The Southern Ocean mechanism of the Late Pleistocene glacial cycling and its implications for the formation of the northern hemisphere ice sheet
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摘要:
目前，学术界普遍认为南大洋对调节晚更新世冰期/间冰期大气二氧化碳分压(pCO2)变化发挥了重要作用。在晚更新世，冰期大气pCO2比间冰期大气pCO2下降约90×10−6。而在约2.7 Ma，随着北极冰盖快速扩张( intensification of Northern Hemisphere Glaciation，iNHG)，冰期旋回振幅增大，大气pCO2也骤降。探究晚更新世冰期及iNHG时期大气pCO2下降的原因，对构建完整的冰期旋回理论意义重大。本文综合晚更新世冰期南大洋北部的亚南极区(Subantarctic Antarctic Zone，SAZ)和南部的南极区(Antarctic Zone，AZ)的洋流、海冰、生产力等记录，分析了两个区域在晚更新世冰期可能的储碳机制，并结合iNHG时期各项地质记录，讨论南大洋洋流、碳储库在iNHG期间所发生的变化。结果认为，SAZ和AZ使冰期大气pCO2下降的机制不完全相同，铁肥输入增强导致SAZ生物泵效率增强，增加了海洋固碳，而在AZ，深水通风减弱、海冰扩张、深海分层增强是加强深海碳封存的关键机制。同时，iNHG时期洋流、碳储库等记录表明，南源水向北大西洋、北太平洋深部显著扩张，南大洋海冰扩张，铁肥输入增强，太平洋碳储库增大，暗示iNHG时期南大洋机制可能是大气pCO2下降的原因，直接造成了晚上新世北极冰盖的最终形成。
Abstract:It has been generally believed that the Southern Ocean has played an important role in modulating glacial/interglacial changes of the atmospheric partial pressure of carbon dioxide (pCO2) during the Late Pleistocene. In the late Pleistocene, the atmospheric pCO2 during the glacial periods was about 90×10−6 lower than that during the interglacial periods. Furthermore, in around 2.7 Ma, with the intensification of the Northern Hemisphere Glaciation (iNHG), the amplitude of glacial cycles increased, while the atmospheric pCO2 greatly decreased. Exploring the reasons for the decline in atmospheric pCO2 during the Late Pleistocene glaciation and the iNHG period is of great significance for constructing a complete theory of the Ice Ages. We combined the records of ocean currents, sea ice, and productivity in the Subantarctic Antarctic Zone (SAZ) in the northern part of the Southern Ocean and the Antarctic Zone (AZ) in the southern part of the Southern Ocean during the Late Pleistocene glaciation, investigated the possible carbon storage mechanisms in these two regions during this period, and discussed the changes in the Southern Ocean currents and carbon reservoirs during the iNHG period by integrating geological records. We proposed that SAZ and AZ had different carbon storage mechanisms during ice ages. The enhancement of iron fertilization increased the biological pump efficiency in the SAZ, thus increasing ocean carbon sequestration. Meanwhile, in the AZ, weakened deep-water ventilation, sea ice expansion, and enhanced deep-sea stratification were the key mechanisms for enhancing deep-sea carbon sequestration. Additionally, records of ocean currents and carbon reservoirs during the iNHG period indicate that southern ocean sourced waters expanded significantly towards the deep North Atlantic and North Pacific, with an expansion of sea ice in the Southern Ocean, enhancement in iron fertilization, and the increase in the Pacific carbon reservoir. We infer that the Southern Ocean mechanisms of the Late Pleistocene ice glacial cycling had probably contributed greatly to the decrease in the atmospheric pCO2 during the period of the iNHG, which triggered the final formation of the northern hemisphere glaciation.
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岩石是一种由矿物颗粒和胶结物组成的不规则的、非均质的集合体，它内部具有许多微裂隙、孔洞、纹理等结构和构造，这些细观结构在一定的条件下表现出复杂的力学行为，而造成这一复杂行为的内部机制目前尚不明晰[1]。地球深部地层在高应力、高地温、拉张、挤压等环境下将发生复杂形变，其过程可用岩石样本循环加载和卸载实验来模拟，因此循环载荷下的饱和岩石力学性质研究具有重要意义[2]。
摩擦是一种普遍存在的自然现象，在各种尺度上都有发生的可能，如在微观尺度上的微细裂缝表面，在较大尺度的单个岩石中或集合体小块间[3-4]。地球在长期的复杂地质构造运动中，岩石圈地层中发育许多不连续面，如俯冲带、断层、节理、劈理、线理、断裂等，也存在中-大型构造尺度的相互摩擦现象[5-6]。岩石孔隙流体在俯冲带地震、地幔部分熔融、岩浆以及海底热液活动等地质作用中扮演了重要角色[6]，研究不同饱和流体的岩石形变及摩擦特征，有助于了解流体在俯冲带地震、岩浆作用、现代海底热液活动中的过程[7]。
Brace和Byeflee指出地震的产生与黏滑摩擦有极大的关系，通过实验发现只有在微裂隙面上的摩擦滑动才由稳滑向黏滑转化[8]。地震的初始阶段是“滑”，首先是断层的短暂运动；接着是黏滑，断层受到的应力不超过抗拉强度，这是地震发生时弹性应变累积的过程。当黏滑持续了一段时间后，阻力变得均匀，岩石受力达到某一临界值，错动面的阻力迅速地由静摩擦转变为动摩擦，导致动态失稳[9]。在实验室中对岩石开展循环载荷实验，分析饱和岩石的细观弹性材料[10]的非线性特征，对揭示岩石内部摩擦规律具有重要作用。
Gordon和Davis的岩石循环载荷实验认为，当应变较小时，岩石衰减呈线性[11]。McKavanagh和Stacey认为，当岩石为中等应变时，衰减表现为线性，应力-应变的滞后导致曲线出现尖端[12]。Spencer通过加载和卸载的实验装置发现在饱和岩石中存在弥散、弛豫、衰减[13]。Day和Minster认为衰减是滞后的原因[14]，而McCall和Guyer认为滞后是引起岩石衰减的原因[15]。Holocmb认为原子弹性材料的非线性是由原子/分子晶格的不谐和引起，产生非线性弹性性质是由于岩石内部特殊的细观结构导致“疲劳损伤”的结果，颗粒与颗粒之间存在接触面、裂隙、位错等缺陷，可产生非线性响应[16]。席道瑛、尤明庆、陈运平等基于MTS岩石正弦荷载实验获得了岩石滞后回线面积、应变随频率变化，以及不同状态下岩石的杨氏模量、泊松比、衰减值、弹性波速度等弹性响应特征[17-21]。
陈顒等[22-24]认为岩石表面之间的运动主要表现为两种摩擦滑动，一种是滑动平稳地发生，称为摩擦滑移；另一种是在地震机制和前兆中突发式破坏的黏滑[25]，认为黏滑的主要原因是由岩石中的微裂隙、蚀变矿物、温度、压力、孔隙流体决定[26-27]。颗粒表面具有粗糙体，当一个表面上粗糙体受力的挤压与另外一个表面上的粗糙体接触碰撞时，在合适的速度下，它们就会进行相对运动，运动的程度依赖于接触面上粗糙体的刚度和施加载荷的动态刚度[28-30]。根据岩石颗粒间的摩擦滑动与地球尺度上断层中岩层摩擦滑动的相似性，通过载荷实验探讨岩石的非线性特征和摩擦阻力作用，可深入了解岩体失稳的动力学过程和研究地壳变形、断层黏滑失稳过程、地震发生机制[31-36]。
汪泓和刘燕等[37-39]开展了干燥和饱水状态下岩石单轴循环载荷实验和声发射监测试验，获得了干燥和饱和试件的强度、变形和声发射特征，认为加载和卸载响应比是不同饱和状态下弱胶结砂岩的破坏前兆。王来贵等[40]利用自制滑动摩擦试验装置对劈裂砂岩节理开展滑动摩擦试验，测量滑动过程中磨损面积、摩擦质量、摩擦系数和表面粗糙度的变化，表明初始滑动时砂岩节理表面的初始粗糙度值较大，磨损面积较小，磨损质量和摩擦系数都较大，磨合阶段已磨损区域表面的微凸体不断被剪断、磨平，表面粗糙度降低趋势变缓；在稳定滑动阶段，表面粗糙度趋近于定值，磨损质量和摩擦系数都逐渐趋于稳定。
本文基于来自大庆、南京、合肥等地的砂岩样品，利用电液闭环伺服控制压机系统（Material Testing System，MTS），开展不同饱和流体砂岩的应力-应变滞回曲线、不同载荷频率、不同层理方向加载和卸载对岩石杨氏模量的比对研究，探讨循环载荷下饱和流体的作用，岩石衰减机制及影响因素，杨氏模量与围压、摩擦阻力间的关系，以期阐明饱和岩石的非线性响应特征，探讨摩擦效应在岩石非线性形变过程中的作用。
1. 样品和试验方法
实验所用样品采自合肥、南京、大庆等地出露于地表的砂岩，共15个样品。实验砂岩样品的外观基本一致，肉眼观察为灰色，呈砂状碎屑结构，条带纹层构造，主要矿物成分为石英。其中，合肥砂岩显微镜下观察主要由石英（含量80%）、绢云母（含量18%）、斜长石（含量1%）、铁质物（含量1%）组成，碎屑含量约70%，由石英和斜长石组成；南京砂岩由石英、绢云母、方解石、铁质物组成，胶结类型为间隙胶结，局部为铁质胶结，填隙物含量约30%；大庆砂岩是一种长石砂岩，其长石碎屑含量超过25%，内部含较多的云母和重矿物，呈粗砂状结构，分选性和磨圆度变化较大，胶结物为碳酸盐质、硅质、铁质。
实验将所用的岩样加工成直径约20 mm，高约50 mm的圆柱形试样，样本两端面间相互平行，其误差≤0.02 mm。先将标本在约45 ℃的烘箱中烘烤12天使其干燥。干燥样品的一部分直接用于实验，另一部分在真空室里抽真空后，分别放入装有泵油加沥青、泵油、蒸馏水的箱中，浸泡20～30天后作为饱和样品。当饱和样品从箱中取出擦干表面后，就立刻称量、封蜡，然后放到压机下进行实验，以防饱和流体散失。
实验所用装置为中国科学院武汉岩土力学研究所的电液闭环伺服控制压机系统（MTS)。由加载、控制器、测量等分系统构成，全程计算机控制数据采集及处理。具体实验步骤：① 调整MTS，将测量应变的传感器固定在放置样品的中部并插好销钉；② 把样品从烘箱中取出，表面擦干后立即放到MTS上，并处于样品接触面的中心；③ 调整好压机使其上下端面与标本充分接触，并用环氧树脂固定；④ 实验开始拔掉销钉，对样品施加循环载荷。施加载荷时，静载稍大于动载，在正弦波幅值超过屈服点但不超过抗拉强度的情况下，分别对不同状态下的砂岩进行频率为5、10、15 Hz的循环加载，模拟地壳中的地震波对岩石作用的过程；⑤ 记录时间（s）、两端面距离（mm）、压力（kN）、轴向应变（mm/mm）、横向位移（mm）等参数的变化过程，测量样品滞回现象随载荷频率及应力的变化。
2. 实验结果
2.1 孔隙流体与岩石应力-应变
从循环载荷应力-时间和应变-时间曲线上可以观察到：在加载阶段，饱泵油砂岩、饱水砂岩、饱“沥青+泵油”砂岩的应变相位相等或落后于应力的相位；在卸载阶段，应力与应变相位也不同步。无论在卸载还是加载阶段，应变相对应力总是具有滞后性（图1）。在外力的作用下，岩石应力与应变的相位不同步，是造成应力-应变曲线发生滞后现象的直接原因，而岩石出现这一偏离虎克定律的非线性弹性行为，与其内部的细观结构，如裂隙、孔隙流体、微结构、孔洞、颗粒接触面等有关，为岩石自身材料的一种综合属性。
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图 1 不同饱和流体岩石的应力、应变-时间曲线Figure 1. Time variation of axial stress and strain curves of the rocks with different saturated fluids图2为循环载荷实验的应力-应变滞回曲线。砂岩样品在饱“泵油+沥青”、饱泵油、饱水和干燥四种状态下施加5 Hz循环载荷得到的应力-应变相位不同步的反馈信息，表明处于不同状态下的岩石，其应变相对于应力具有滞后性，存在非线性弹性形变特征，且随着循环次数的增加，应力-应变滞回圈彼此愈来愈靠近，在末尾端出现尖端现象。在应力加载的第1次和第2次循环中，不同饱和孔隙流体的岩石样品的滞回曲线存在较大差别，表明孔隙流体类型对岩石滞后模量具有影响，且存在饱油岩石的滞后模量比饱水岩石的滞后模量要大，饱水岩石的滞后模量比干燥岩石的滞后模量要大的规律。后续随着多次应力的加载和卸载，它们的滞回曲线都基本趋于稳定。
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图 2 不同饱和流体岩石的应力-应变曲线Figure 2. Rock stress and strain curves with different saturated fluids2.2 载荷频率、孔隙流体与岩石衰减
衰减是波在传播过程中各种能量耗散的总和。波在岩石中的衰减随着应变振幅的变化而变化，由内部裂纹的密度、构造、孔隙流体和所受外力的频率、振幅等相互作用决定，与岩石的宏观特征无关[11, 13]。因此，通过循环载荷下加载不同应力频率、修改岩石所处的状态（如孔隙流体），可有效模拟地震波在地球圈层中应变衰减过程来探讨地震应变的衰减机制及影响程度。有实验数据表明，当应变超过10−6时，衰减才与应变振幅有关[20]。在本文的实验中加载应力导致的岩石样本应变，其振幅都超过了10−3。岩石作为一种粘滞性材料，其本构关系可用Boltzmann记忆衰退原理[41]的遗传卷积方程式（1）表示。
$$\sigma \left(t\right)={\displaystyle\int }_{-\infty }^{t}G\left(t-\tau \right)\mathrm{d}\varepsilon \left(\tau \right)$$ (1) 式（1）中，
$ \sigma \left(t\right) $ 、$ \varepsilon \left(t\right) $ 分别为应力和应变；$ G\left(t\right) $ 为松弛模量。由于应力与应变之间存在一个直接与粘滞性有关的量，假设应力和应变都为正弦形式，$ \sigma ={\sigma }_{0}{\mathrm{e}}^{i\omega t} $ ，$ \varepsilon ={\varepsilon }_{0}{\mathrm{e}}^{i(\omega t-\varphi )} $ ，常用复模量形式表示[42]：$$ \sigma =\widetilde {M}\varepsilon $$ (2) 上式中
$ \varphi $ 为应力作用岩石产生应变的相位延迟，$ \mathrm{\tau } $ 为弛豫时间，$ \mathrm{\omega } $ 为圆频率，$ {\sigma }_{0} $ 、$ {\varepsilon }_{0} $ 分别为应力、应变初值，$ \widetilde {M} $ 为与频率相关的复模量，其可定义为$$\widetilde {M}={M}_{\infty }+\frac{{M}_{0}-{M}_{\infty }}{1+i\omega \tau }$$ (3) 其实部和虚部分别为
$$\mathrm{R}\mathrm{e}\left[\widetilde {M}\right]={M}_{\infty }+\frac{{M}_{0}-{M}_{\infty }}{1+{\left(\omega \tau \right)}^{2}}$$ (4) $$\mathrm{I}\mathrm{m}\left[\widetilde {M}\right]=\frac{{(M}_{0}-{M}_{\infty })\omega \tau }{1+{\left(\omega \tau \right)}^{2}}$$ (5) 式（2～5）中，当
$ \omega \to $ 0时，$ \widetilde {M}={M}_{0} $ ；当$ \omega \to \mathrm{\infty } $ 时，$ \widetilde {M}={M}_{\infty } $ 。因此$ {M}_{0} $ 和$ {M}_{\infty } $ 分别表示复模量$ \widetilde {M} $ 的低频和高频极限，又称为弛豫模量和未弛豫模量；$ \mathrm{R}\mathrm{e}\left[\widetilde {M}\right] $ 为存储弹性模量，$ \mathrm{I}\mathrm{m}\left[\widetilde {M}\right] $ 为损耗弹性模量。假设流体粘滞性系数$ \Delta W $ 为实验过程中振动一周单位体积所消耗的能量，$ W $ 为振动周期中最大储备能量值，$ \varphi $ 为相位延迟，则衰减因子$ {Q}^{-1} $ [41-42]为：$$\Delta W=\oint \sigma \mathrm{d}\varepsilon =\pi \mathrm{I}\mathrm{m}\left[\widetilde {M}\right]{{\sigma }_{0}}^{2}$$ (6) $$W=\int_{0}^{{}^{\pi } \diagup {}_{2}\;}{\sigma \text{d}\varepsilon =\frac{1}{2}\text{Re}\left[ {\tilde{M}} \right]{{\sigma }_{0}}^{2}}$$ (7) $${Q}^{-1} = \Delta W/\left(2\pi W\right)=\mathrm{I}\mathrm{m}\left[\widetilde {M}\right]/\mathrm{R}\mathrm{e}\left[\widetilde {M}\right]={\mathrm{t}\mathrm{a}\mathrm{n}}^{-1}\left(\varphi \right)$$ (8) 从式（6～8）可知，
$ {Q}^{-1} $ 为应变对应力一个周期内的积分面积（即损失能量）与平均能量面积的比值，可简化为存储弹性模量与损耗弹性模量的比值，因此计算和统计滞回圈的面积可描述岩石能量衰减的过程。图3 为饱泵油砂岩的滞回圈面积与载荷周期的关系图，表明岩石在反复加载过程中具有不同的应变能损耗，也由于循环载荷频率的差异，导致应变能损耗具有各自的特征。当频率较小时，应变能损耗速度快且损耗差较大；当频率增大时，应变能损耗更慢且损耗差小（表1）。图4为在载荷频率10 Hz条件下对饱和泵油、水和干燥砂岩的滞回圈面积统计图，表明在频率一致时，三者的应变能损耗大小也不一致。饱水后的砂岩其衰减反而比干燥砂岩小，饱泵油和沥青后的砂岩衰减比饱水砂岩小（表2）。由此可知，循环载荷频率、岩石孔隙流体都是引起岩石能量衰减的因素，且饱和孔隙流体对岩石衰减的影响更加显著。
表 1 不同载荷频率下饱和泵油+沥青合肥砂岩的滞回圈面积Table 1. Hysteretic area data of Hefei sandstone saturated with pumped oil and asphalt under different cycle period and stress frequencies载荷
周期1 2 3 4 5 6 7 8 9 5 Hz 0.182 0.181 0.179 0.177 0.171 0.172 0.170 0.173 0.173 10 Hz 0.188 0.179 0.178 0.175 0.175 0.173 0.172 0.175 0.171 15 Hz 0.19 0.183 0.178 0.177 0.174 0.171 0.171 0.171 0.171 表 2 不同饱和流体下合肥砂岩的滞回圈面积Table 2. Hysteretic area data of Hefei sandstone followed by loading cycle periods in different conditions载荷
周期1 2 3 4 5 6 7 8 9 饱水 0.389 0.318 0.308 0.298 0.299 0.275 0.263 0.252 0.241 干燥 1.344 1.260 1.117 1.114 1.112 1.110 0.105 1.102 1.084 饱泵油+沥青 0.143 0.136 0.124 0.115 0.113 0.091 0.071 0.032 0.021 ![]()
图 3 不同频率下泵油+沥青合肥砂岩的滞回面积随载荷周期的变化Figure 3. Hysteretic area curves of Hefei sandstone with pumped oil and asphalt under different cycle periods and stress frequencies![]()
图 4 不同状态下合肥砂岩滞回圈面积随循环次数的变化Figure 4. Hysteretic area vs. loading cycles periods for the Hefei sandstone in different conditions2.3 岩石围岩、层理方向与杨氏模量
杨氏模量是轴向应变与轴向应力的比值，用于表征材料的抗拉或抗压强度[17-18]。轴向应变的计算方程如式（9）所示：
$$E=\frac{\sigma_{a 2}-\sigma_{a 1}}{\varepsilon_{a 2}-\varepsilon_{a 1}}$$ (9) 式（9）中，
$ \sigma_{a 2}$ ，$ \sigma_{a 1}$ 分别为近于直线段上任意两点对应的轴向应力；$ \varepsilon_{a 2}$ ，$ \varepsilon_{a 1}$ 分别为对应于$ \sigma_{a 2}$ ，$ \sigma_{a 1}$ 的轴向应变。图5为大庆长石砂岩和饱和泵油南京砂岩在受围压影响下的杨氏模量变化。两类砂岩的杨氏模量与围压都呈正相关关系，但是大庆长石砂岩的增速较为稳定，而饱和泵油南京砂岩的增速先慢后快。图6和图7分别为不同层理方向岩石样本取每个滞回圈卸载时最小应力处对应的应变与载荷周期变化的曲线。从中可以看出，随着循环次数的增加，岩石应变快速增大，岩石被压密之后，应变增速减缓，逐渐趋于不变，呈现出非线性过程。当应力平行于层理方向时，饱泵油砂岩、干燥砂岩和饱水砂岩的应变随着循环次数的增加而递增，整体增速较快，且饱泵油砂岩呈阶段状（图6）。当应力垂直于层理方向时，饱泵油砂岩和干燥砂岩的应变都随着循环次数的增加呈阶梯状递增，整体增速较慢；饱水砂岩的递变无规律（图7）。
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图 6 平行层理状态下不同饱和岩石的应变随载荷周期的变化Figure 6. Strain variation of different saturated rocks with loading periods in parallel bedding state![]()
图 7 垂直层理状态下不同饱和流体岩石的应变随载荷周期的变化Figure 7. Strain variation of different saturated rocks with loading periods in vertical bedding state对饱泵油砂岩和干燥砂岩分别进行垂直和平行层理方向的循环载荷实验，并统计出实验获得的杨氏模量数据（图8，图9）。它们分别代表干燥砂岩和饱泵油砂岩的杨氏模量随循环加载次数的变化过程。从整体上看，饱泵油砂岩的杨氏模量随着循环次数的增加而降低，干燥砂岩的杨氏模量随着循环次数的增加而增加。这种饱和岩石和干燥岩石杨氏模量变化不同的现象，说明由于孔隙中的液体影响到岩石杨氏模量的强度。这一平行层理和垂直层理方向上的实验曲线差异，也表明砂岩杨氏模量具有各向异性。
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图 8 干燥砂岩的杨氏模量随载荷周期的变化Figure 8. Variation of Young's modulus of dry sandstone with loading stress periods![]()
图 9 饱泵油砂岩的杨氏模量随载荷周期的变化Figure 9. Variation of Young's lus of saturated pump oil sandstone with loading stress periods3. 讨论
岩石内部产生滞后和衰减等非弹性响应的细观机制非常复杂[30, 35]，从上述孔隙流体与岩石应力-应变，载荷频率、孔隙流体与岩石衰减，岩石围岩、层理方向与杨氏模量的曲线分析，可以窥得岩石非弹性响应特征不取决于宏观的整体性质，而是受岩石内部裂隙层理构造、孔隙流体类型、载荷频率的影响。但孔隙流体、载荷频率、岩石围岩、层理方向等因素是造成岩石应力应变滞后、能量衰减、刚性变化等非弹性响应的外部变量，为了分析并获取其内在原因，需要在循环载荷时分析岩石内部的细观结构才能更好地进行解释，但这一细观结构无法在动态实验中被直接观测记录，特别是加载和卸载应力过程中岩石内部颗粒间的摩擦阻力。针对这一问题，根据上述实验现象，下文对外部变量作用于岩石并导致发生非弹性响应的机制进行讨论。
3.1 饱和孔隙流体的作用机制
孔隙流体类型影响应力-应变滞回曲线、岩石衰减、杨氏模量等岩石物理性质，与岩石内部裂纹错开或恢复时内部颗粒接触面间的摩擦作用存在显著关系（图1～9）。在循环外力的作用下，存在于岩石颗粒接触面之间的孔隙流体将产生震荡运动，黏滞性小的流体，颗粒间的摩擦阻力小，容易在孔隙岩石中流动；反之，黏滞性大的流体，颗粒间的摩擦阻力大，不容易在孔隙岩石中流动。因此，水的黏滞系数比石油小、比空气大。当岩石内部受外力作用时，水的震荡运动比空气难、比石油容易，颗粒接触面之间的摩擦力也会相对于饱油岩石小、比干燥岩石大。由此可解释“载荷循环初始阶段时，饱油岩石相对于饱水岩石具有较高的滞后模量、干燥岩石相对于饱水岩石具有较低的滞后模量”的实验现象。
随着循环载荷次数的增加，实验的4类饱和流体岩石应力-应变曲线的偏移量逐渐变小并趋于稳定的现象，可解释为岩石开始受力时，旧裂纹的张开和新裂纹的产生能够充分扩展，颗粒间的摩擦阻力增大，内部的裂缝受到压力后闭合，颗粒间的摩擦阻力迅速变小，产生较大的应变。而后来的应变差减小是由于应力加载频率较高，第一个循环应力作用下所有微裂隙和微裂缝还未闭合，颗粒间摩擦阻力较大，第2个循环已经使岩石中容易被破坏的部分破坏，摩擦阻力进一步增大，导致最小应变和最大应变继续增大，但随着循环次数的增加，孔洞和裂纹萌生的扩展性越来越小，制造微裂隙与微孔洞的能力也逐渐减弱，颗粒间的摩擦阻力稳定，应变差逐渐减小，岩石整体的刚度增加。因此，应力-应变、杨氏模量、岩石衰减曲线都逐渐趋于稳定。
3.2 载荷频率和围压的作用机制
载荷频率反映的是岩石内部颗粒振荡的快慢，而振荡频率将影响应力作用于岩石颗粒的时间及总能量。振荡频率低，岩石衰减速度快，振荡频率高，岩石衰减速度慢（图3～5）。这一现象是由于岩石内部的摩擦对循环载荷作用下产生的滞后和衰减有一定的影响，振荡快时，岩石裂隙受到的平均作用应力小，导致摩擦阻力小，衰减慢；反之，振荡慢时，岩石裂隙受到的平均作用应力大，摩擦阻力大，衰减快。
围压与孔隙面上的主应力存在显著关系。由于外界围压的增加导致微裂隙闭合，主应力提高了断裂面上的载荷能力，内部颗粒接触面间的滑移受到摩擦力的阻碍，使得岩石杨氏模量增大。但由于孔隙流体的存在一定程度上延缓了微裂隙闭合的进程，滑移受到的摩擦力增速较缓慢，但伴随周压不断增大，微裂隙完全闭合，孔隙流体的作用减弱，使得岩石的强度、裂隙之间的摩擦阻力、杨氏模量都迅速增强。另外围压的存在和多次循环加载、卸载，使得岩石的刚度增加，与图2中所看到的应力-应变滞回曲线最后趋于稳定的现象是一致的。
3.3 层理方向的作用机制
当循环载荷应力垂直于样品的层理方向时，岩石应变曲线增长慢，而平行于样品的层理方向时，岩石应变曲线增长快（图6～9）。从合肥砂岩样品的应变与载荷周期的关系曲线来看，当施加平行层理方向的应力时，微裂缝和孔洞易沿着层理方向处裂开，导致岩石强度降低，且这一过程是不连续地间歇性发生。另一方面将引起层与层之间的滑动摩擦，使得弱层被压实。当受垂直层理方向的加载应力时，仅仅导致岩石细观结构的损伤、裂隙的萌生及扩展，这可能是垂直和平行方向应变曲线递增的方式不同的内在原因。
岩石内部的流体类型会影响加载和卸载实验过程中的岩石杨氏模量（表3）。在循环载荷作用下，塑性应变和弹性应变是同时存在的，且随着施加应力的变化而变化，随着循环次数增多，微塑性不断增加。当饱和液体充填于裂隙中时，会增加岩石的刚度，但当应变率较低时，液体扩散到孔隙中，孔隙的压力升高，导致岩石破坏的强度变低，杨氏模量变小。加载时杨氏模量稳定平缓地增加，而卸载时杨氏模量存在一定波动，是由于岩石微裂缝表面、流体或者颗粒接触面之间的摩擦作用，导致卸载时应变不会立刻松弛，使得岩石杨氏模量的变化更加复杂。但是多次循环的加载、卸载，使得岩石的刚度增加，应变中不可恢复的部分越来越少，应力-应变滞回圈和杨氏模量将趋于稳定，再随循环载荷应力加载的时间增加，岩石不断产生新的裂缝，导致岩石由硬化到软化。
表 3 不同饱和流体砂岩的杨氏模量Table 3. Young's modulus of sandstone with different saturated fluid杨氏模量/MPa 循环次数 垂直层理 平行层理 加载阶段 卸载阶段 加载阶段 卸载阶段 饱泵油砂岩 干燥砂岩 饱泵油砂岩 干燥砂岩 饱泵油砂岩 干燥砂岩 饱泵油砂岩 干燥砂岩 1 14.444 13.084 14.810 12.999 16.069 12.871 16.144 12.625 5 14.378 13.210 14.469 13.222 16.042 13.010 16.075 13.118 10 14.283 13.254 14.411 13.249 16.012 13.069 16.031 13.098 15 14.238 13.275 14.253 13.261 16.002 13.082 16.004 13.166 20 14.211 13.290 14.266 13.313 15.971 13.100 16.005 13.181 25 14.183 13.304 14.189 13.321 15.969 13.112 16.022 13.140 30 14.160 13.305 14.170 13.284 15.950 13.120 15.976 13.208 35 14.158 13.317 14.202 13.286 15.950 13.132 15.887 13.156 40 14.377 13.195 14.555 13.214 16.050 12.914 16.097 12.949 由上述讨论可知，岩石在受到“孔隙流体、载荷频率、围压变化、层理方向”等外部因素影响时，岩石接触面颗粒之间的摩擦阻力在岩石应力-应变曲线滞后、能量衰减、杨氏模量、刚度变化过程中发挥了作用。它通过岩石细观结构损伤、破坏、闭合及新生裂纹，影响下一个循环加载应力作用于岩石应力-应变滞后、能量衰减、杨氏模量等非线性过程。因此，它在外部应力作用岩石发生非线性弹性形变的过程中充当了一种传递媒介，上述外部因素通过改变岩石内部的摩擦效应，进而导致岩石发生衰减、滞后等非线性响应行为，反映出岩石颗粒间的摩擦阻力是致使岩石发生非线性响应的一种内在因素。
4. 结论
本文通过对饱“沥青+泵油”、饱泵油、饱水和干燥砂岩的循环载荷实验，获得了饱和砂岩的非线性响应特征，表明砂岩在循环载荷下孔隙流体、载荷频率、围岩、层理方向是造成应力-应变滞后、能量衰减、刚性变化的外部因素，且饱油砂岩的滞后模量大于饱水砂岩，饱水砂岩的滞后模量大于干燥砂岩；围压的存在提高断裂面上主应力和摩擦阻力，多次加载和卸载将增加岩石的刚度；当循环载荷应力垂直于样品的层理方向时，砂岩应变是突变式的增长，而平行于样品的层理方向时，砂岩应变呈曲线缓慢式的增长；饱泵油砂岩的杨氏模量随载荷周期增加而降低，干燥砂岩的杨氏模量随载荷周期的增加而增加。经过对岩石非弹性响应过程的深入分析，我们认为接触面颗粒之间的摩擦阻力是岩石发生非线性响应的一种内在因素，其通过对岩石细观结构损伤、破坏、闭合及新生裂纹，改变岩石内部的摩擦效应，影响下一个循环加载应力作用于岩石的响应过程，进而导致岩石发生衰减、滞后等非线性行为。
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图 1 80万年来气候变化记录
a：65°N夏季太阳辐射量[22]，b：地球轨道参数斜率[22]，c：全球底栖有孔虫δ18O综合曲线LR04[2]，d：根据南极Vostok冰芯重建的大气δ18O[9]，e：根据南极冰芯重建的pCO2[9, 23]，f：晚更新世底栖有孔虫δ18O（LR04）[2]频谱分析（采用origin软件），g：晚更新世65°N夏季太阳辐射量频谱分析[22]（采用origin软件）。
Figure 1. Records of climate change over the last 800 thousand years
a: Insolation of 65°N[22], b: obliquity[22], c: a compilation of benthic foraminiferal δ18O records(LR04)[2], d: δ18Oatm as reconstructed from Vostok ice core[9], e：pCO2 as reconstructed from Antarctic ice cores[9,23], f: spectrum analysis of benthic foraminiferal δ18O[2] over the Late Pleistocene, g: spectrum analysis of insolation of 65°N over the Late Pleistocene[22].
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图 2 南大洋洋流机制图 [10]
a：现代海洋，b： LGM时期可能的机制。NADW：北大西洋深水，GNAIW：冰期北大西洋中层水，AABW：南极底层水，AAIW：南极中层水，SAMW：亚南极模态水，ITF：印尼贯穿流，AE：阿古拉斯涡旋，ITF和AE将表层水从太平洋运输至大西洋，圆圈点表示从页面中流出，十字表示流入，SAZ：亚南极区，ACC：绕南极流，PAZ：极地南极区。内部气流的线条颜色表示其通风源区域，蓝色表示NADW 或 GNAIW，黄色表示AABW，绿色表示NADW、AABW混合，线条的粗细变化表示流速变化。红色实线：碳酸盐溶跃面深度，红色虚线：碳酸盐溶跃面深度变浅，海底CaCO3减少，增加海洋碱度。深紫色阴影表示再生型营养物质浓度较高，即再生型CO2含量高，黄色点表示亚南极区Fe肥输入。
Figure 2. Summary cartoon of Southern Ocean mechanisms of Late Pleistocene glacial cycling [10].
a:The global ocean today, b: possible mechanisms during LGM. NADW: North Atlantic Deep Water; GNAIW: Glacial North Atlantic Intermediate Water; AABW: Antarctic Bottom Water; AAIW: Antarctic Intermediate Water; SAMW: Subantarctic Mode Water; ITF: Indonesian Through-Flow; AE: Agulhas Eddies (ITF and AE return surface water from the Pacific to the Atlantic. The circled dots showing transport out of the page and circled crosses showing transport into the page); SAZ: Subantarctic Zone; ACC: Antarctic Circumpolar Current; PAZ: Polar Antarctic Zone, line colors of interior flows indicate their ventilation source region. Blue: NADW or GNAIW; yellow: AABW; green: mixed NADW and AABW. Line thickness changes among panels denote changes in flow rate. Solid red line: steady-state lysocline; dashed red line: transient shoaling of the lysocline, causing a transient decrease in seafloor CaCO3 burial that increases ocean alkalinity. Dark purple shading in the interior indicates a higher concentration of regenerated nutrient and thus regenerated CO2. Yellow dots: Subantarctic iron fertilization.
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图 3 晚上新世—早更新世气候变化记录
a：全球底栖有孔虫δ18O（LR04）[2]，b：大气pCO2.红色三角数据来自参考文献[83]，蓝色圆点数据来自参考文献[84])，c：ODP 882站的蛋白石堆积速率[74]，d：ODP 907站的冰筏碎屑沉积IRD[6]。
Figure 3. Records of climate change during the Late Pliocene-Early Pleistocene
a: Global benthic foraminifera δ18O(LR04) [2]; b: atmosphere pCO2(red triangle references from [83], blue dots references from [84]); c: Biogenic opal mass accumulation rates (MAR) at ODP Site 882[74]; d: Ice-rafted debris (IRD) of ODP Site 907[6].
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图 4 北极冰盖快速扩张期间多地化指标记录
a：全球底栖有孔虫δ18O记录（LR04）[2]，b：U1489站的碳酸根离子浓度[103]，c：U1489站的εΝd[103]，d：U1308站的δ13C[106]，e：U1313站的εΝd [102]，f：ODP 1091站的蛋白石积累速率[105]，g：ODP1090站的铁积累速率[96]。
Figure 4. Records of Multi-geochemical proxies during the iNHG (intensification of Northern Hemisphere Glaciation)
a: Global benthic foraminifera δ18O(LR04) [2]; b: Δ[$\rm CO^{2-}_3 $] from Site U1489[103]; c: εΝd from Site U1489[103]; d: δ13C from Site U1308[106]; e: εΝd from Site U1313 [102]; f: MAR of opal at Site ODP 1091[105]; g: MAR of iron at Site ODP 1090[96].
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