclusions.

  1. 1.

    The instantaneous strength and long-term strength of the water-saturated rocks are lower than the dried rocks, indicating that the interaction between rock and water can dissolve and hydrolyze some soluble substances, loosening the connection between particles in rock masses. This will lead to the decrease of mechanical strength and softening of rock masses.

  2. 2.

    The creep properties of medium-coarse sandstone in a water-saturated state are more obvious than that in a dried state, and the times of steady creep are much longer. In addition, the water-saturated rocks have more obvious creep deformations under small stress, and the strains are more evident with the change of stresses. The differences show that the rock-water interaction affects the creep characteristics of rocks.

  3. 3.

    In this paper, the long-term mechanical properties of the dried and water-saturated rocks in the former load-bearing columns were evaluated. The results show that the safety factors will be further reduced and the columns may fail under the continuous deterioration caused by weathering. We should take timely waterproof protection measures to effectively protect the world cultural heritage, the Yungang Grottoes.

The experimental results provide a reference for the long-term strength evaluation of column rock masses, and provide a theoretical basis for the waterproof protection of the World Cultural Heritage, the Yungang Grottoes.