Characteristics of water absorption capacity of weathered sandstone based on nuclear magnetic resonance and wave velocity testing
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摘要:
水是岩石风化破坏的关键因素，高吸水性岩石一般更易受到风化破坏，但一直缺少原位评估岩石吸水能力的方法。为探究岩石吸水能力的控制因素，以云冈石窟不同风化程度砂岩为研究对象，采用核磁共振技术测得岩石样品的孔隙度和孔径分布，建立砂岩自由吸水率与密度、孔隙度、孔径的关系。结果表明：砂岩自由吸水率与密度呈线性关系，但两者的斜率与风化程度有关；砂岩自由吸水率与孔隙度、小孔（0.1～1.0 μm）占比均呈正相关性，其中孔隙度是控制砂岩自由吸水率的主要原因，孔隙结构是控制砂岩自由吸水率的次要原因；由于波速受孔隙度和孔隙结构控制，自由吸水率与波速有良好的线性关系，因此提出可以通过原位测试波速估算岩体表层自由吸水率。本研究加深了对风化砂岩吸水性控制机理的认识，并提出了一种可以原位获得石质文物自由吸水率的方法，对石质文物保护具有重要的指导意义。
Abstract:Water is a key factor in the weathering and erosion of rocks, and highly porous rocks are generally more susceptible to weathering. However, there has been a lack of in-situ methods for assessing the water absorption capacity of rocks. To investigate the controlling factors of rock water absorption capacity, sandstone with different degrees of weathering collected from the Yungang Grottoes were selected as the study material. Nuclear magnetic resonance (NMR) technology was employed to test the porosity and pore size distribution of rock samples, and to establish the relationship between the free water absorption rate of sandstone and its density, porosity, and pore size. The results indicate that there is a linear relationship between the free water absorption rate and the density of sandstone, with the slope of the relationship being influenced by the degree of weathering. Additionally, the free water absorption rate of the sandstone is positively correlated with porosity and the proportion of small pores (0.1－1.0 μm), with porosity being the primary controlling factor and pore structure being the secondary controlling factor. This study deepens our understanding of the mechanisms controlling the water absorption of weathered sandstone. Furthermore, since wave velocity is also influenced by porosity and pore structure, a good linear relationship was observed between the free water absorption rate and wave velocity. Therefore, it is suggested that the free water absorption rate of rock mass can be estimated by in-situ testing of wave velocity.
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岩石风化是指表层岩石在物理、化学和生物等因素作用下发生物理崩解和化学分解的过程[1 − 2]，在地球生态系统和地貌演化中发挥着不可忽视的作用[3 − 4]，尤其对石质文物而言是一大危害[5 − 8]。对于完全干燥的岩石，即使温度发生大范围波动也不会产生物理和化学风化[9 − 11]。由于岩石通常具有吸水能力，雨水淋湿[12 − 13]、水汽凝结[14 − 16]和毛细上升[17 − 18]等作用都会增大岩石含水率。例如前人[19]指出石窟洞内的大气湿度会直接控制浅层砂岩的含水率。干湿交替条件下，岩石中的水分会引发物理、化学和生物风化[9, 20 − 24]。量化岩石的吸水能力及其控制因素有助于为石质文物风化防治提供决策依据。
如何利用无损的原位测试方法表征岩石吸水能力是岩石风化、工程地质等领域亟需解决的技术问题。岩石自由吸水率是表征岩石吸水能力的最常用指标，也是衡量岩石强度的重要指标之一[25]，是指长时间浸泡条件下吸收的水分体积与岩石总体积的比值[26]，属于有损检测方法。Ozcelik等[25]建立了多种岩石自由吸水率与密度的负相关性，但由于密度无法无损获得，无法用于无损估算岩石自由吸水率。岩石的声波速度可以通过无损的原位测试方法获得，与岩石的孔隙结构、温度、节理、裂隙等密切相关[27 − 28]。在岩性相同的情况下声波速度受孔隙结构控制[26]，且与孔隙度[29]呈负相关性、与密度[30]和抗压强度[28]呈正相关性。黄继忠等[31]研究指出云冈石窟砂岩孔隙度作为控制水分进入岩石的关键因素，与渗透率和水汽扩散系数有密切的正相关性。由于岩石自由吸水率也受孔隙度[32]和孔隙结构[33 − 34] 的控制，声波速度的无损检测优点及其与孔隙度、孔隙结构的相关性，为利用声波速度间接获得岩石自由吸水率提供了可能。Park等[35]提出砂岩在冻融循环的作用下声波速度与自由吸水率呈负相关性，然而目前尚未探究在自然受风化破坏的情况下，二者之间的关系。
本文以云冈石窟所在山体为研究区，采集水平方向不同风化程度的砂岩开展自由吸水率和密度测试，采用核磁共振（nuclear magnetic resonance，NMR）技术测定岩样的孔隙度和孔隙结构。在分析自由吸水率、波速控制机理的基础上，建立波速与自由吸水率的定量关系，提出了一种利用波速估算岩体表层自由吸水率的方法。
1. 研究区概况
云冈石窟位于山西省大同市，气候类型为大陆季风性半干旱气候，冬季寒冷干燥，夏季炎热多雨。云冈石窟拥有洞窟252个，大小石雕造像有5.1万余尊，具有极高的艺术文化价值，被列为世界文化遗产[36]。然而在自然和人为因素影响下，云冈石窟多数洞窟窟内佛像、壁面遭受了严重的风化破坏（图1）。
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图 1 云冈石窟窟内佛像风化破坏现象Figure 1. Deterioration of buddha statues in a cave of the Yungang Grottoes云冈石窟山体以中粗粒长石砂岩为主，存在少量颗粒较细的粉砂岩和页岩[37]。砂岩的多孔结构有利于吸收和储存水分，雨季的降水入渗和水汽在砂岩表面或内部凝结是造成云冈石窟风化破坏的重要原因[19, 38]，但目前尚无云冈石窟砂岩孔隙结构和吸水性的定量研究。
2. 材料与测试方法
2.1 砂岩风化样品的采集和制备
本次测试岩样取自云冈石窟3窟加固工程的6个水平孔。将采集的岩样加工为直径为2.5 cm，高为5 cm的规则圆柱状岩芯，共获得60个样品。图2为部分处理好后的岩芯。测定所有岩芯密度、自由吸水率后，选取22个岩芯进行核磁共振测试。
2.2 密度和自由吸水率测试
本次研究采用精度为0.001 g的天平测量岩石样品质量（mr）, 采用精度为0.05 mm的游标卡尺测量圆柱体岩样高度（h）和直径（d）。计算岩石密度（ρ）：
ρ=14mrπd2h (1) 岩石自由吸水率是表征岩石在正常大气压下吸水能力的指标，可以用质量含水率或体积含水率表示。依据《工程岩体试验方法标准》（GB/T 50266—2013）[39]，质量吸水率（ωB），定义为岩石浸水48 h吸水后的质量（m0），与烘干后岩石的质量（ms）之比减1：
ωB=m0−msms=m0ms−1 (2) 为直观对比砂岩自由吸水率和孔隙度之间的关系，将质量吸水率转化为体积吸水率（ωV）：
ωV=ωB×ρd (3) 式中：ρd——砂岩干密度/（g·cm−3）。
2.3 核磁共振测试
自1946年哈佛大学Purcell和斯坦福大学Bloch发现核磁共振现象以来，NMR技术因其具有快速准确表征岩石孔隙度和微观孔隙结构的能力在水文地质、岩土力学和油气储层等领域广泛应用[40 − 43]。NMR技术的基本原理是：岩石孔隙水中氢原子核在外加磁场的作用下会发生共振，在共振过程中由于碰撞能量不断消减，通过测量核磁共振信号强弱及能量达到稳定所用的时间即弛豫时间可以间接表征岩石内部的孔径分布情况[44]。通常共振信号量与孔隙内部赋存的水量成正比，氢核的弛豫时间（T2） 与孔隙半径呈正比[45]。当所测岩石内部孔隙被水充满时，测得的共振信号量与孔隙体积成正比，所以低场核磁共振测试可以反映岩石内部的孔径分布情况。此外通过测试获得的T2谱图还可以反映岩石内部孔径分布特征：例如峰值的位置对应孔径的尺寸，峰的面积对应一定范围内的孔隙体积，峰的形状对应各类孔隙的连通性。光滑的峰通常表示孔隙具有良好的连通性，不规则或分散的峰可能表示孔隙之间缺乏有效的连接[46]。
本次测试在中国地质大学（北京）煤储层物性分析实验室完成，仪器型号为苏州纽迈公司生产的MacroMR低场核磁共振仪。参数设定如下：主磁场为0.047 T，氢核共振频率为2 MHz，磁体控制温度为35 °C，射频功率300 W，扫描次数（NS）为32次，回波间隔（TE）为0.3 ms，等待时间（TW）为
3000 ms，回波个数（NECH）为8000 个。测试的具体过程为：（1）将岩芯放置烘箱进行烘干，温度设置为105 °C，时间设置为48 h；（2）烘干后将岩芯放入高压容器，对容器进行抽真空处理，再以30 MPa高压向容器中注入蒸馏水；（3）饱和完成后，擦干岩芯表面的水分进行低场核磁共振的测量。
2.4 声波速度测试
岩石声波速度实验采用ZBL-U520 非金属超声检测仪，厂家为北京智博联科技有限公司。其基本原理是在一定的压力和温度条件下测试声波穿过岩样的时间，通过岩样长度除以穿透时间获得岩样的波速：
vp=Ltp (4) 式中：vp——岩体的纵波波速/（km·s−1）；
L——岩样长度/mm；
tp——纵波穿过岩体经历的时间/μs。
3. 结果
根据60个样品的自由吸水率和密度测试结果，发现岩石样品自由吸水率的均值为8.37%，最大值和最小值分别为11.04%和4.71%。密度的均值为2.42 g/cm3，变化范围为2.28～2.56 g/cm³。依据风化岩分带指标定量范围值法（TR分带法）[47]确定强风化砂岩与弱风化砂岩的密度临界值为2.43 g/cm3。通过统计发现36个样品的密度小于2.43 g/cm3，属于强风化砂岩，自由吸水率均值为9.59%；24个样品的密度大于2.43 g/cm3，属于弱风化砂岩自由吸水率均值为7.26%，明显小于强风化砂岩。
表1为22个岩石样品自由吸水率、波速、密度、孔隙度的测试结果以及微孔（<0.1 μm）、小孔（0.1～<1 μm）、中孔（1～10 μm）和大孔（>10 μm）的占比情况。孔隙度分布范围为7.69%～13.62%，均值为10.80%。所有样品的自由吸水率均小于孔隙度。波速平均值为3.12 km/s，最大值和最小值分别为2.50，3.68 km/s，波速最小值样品与自由吸水率最大值样品存在对应关系。
表 1 岩石样品的物理参数及各类孔隙占比Table 1. Physical parameters and proportions of different types of pores of the rock samples岩芯编号 自由吸水率/% 波速/（km·s−1） 密度/（g·cm−3） 孔隙度/% 微孔占比/% 小孔占比/% 中孔占比/% 大孔占比/% 1 9.44 3.38 2.33 12.28 0.21 25.46 54.47 19.86 2 8.17 3.57 2.39 10.59 5.53 23.91 53.92 16.65 3 9.10 3.47 2.37 10.50 0.00 21.59 55.62 22.79 4 8.86 3.38 2.38 10.41 0.25 12.13 59.96 27.65 6 8.67 2.91 2.44 10.20 1.40 32.96 45.37 20.27 10 8.74 3.14 2.42 10.65 0.00 17.33 56.35 26.32 16 9.13 3.09 2.40 10.72 0.00 20.40 53.26 26.35 21 8.83 3.22 2.44 10.64 1.33 21.91 50.31 26.45 111a 9.51 3.13 2.36 10.94 2.87 26.31 57.41 13.40 111b 9.49 2.90 2.33 11.34 6.17 28.11 52.48 13.24 112a 10.67 2.75 2.32 13.06 1.75 35.40 44.09 18.76 112b 10.10 2.74 2.43 12.81 2.64 42.76 41.59 13.01 136a 9.42 2.98 2.37 9.78 0.00 21.00 61.13 17.87 136b 9.36 2.90 2.40 9.84 3.96 25.27 59.33 11.45 136c 9.01 3.13 2.36 9.26 0.00 19.81 59.46 20.73 137a 8.90 3.29 2.41 9.16 0.00 29.94 52.98 17.08 137b 9.02 3.68 2.41 12.40 7.13 38.00 43.01 11.87 137d 9.06 3.47 2.37 10.51 5.57 35.05 51.10 8.28 39a 9.88 2.75 2.29 13.62 4.31 28.42 49.45 17.82 39b 10.77 2.50 2.30 12.60 4.85 33.55 48.65 12.94 40a 8.66 3.29 2.45 7.69 0.00 31.94 57.80 10.26 40b 8.84 3.03 2.41 8.68 7.08 34.46 48.80 9.66 岩石样品中微孔体积占比范围变化较小，为0～7.13%；中孔变化范围较大，为41.59%～61.13%；小孔变化范围为12.13%～35.40%；大孔变化范围为8.28%～27.65%。
4. 讨论
4.1 自由吸水率与密度的关系
通过绘制自由吸水率和密度的关系图（图3）可以发现自由吸水率与密度整体呈负相关，与Ozcelik等[25]的结论一致。依据风化岩TR分带法[47]，强风化砂岩与弱风化砂岩的密度临界值为2.43 g/cm3。对于密度大于2.43 g/cm3的弱风化岩石样品，自由吸水率与密度之间存在很好的相关性，相关系数（R2）高达
0.8577 ，两者的斜率为−34.78；对于密度小于2.43 g/cm3的强风化岩石样品，自由吸水率与密度之间也存在相关性，但R2仅为0.3974 ，且两者的斜率仅为−10.62。![]()
图 3 不同风化程度砂岩的自由吸水率随密度变化规律Figure 3. Variation of free water absorption rate with density of sandstone with different degrees of weathering这是因为强风化砂岩由于受到风化作用内部存在较多的风化裂隙和大孔，大孔的比表面积小，没有足够的毛细吸力持水，所以相比于弱风化砂岩，强风化砂岩自由吸水率虽然较大，但小于预期的自由吸水率。如果利用弱风化岩石的自由吸水率随密度变化规律预测强风化岩石的自由吸水率，显然会高估其自由吸水率。可见，对于风化程度存在明显差异的砂岩，无法用单一函数刻画自由吸水率与密度的关系。
4.2 孔隙度和孔隙结构对自由吸水率的控制作用
为探究砂岩自由吸水率和波速的控制因素，选择部分岩石样品利用NMR技术测得孔隙度和孔径分布。分析表明，砂岩自由吸水率和孔隙度之间存在较好的线性正相关关系（图4a），表明孔隙度对自由吸水率有重要控制作用。
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图 4 砂岩自由吸水率随孔隙度（a）及小、中孔占比（b）的变化规律Figure 4. Variation of free water absorption rate of sandstone with porosity (a), and proportion of small pores and medium-sized pores (b)通过回归分析发现孔隙结构对自由吸水率也有控制作用。线性回归中的t检验是对单个变量系数的显著性检验，p值是衡量该系数是否显著不同于0的标准。如果p值小于0.05表示该自变量对因变量有显著的控制；如果p值大于0.05小于0.10表示该自变量对因变量有一定的影响。通过回归分析建立4种孔径与自由吸水率的线性关系，发现吸水率与微孔、大孔占比之间线性关系的显著性p值高达0.60和0.37，表明微孔、大孔对自由吸水率无明显贡献，其原因为岩石自由吸水状态下水分很难进入微孔（<0.1 μm），同时大孔（>10 μm）很难持水。砂岩自由吸水率与小孔占比呈线性正相关，与中孔占比呈线性负相关（图4b），显著性p值分别为0.06和0.09。小孔和中孔对自由吸水率的控制机理可以解释为小孔比表面积大，有利于岩石吸水，中孔比表面积小，没有足够的毛细吸力持水，不利于岩石持水。由于自由吸水率—孔隙度线性关系的R2大于自由吸水率—小孔和中孔占比线性关系，本文认为孔隙度是控制砂岩自由吸水率的主要原因，孔隙结构是控制砂岩自由吸水率的次要原因。
自由吸水率随孔隙度线性变化的斜率在一定程度上可以表征具有吸水、持水能力孔隙（0.1～10.0 μm）的占比，斜率大表示具有吸水、持水能力的孔隙（0.1～10.0 μm）占比大。云岗石窟砂岩的斜率为0.64，略小于小孔和中孔占比平均值80.1%。其他3种岩石自由吸水率随孔隙度变化斜率见表2。大理岩和灰岩的斜率分别为0.44和0.47，与这2种岩石较为致密不利于吸水密切相关。例如，文献[48]提出灰岩微孔占比为34%～88%。安山岩的斜率高达0.83，推测其孔隙有利于持水。Çelik等[17]研究认为安山岩的小孔和中孔占比高达88.20%。
表 2 不同岩石自由吸水率随孔隙度的变化斜率Table 2. Slopes of the variation of free water absorption rate with porosity for different types of rocks岩石类别 k 云岗砂岩 0.64 灰岩 0.47 大理岩 0.44 安山岩 0.83 注：k表示自由吸水率随孔隙度的变化斜率；灰岩、大理岩和安山岩k值据文献[25]；云岗砂岩的k值为本次研究结果。 4.3 吸水性与波速的定量关系对原位预测自由吸水率的启示
纵波在穿过裂隙和孔隙时存在一定的反射和折射，微小孔数量过多会增大声波在砂岩内部的传播阻力，导致波速较小，而中孔数量少会减小声波在砂岩内部的传播阻力，导致波速较大[49]。因此，砂岩波速与孔隙度及小孔、中孔占比的对应关系和自由吸水率与孔隙度及小孔、中孔占比的对应关系刚好相反，即砂岩波速和孔隙度之间呈线性负相关（图5a），与小孔占比呈负相关，与中孔占比呈正相关（图5b）。
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图 5 砂岩波速随孔隙度（a）及小孔、中孔占比（b）的变化规律Figure 5. Variation of wave velocity of sandstone with porosity (a) and proportion of small pores and medium-sized pores (b)由于孔隙度、孔隙结构对波速和自由吸水率均有控制作用，统计发现自由吸水率与波速之间存在较好的线性关系（图6），R2达到
0.7492 ，显著性p值小于0.01，且不存在图3自由吸水率—密度关系分段特征。徐松林等[50]通过研究指出，对于岩性较为均匀的岩石，波速的尺度效应可以忽略。因此，根据波速与吸水率之间的良好线性关系，可以采用无损方法在野外现场多个不同部位原位测试石窟表层砂岩的波速，从而确定砂岩表层自由吸水率在空间上的相对大小，判断易风化程度。![]()
图 6 砂岩自由吸水率与波速关系Figure 6. Relationship between free water absorption rate and wave velocity of sandstone5. 结论
（1） 砂岩自由吸水率与密度整体呈线性负相关关系，但强风化砂岩与弱风化砂岩自由吸水率随密度变化的斜率存在较大差异，因此密度不适合用于估算岩石吸水性。
（2） 砂岩自由吸水率受孔隙度和孔径控制，其中砂岩自由吸水率与孔隙度、小孔（0.1～1.0 μm）占比呈线性正相关性，与中孔（1～10 μm）占比呈线性负相关性。对比两者的相关系数大小发现孔隙度是控制砂岩自由吸水率的主要原因，孔隙结构是控制砂岩自由吸水率的次要原因。
（3） 砂岩波速与孔隙度、小孔（0.1～1.0 μm）占比呈负相关。由于砂岩的自由吸水率和波速具有较好的线性负相关关系，可以在野外原位测试波速从而估算岩石表层自由吸水率的空间分布，评估易风化程度。
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图 1 云冈石窟窟内佛像风化破坏现象
Figure 1. Deterioration of buddha statues in a cave of the Yungang Grottoes
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图 3 不同风化程度砂岩的自由吸水率随密度变化规律
Figure 3. Variation of free water absorption rate with density of sandstone with different degrees of weathering
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图 4 砂岩自由吸水率随孔隙度（a）及小、中孔占比（b）的变化规律
Figure 4. Variation of free water absorption rate of sandstone with porosity (a), and proportion of small pores and medium-sized pores (b)
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图 5 砂岩波速随孔隙度（a）及小孔、中孔占比（b）的变化规律
Figure 5. Variation of wave velocity of sandstone with porosity (a) and proportion of small pores and medium-sized pores (b)
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图 6 砂岩自由吸水率与波速关系
Figure 6. Relationship between free water absorption rate and wave velocity of sandstone
表 1 岩石样品的物理参数及各类孔隙占比
Table 1 Physical parameters and proportions of different types of pores of the rock samples
岩芯编号 自由吸水率/% 波速/（km·s−1） 密度/（g·cm−3） 孔隙度/% 微孔占比/% 小孔占比/% 中孔占比/% 大孔占比/% 1 9.44 3.38 2.33 12.28 0.21 25.46 54.47 19.86 2 8.17 3.57 2.39 10.59 5.53 23.91 53.92 16.65 3 9.10 3.47 2.37 10.50 0.00 21.59 55.62 22.79 4 8.86 3.38 2.38 10.41 0.25 12.13 59.96 27.65 6 8.67 2.91 2.44 10.20 1.40 32.96 45.37 20.27 10 8.74 3.14 2.42 10.65 0.00 17.33 56.35 26.32 16 9.13 3.09 2.40 10.72 0.00 20.40 53.26 26.35 21 8.83 3.22 2.44 10.64 1.33 21.91 50.31 26.45 111a 9.51 3.13 2.36 10.94 2.87 26.31 57.41 13.40 111b 9.49 2.90 2.33 11.34 6.17 28.11 52.48 13.24 112a 10.67 2.75 2.32 13.06 1.75 35.40 44.09 18.76 112b 10.10 2.74 2.43 12.81 2.64 42.76 41.59 13.01 136a 9.42 2.98 2.37 9.78 0.00 21.00 61.13 17.87 136b 9.36 2.90 2.40 9.84 3.96 25.27 59.33 11.45 136c 9.01 3.13 2.36 9.26 0.00 19.81 59.46 20.73 137a 8.90 3.29 2.41 9.16 0.00 29.94 52.98 17.08 137b 9.02 3.68 2.41 12.40 7.13 38.00 43.01 11.87 137d 9.06 3.47 2.37 10.51 5.57 35.05 51.10 8.28 39a 9.88 2.75 2.29 13.62 4.31 28.42 49.45 17.82 39b 10.77 2.50 2.30 12.60 4.85 33.55 48.65 12.94 40a 8.66 3.29 2.45 7.69 0.00 31.94 57.80 10.26 40b 8.84 3.03 2.41 8.68 7.08 34.46 48.80 9.66 
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